This paper investigates the optimal bipartite consensus tracking control issue of unmanned aerial vehicle (UAV) and unmanned ground vehicle (UGV) swarms under global actuator constraints and non-fully periodic disturbances. A novel UAV-UGV swarm bipartite consensus tracking control framework is established. Multiple gusts in the environment or irregular electromagnetic oscillations in the equipment can generate non-fully periodic disturbances in the system. Meanwhile, some physical or electromagnetic uncertainties cause unknown persistent actuator saturation that should not occur, which indirectly affects the observation and compensation of composite disturbances, and this can be addressed by the control input increment. Hence, a composite anti-disturbance control method based on a multiple harmonic disturbance observer and robust theory is proposed, which observes and compensates for periodic disturbances, and suppresses the residual disturbance through the improved robustness of each system. A reinforcement learning (RL) algorithm under the gradient descent method is utilized to construct an actor-critic-identifier (ACI) structure, which decouples the actuator constraints in the multiple harmonic disturbance observer, and obtains the ideal control input increment compensation. Additionally, to mitigate potential excessive trajectory amplitude caused by initial actuator constraints in the swarm, where control input compensation remains incomplete during the startup phase, an improved decay function is proposed to ensure trajectory error convergence under actuator constraints from the initial movement, while offering the advantage of adaptive self-tuning. Then, an adaptive ACI structure within the decay function is designed, and an optimal bipartite consensus tracking anti-disturbance control strategy under actuator constraints is proposed for the UAV-UGV swarm. Finally, simulations and experimental results are performed to demonstrate the efficacy of the proposed approach.

Addressing the dual challenges of complex road conditions in mine tunnels and adverse communication environments, this article proposes a reliable gain-scheduling control for industrial mining truck active suspension systems (MTASSs) under fading channels. First, by integrating interval type-2 (IT-2) fuzzy models and Markov processes, a dynamic model is constructed that captures system intrinsic uncertainties and external time-varying disturbances. Second, a simulated fading channel is established using prior statistical information to quantify signal attenuation, and a measurement censoring mechanism integrating dynamic monitoring and adaptive filtering is designed to enhance transmission reliability. On this basis, a time-sequence enhancement switching-type gain-scheduling (TESG) observer-assisted fuzzy control law with homogeneous polynomially parameter-dependent properties is developed. It incorporates a time-sequence enhancement using normalized fuzzy weighted membership functions (NFWMFs) from both current and historical moments, alongside a switching mechanism that exploits the implicit algebraic properties of these NFWMFs for more flexible control gain allocation, thereby reducing design conservatism. Experimental results demonstrate that the proposed approach improves the system’s anti-vibration capability and saves energy.

This paper develops an adaptive optimal control with a state-safety-aware regulation mechanism for uncertain nonlinear active quarter-vehicle suspension systems (AQVSS), in which safety influence is adaptively regulated according to operating conditions to ensure constraint satisfaction without excessive conservatism in optimal performance. Within this control framework, an unscented Kalman filter (UKF)-based adaptive dynamic programming (ADP) approach is developed to combine accurate state estimation with optimal policy learning under unknown disturbances, while satisfying multiple safety constraints including dynamic deflection, wheel load, and actuator force limits. The optimization incorporates safety constraints through control barrier function (CBF)-based penalty terms with a state-safety-aware regulation mechanism. This enables automatic strengthening of safety influence during aggressive operation or large state deviations, and avoids undue conservatism near steady state. The actor-estimator-critic structure is employed for efficient policy learning. Theoretical analysis establishes the convergence properties of the proposed method. Simulation results and hardware-in-the-loop (HIL) experiments demonstrate improved ride comfort, effective constraint enforcement, and reduced control energy consumption, while maintaining robust safety performance.

In the open network environment of intelligent connected vehicles, both driving safety and ride comfort are threatened by cyber attacks. This paper focuses on the resilient defense strategy for active vehicle suspension systems (AVSS) against malicious attacks. To address the limitation that constructing a precise attack model is overly idealized, an incomplete Markov attack model is designed. This model accommodates uncertain transition probabilities, which are reasonably reconstructed via a probability fusion method, and is compatible with scenarios involving insufficient attack knowledge. More importantly, a risk-driven gain-scheduling mechanism is proposed under the polynomial fuzzy framework, where multiple operating modes are cooperatively switched based on real-time membership degree structures and risk severity. Specifically, a refined scheme assisted by the dynamic slack method is proposed to counteract compound disturbances from concurrent road excitations and attacks in risk system mode. By contrast, a simplified scheme is adopted to avoid the additional overhead caused by unnecessary switching in safe system mode. Finally, hardware-in-the-loop experiments demonstrate the superiority of the proposed method.

This article is concerned about the driving performance of human-machine shared steering systems under different fatigue level of drivers. To mitigate risks arisen from driver fatigue, a novel framework featuring an interpretable driver fatigue inference mechanism coupled with a flexible gain scheduling control scheme is proposed. First, an interval type-2 fuzzy logic system (IT2 FLS) with Gaussian membership functions that adhere to interpretability constraints is employed to monitor the driver’s fatigue level. This design provides a reliable basis for dynamic authority allocation that sensitively perceives changes in fatigue level while maintaining inference consistency. Second, a polynomial-driven switching gain-scheduling (PDSGS) scheme is constructed for path-tracking assistance in the human-machine shared steering system. Driven by the homogeneous polynomials technique, the PDSGS scheme can achieve more flexible steering assistance responses with the integration of dynamic gain matching mechanism. Indeed, by systematically classifying the membership distribution into distinct subsets, gain matrices are switched in real time to improve shared steering performance. Finally, the effectiveness of the proposed method is verified by the driver-in-the-loop simulation platform.

This paper investigates the critical challenges of mode information loss and complex transition probability uncertainties, collectively termed as dual-domain uncertainty, in stochastic nonlinear cyber-physical systems (CPSs). Oriented towards the emerging wireless architectures in future vehicles, a memory-gain-scheduling framework is developed, which strategically incorporates memory-dependent membership functions to enhance controller design by leveraging past and present scheduling information. Unlike existing scaling-based methods, our approach utilizes a polytopic reconstruction of the transition probability matrix to fundamentally eliminate structural conservatism. This is integrated with a dual-mode polynomial controller that adaptively switches based on real-time mode information availability, exhibiting enhanced robustness against data loss disruptions. Furthermore, by employing homogeneous polynomial techniques, this memory-gain-scheduling strategy effectively enlarges the feasible solution region by guaranteeing structural consistency. The practical effectiveness and superior performance of the proposed method are conclusively validated through rigorous hardware-in-the-loop experiments on an active vehicle suspension system, demonstrating significant improvements in ride comfort and stabilization under various road disturbances.

Driver-automation collaboration of steering control systems remains brittle in dynamic authority allocation and managing conflicts under safety-critical driving conditions. This article introduces a safety-critical collaboration framework that systematically blends data-driven perception with physics-aware control synthesis. To start with, an enhanced authority allocation strategy is proposed, which integrates conditional variational autoencoder-based probabilistic trajectory prediction for risk awareness with an interval type-2 fuzzy inference engine. This is further augmented by a novel driver reactive capability assessment module to ensure smoother authority transitions by modulating control shares based on real-time driver state and context. The collaborative dynamics and driver-automation authority allocation strategy are encapsulated within a unified Takagi–Sugeno fuzzy framework, which natively represents the shared steering characteristics. A switched memory-gain-scheduling controller is synthesized, building upon the core of the polynomials-empowered scheme, and explicitly accounts for transmission failures with probabilistic uncertainty. This strategy reduces design conservatism while ensuring enhanced robustness and adaptability to driving modalities. Driver-in-the-loop experiment validates the effectiveness of the proposed approach, demonstrating notable improvements in risk management, tracking accuracy, and system resilience under both typical and extreme driving conditions.

The integration of industrial systems and cloud-interaction technologies enhances resource coordination and regulation efficiency, while also introducing new security threats. This article focuses on a unified attack–defense strategy design for active minecart suspension systems (AMSSs). First, to overcome the limitations of existing attack models that often neglect measurement data and adopt undifferentiated attacks, an importance-driven variable-intensity (IDVI) attack strategy is proposed based on the fluctuation severity of measurement data. This strategy dynamically differentiates data importance to launch targeted attacks, thereby amplifying disruptive impact. Second, an observed-attack-mode-dependent (OAMD) resilient security defense mechanism is correspondingly designed. To handle intermittent mode loss and the mismatch between detected and actual modes caused by practical uncertainties, observation probabilities (OPs) are introduced. Meanwhile, a nonconservative probability block technique is developed to accommodate partially unknown OPs. Furthermore, a membership function combination framework characterized by polynomial degrees is incorporated into the controller design to align with the fuzzy structure of AMSSs and improve gain scheduling flexibility, thereby potentially enhancing ride comfort. Finally, simulations and simulations and hardware-in-the-loop (HIL) experiments demonstrate the superiority of the proposed attack strategy and defense mechanism.

Cooperative positioning enhances positioning performance but suffers significantly from unstable communication and measurement biases. To address these challenges, this work proposes a communication and measurement robust message passing (CMR-MP) method. First, we establish a multicentralized framework that decouples communication from measurement processes. Accordingly, a communication-robust factor graph is designed with constraints adapting to varying communication statuses, enabling neighbor state propagation without control information. This allows full data exploitation even when communication status changes. Second, to mitigate biases, we incorporate a general robust kernel into the Gaussian message passing process. This adaptive robust factor dynamically fits bias distributions to properly weight measurements. Experimental results demonstrate that CMR-MP outperforms state-of-the-art methods; specifically, its circular error probability is at least two times better than conventional approaches under unstable communication and mixed bias conditions.

This article investigates the switching control problem of active vehicle suspension systems (AVSSs) operating over a bandwidth-limited controller area network (CAN). To characterize an AVSS under varying operating conditions, it is modeled as a multimode switched system, where each mode corresponds to a specific vehicle body height. On this basis, a design framework relying on multiple time-varying Lyapunov functions is developed to construct a sampled-data, state-dependent switching (SDS) law that alleviates the communication burden on the CAN while improving suspension performance. To further enhance the utilization of communication resources, a dynamic event-triggered scheme (ETS) is proposed, in which data transmission is scheduled using only sampled state information, thereby eliminating the need for continuous monitoring of the triggering condition. Under the proposed switching law and dynamic ETS, a set of numerically tractable sufficient conditions are established that simultaneously guarantees the desired suspension performance and communication efficiency. The proposed strategy is validated through detailed numerical simulations and hardware-in-the-loop (HIL) experiments, which demonstrate notable improvements in ride comfort and a significant reduction in communication load. In particular, the HIL experiments show that, under pulse road excitation, the proposed controller achieves a 69.05% reduction in vehicle body acceleration compared with a passive suspension.

In the Industry 4.0 era marked by cyber–physical systems (CPSs), the flourishing Internet of Things (IoT) technologies offer development potential for intelligent transportation systems. Physical devices in automobile systems are connected to the Internet to enable data collection and exchange. However, due to vulnerabilities in IoT devices and communication protocols, IoT-enabled CPSs are susceptible to attacks. As a core component of vehicle systems, malicious attacks on the vehicle’s active suspension can severely degrade passenger comfort and threaten vehicle safety. This article investigates the security of IoT-enabled active vehicle suspension systems (AVSSs) under resourceful attackers. First, a discrete-time Takagi–Sugeno fuzzy suspension model is developed to capture the inherent system uncertainties. Second, to counter resourceful false data injection (FDI) attackers who can acquire system knowledge and construct attacks, a dual-mode security algorithm integrating proactive and reactive defense mechanisms is proposed. The proactive defense mechanism leverages the moving target defense (MTD) strategy, which dynamically alters system parameters to hinder attackers’ reconnaissance capabilities. This increases attackers’ costs while reducing defenders’ burden in countering attacks. Furthermore, a high-order observer-based controller is designed to resist attacks, incorporating both the MTD strategy and a homogeneous polynomial parameter-dependent control law. On the other hand, the reactive defense mechanism employs an MTD-based detector to detect attacks. Finally, the proposed method is validated through simulations and hardware-in-the-loop (HIL) tests.

The Metaverse is a user-generated virtual world, aiming to provide highly personalized experiences for users. A product personalization design platform is a critical direction for the Metaverse’s future development, enhancing user experience by offering personalized services. Blockchain technology ensures the security and privacy of user data, and enables personalized services through smart contracts, offering opportunities for personalization platforms. However, blockchain’s decentralization can lead to excessive product data, resulting in ineffective data management and optimization, subsequently confusing personalized product design styles, which diminishes user experience. To address these issues, this study proposes the product style automatic generation system (PSAGS), centered on an image generation unit. The system outputs images with style information based on the input product text, achieving precise quantization and visualization of product styles, thereby enhancing user engagement and loyalty to the Metaverse. The image generation unit, with a standardization module can standardize the product style, namely, the relationship between product design elements and user emotions, addressing the problem of managing vast style data due to blockchain’s decentralization. The generation module utilizes a diffusion model enhanced with contrastive language-image pretraining (CLIP) to generate style images, deepening the Metaverse experience. Optimizations include dilation convolution in the UNet architecture to enhance image quality and fine-grained CLIP transformations for improved image and text alignment. Results demonstrate the system’s effectiveness in streamlining design processes and improving image quality in personalized product design, with wide applications in the Metaverse.

In order to handle the uncertainty of a class of cyber-physical systems with external disturbances, an observer-assisted gain-scheduling tracking control scheme is proposed in this article. First, a covert-switching-based (CSB) attack mechanism is proposed from the attacker’s point of view for the first time to enhance the expected destructive power. The sensor-to-observer (STO) channel and the observer-to-controller (OTC) channel are subjected to mixed network attacks and deception attacks, respectively. Different from most existing attack models, the attack mechanism proposed in this article can dynamically select the channel where the attack occurs by changing the scheduling parameters. Therefore, greater system performance degradation can be expected. Second, corresponding to the proposed CSB attack mechanism, the controller and observer are designed from the defender’s perspective through the high-order multi-mode switching free-weighting matrix (HMSFM) mechanism to reduce the negative impact of the attacks. At the same time, many time-varying balance matrices (TVBMs) for various switching modes of system dynamics are proposed to reduce the conservatism of the designed controller and observer. Then, a sufficient condition for exponential stability is successfully established to guarantee the$H_{\infty }$performance of the augmented error system. Eventually, the dynamic adjustment ability of the CSB attack mechanism and the anti-attack performance of the HMSFM mechanism are demonstrated through experimental simulation and active suspension hardware-in-loop (HIL) tests, and the advancement of the proposed attack-defense mechanism is thus verified.

This article explores the optimized tracking control problem of autonomous aerial vehicle (AAV) and autonomous ground vehicle (AGV) swarm with mismatched disturbances and Byzantine attacks. Unlike traditional AGV-AAV models with different orders, multiple internal and external disturbances within the physical structure are considered in a novel second-order AAV-AGV swarm, which constructs the mismatched disturbances. Since the external environment may induce the swarm to generate and propagate false signals (called Byzantine attacks) to its neighbors, this article reinterprets it as the management of unknown variables in the control inputs. Then, a reinforcement-learning-based approach is introduced to address the unknown control inputs generated by Byzantine attacks. In conjunction with the Hamilton-Jacobi–Bellman (HJB) equation, an adaptive actor-critic–identifier (ACI) structure is designed using the gradient descent method. With the unknown terms estimated by ACI, an optimal robust control strategy under mismatched disturbances is proposed, and a pivotal scaling technique is employed for formation stability analysis. Finally, simulations and experimental results are performed to demonstrate the efficacy of the proposed approach.

cooperative localization (CL) is a promising approach to improve the localization performance. However, many existing CL methods inadequately utilize the correlations within multiagent systems and underperform in scenarios involving nonlinear system model. To address this issue, this work proposes an unified CL (UCL) estimator for both cooperative self-localization (CSL) and cooperative relative-localization (CRL) processes. By incorporating an additional pseudo-CRL process, a consensus strategy and relative motion constraints, a novel augmented factor graph (FG) framework is designed to fully exploit the potential constraints in a multiagent system. Additionally, a novel error state message passing (ES-MP) scheme in error state domain is employed to improve the validity of linearization process when dealing with nonlinear system models, thereby further improving the estimation accuracy. The simulation and experimental results demonstrate that UCL outperforms many existing CL methods in both CSL and CRL accuracy. Moreover, UCL achieves a better performance compared to particle sampling-based methods with significant lower computational load, making it a computationally efficient choice for CL systems.

The rapid development of the Internet of Things (IoT), along with the widespread adoption of 5G and time-sensitive networking (TSN), has provided reliable communication support for the development of Internet of Vehicles technologies. As a critical component of intelligent vehicles, active suspension systems under IoT environment play a vital role in enhancing ride comfort and vehicle safety. However, failure to process data uploaded to the cloud promptly may lead to data accumulation, which can subsequently cause data loss, resource wastage, or system response delays. In this article, an adaptive step value iteration (ASVI) algorithm is designed for solving the optimal control problem of active quarter-vehicle suspension systems (AQVSSs), significantly improving the data analysis efficiency of the cloud layer. To prevent divergence caused by excessive policy evaluation step sizes under immature policies, this algorithm incorporates an adaptive step-size adjustment function that is upper bounded and monotonically nondecreasing. Based on convergence of the value function and stability criteria of control policies, an integrated ASVI (IASVI) algorithm is proposed, which avoids the need of admissible control policies and greatly improves learning efficiency. Feasibility and superiority of the IASVI algorithm are verified through a hardware-in-the-loop (HIL) simulation.

The rapid development of the Internet of Things (IoT) facilitates data exchange and communication across numerous devices and sensors. As a cornerstone of intelligent vehicles, active quarter-vehicle suspension systems within IoT ecosystems critically enhance ride comfort and safety. This paper proposes a safe Q-learning (QL) algorithm based on a novel adaptive control barrier function (ACBF) to design a safe optimal controller. Periodically optimize policies in the cloud, download them, deploy them on edge devices, and implement millisecond-level correspondence in the edge processing layer. In the edge computing layer, the controller guarantees that constrained states of nonlinear systems remain strictly within a safe region while simultaneously achieving optimal performance. First, the ACBF with adaptive factor under the current state is introduced. Then, the Q-function is designed, integrating a positive-definite ACBF with the current state. This integration ensures the concurrent enforcement of safety and optimality constraints. This algorithm utilizes data collected within the safe region—rather than a mathematical model—to seek safe optimal policies. Third, rigorous theoretical guarantees are established for the monotonicity, safety, and optimality of the proposed algorithm. Furthermore, a critic neutral network and an action neutral network with provable approximation capabilities are established to facilitate the execution of the ACBF-based safe Q-learning (ACBF-SQL) algorithm. Finally, hardware-in-the-loop (HIL) simulation experiments validate the effectiveness and superiority of ACBF-SQL.

This article investigates the problem of adaptive fixed-time optimal consensus tracking control for nonlinear multiagent systems (MASs) affected by actuator faults and input saturation. To achieve optimal control, reinforcement learning (RL) algorithm which is implemented based on neural network (NN) is employed. Under the actor-critic structure, an innovative simple positive definite function is constructed to obtain the upper bound of the estimation error of the actor-critic NN updating law, which is crucial for analyzing fixed-time stabilization. Furthermore, auxiliary functions and estimation laws are designed to eliminate the coupling effects resulting from actuator faults and input saturation. Meanwhile, a novel event-triggered mechanism (ETM) that incorporates the consensus tracking errors into the threshold is proposed, thereby effectively conserving communication resources. Based on this, a fixed-time event-triggered control scheme grounded in RL is proposed through the integration of the backstepping technique and fixed-time theory. It is demonstrated that the consensus tracking errors converge to a specified range in a fixed time and all signals within the closed-loop systems are bounded. Finally, simulation results are provided to verify the effectiveness of the proposed control strategy.

This study examines denial-of-service (DoS) attacks on networked control systems (NCSs) caused by TCP/IP protocol vulnerabilities. It conducts a comprehensive analysis of hacker tactics to uncover vulnerability exploitation techniques. The research reformulates the performance error estimation (PEE) problem, framing it as a search for ellipsoid constraints within a P-dependent set. It introduces the Higher-Order Weight Method (HOWM) to optimize sampling intervals, leveraging the unique properties of zero-order-hold sampling. The study enhances Lyapunov-Krasovskii functions (LKFs) using HOWM by partitioning integral terms and applying quadratic scaling to optimize control algorithms, thereby reducing conservatism and tightening upper-bound criteria. Additionally, it proposes an innovative Integral Event-Triggered Control (IETC) strategy for estimating system performance errors. The performance of the proposed control algorithm is rigorously evaluated through simulations on a complex 2-degree of freedom (DoF) helicopter system (HS). Note to Practitioners—This study delves into DoS attacks targeting NCSs due to TCP/IP protocol vulnerabilities. It conducts an exhaustive analysis of hacker tactics to uncover techniques used to exploit these vulnerabilities. The research reframes the PEE problem, casting it as a search for ellipsoid constraints within a P-dependent ellipsoidal set. It introduces the HOWM to optimize sampling intervals, leveraging the unique characteristics of zero-order-hold sampling. Additionally, the study enhances LKFs using HOWM by partitioning integral terms and applying quadratic scaling to optimize the control algorithm, thereby reducing conservatism and tightening upper-bound criteria. Moreover, it introduces an innovative IETC strategy for estimating system performance errors. The performance of the proposed control algorithm is rigorously evaluated through simulations on a complex 2-DoF HS.

This paper studies the fuzzy-based synchronization control problem of coupled neural networks under cyber attacks, where the considered attacks can block the communication links between fuzzy sub-neural networks. Firstly, an improved fuzzy network model is developed, which takes into account the inherent vulnerabilities of network. We design a fuzzy logic-based event-triggered delayed impulsive controller, where impulsive signals are generated by a dependent-Lyapunov intelligent impulsive selection algorithm. Particularly, it can mitigate attack effects, ensure the desired performance of fuzzy networks, and effectively exclude the Zeno behavior. Then, based on the proposed algorithm, some delay-dependent synchronization criteria are established for fuzzy networks on different scales delays, respectively. Finally, a practical example about resistance-capacitance circuit network is provided in different scenarios to show the validity of the theoretical results.Note to Practitioners—This paper was motivated by existing results on impulsive synchronization control of neural networks. Most existing results ignore the effects of external cyber attacks and delay during signal transmission, which is quite difficult to simulate the practical network model. This paper constructs a more general model to consider the inherent vulnerabilities of networks. Then, an intelligent impulsive selection algorithm is designed to resist the risks of attacks and obtain the expected performance. The obtained results are applied to resistance-capacitance circuit systems to verify the effectiveness, and it is expected that the proposed approach can be extended to more mechanical systems.

It is challenging to ensure the safety of vehicles in the presence of malicious attacks. For this reason, the security control problem of nonlinear active quarter-vehicle suspension systems (QVSSs) is investigated in this paper. Within transportation cyber-physical systems, a specific Takagi-Sugeno fuzzy representation is adopted to capture the nonlinear behavior of vehicle dynamics. Firstly, accurately capturing the randomness and variability of attacks within complex driving environments poses a challenge. To precisely model the randomness of attacks, a probabilistically uncertain denial of service (PUDoS) attack strategy is adopted, thereby providing a practical range for potential attacks. Secondly, a novel probability-dependent homogeneous polynomial non-quadratic control law (PHNQCL) is designed. On the one hand, the high-order character of the controller enables the introduction of more groups of gain matrices, enhancing the control flexibility and reducing the conservatism. On the other hand, the designed controller exhibits strong defense capabilities against PUDoS attacks. Subsequently, feasible criteria for the PHNQCL are established using a high-order Lyapunov function, which not only stabilizes the active QVSSs but also reduces the conservatism. Finally, hardware-in-the-loop tests serve to validate the feasibility of the proposed method. Note to Practitioners—As a critical part of automotive chassis, the active quarter-vehicle suspension systems (QVSSs) are crucial for improving ride comfort and ensuring handling stability. However, in real-world environments, external disturbances, uncertainties, and nonlinearities can degrade their performance. As networks evolve, the interconnections in active QVSSs increase. This makes communication channels more vulnerable to attacks, further compromising vehicle safety. This paper explores security control for nonlinear QVSSs, modeling them using T-S fuzzy logic to capture vehicle dynamics. To simulate a complex vehicle driving environment, a probabilistically uncertain DoS attack strategy is designed. The challenge is to design new control methods to mitigate the performance degradation caused by attacks while enhancing vehicle safety in diverse scenarios. Hardware-in-the-loop tests are performed to verify that the proposed control algorithm can provide strong operational stability, ride comfort, and protection of vehicle components.

This paper investigates the static output feedback (SOF) control problem of T-S fuzzy systems based on higher-order Lyapunov functions (HO-LFs). Firstly, to alleviate the conservatism of controller design, an advanced high-order time-varying relaxation matrix (HO-TVRM) approach is proposed. The HO-TVRM approach can completely adapt to the homogeneous polynomial analysis framework and effectively utilize the potential characteristics of fuzzy control to broaden the feasible domain of the reference problem. Secondly, to deal with the non-convex constraints caused by SOF control, a more flexible switching sequence convex optimization (SSCO) algorithm is developed, which adopts a switching-type optimization variable structure and combines variable-weight-based switching mechanism to alternately linearize non-convex terms during the iteration process. As a result, a convex optimization problem that approximates the original problem is obtained. Finally, simulations are presented to testify the effectiveness of the relaxed SOF control strategy.

This paper concerns the distributed set-membership fusion estimation (SMFE) problem of complex networks subject to communication constraints and unknown-but-bounded (UBB) noises, where nodes communicate with their neighbours based on a given topology. There are three main contributions: 1) an event-based coding-decoding mechanism (CDM) is designed in each communication channel to code the transmitted data with a finite bit rate, where the purpose is to save communication resources and enhance transmission security; 2) a fusion estimation method, which can fusion a group of local estimation sets, is introduced to estimate the system state with a trace-maximal ellipsoid, where the local estimators make full use of the information from itself as well as its neighbours. It helps to improve the accuracy and precision of the estimation effectively; 3) a genetic algorithm (GA) is firstly adopted to tackle the co-design issue of bit rate allocation protocol and estimator gain. It aims to reduce decoding errors while ensuring good estimation performance. To demonstrate the superiority of the above contributions, a numerical simulation is provided to validate the proposed SMFE method.Note to Practitioners—Complex networks can be applied to various practical problems, such as biological networks, neural networks, and social networks. The set-membership estimation (SME) method limits the state of the system to an ellipsoidal region. This paper studies the SMFE method, which fuses an ellipsoidal set containing the intersection of all local ellipsoidal sets to form a relatively small region containing the system state, thereby improving the estimation performance. Each communication channel equals with event-based CDM, which improves the robustness and security of data transmission. The bit rate allocation mechanism optimized by GA breaks the traditional uniform allocation scheme, which can reduce decoding error and improve estimation accuracy. Therefore, the method proposed in this paper can be used for navigation and positioning devices.

This paper investigates the secure state estimation problem for time-varying singularly perturbed discrete sequential systems (SPDSSs) under bandwidth-constrained and multichannel-enabled wireless communication environment. Firstly, to avoid the potential data collision as well as fully utilize the available wireless channels, a round-robin-like multichannel access policy (RRL-MAP) is presented for scheduling the transmission of measurement signals. The considered SPDSS is further assumed to be compromised by deception attack, and then the measurement outputs are updated based on the RRL-MAP and the attack driven by a Bernoulli process. In light of the constructed measurement model, distributed recursive state estimators are designed with the proposing of an algorithm that determines the estimators’ gains. Finally, the efficiency of the developed state estimation method for the envisioned SPDSS is verified by both theoretical analysis and simulation experiments.Note to Practitioners—State estimation for SPDSSs is critical given the widespread application of the systems, however it is challenged by limited communication resource and stochastic cyber attacks. Traditional RR protocol is viewed as a desirable method for mitigating the limitation of network bandwidth, but which becomes inefficient under practical multichannel communication scenario. In addition, deception attack is acknowledged as a kind of hardly detected cyber attacks, and will seriously threaten the data integrity. In view of this, this paper presents the RRL-MAP to guarantee efficient data transmission by appropriately scheduling the available communication channels, and uses Bernoulli process to properly describe deception attack. Then, by further considering the structural characteristics of SPDSSs, distributed recursive state estimators are designed to achieve desired system performance. The effectiveness of the estimators is also comprehensively evaluated, which validates the practical applicability of the proposed state estimation method.

This article is centered on an optimal tracking control problem for nonlinear networked systems with limited network bandwidth and unavailable dynamics. Foremost, considering the absence of system dynamics, a state identifier grounded in generalized fuzzy hyperbolic model (GFHM) is estabilshed to eliminate the reliance on known system states. Meanwhile, in order to efficiently utilize the limited communication resources within the network, a dynamic event-triggered mechanism (DETM) with an adaptive threshold is adopted. Subsequently, the DETM-based Hamilton-Jacobi-Isaacs (HJI) equation is constructed following the Bellman optimality theory. Furthermore, we develop a particle swarm optimization (PSO)-driven reinforcement learning (RL) algorithm to achieve the desired optimal tracking control strategy. It is demonstrated that the tracking error system can be promised to be uniformly ultimately bounded (UUB) stability. Eventually, a numerical experiment is provided to illustrate the validity of the developed RL algorithm.Note to Practitioners—This study targets the optimal tracking control issue of unknown networked systems, which holds practical significance in various fields such as robotics, autonomous vehicles and industrial control. In real-world environments, the dynamics of networked systems are not always accessible, thus this paper employs GFHM to approximate unknown dynamic information. Additionally, due to the involvement of the network, the restriction of communication resources is an unavoidable concern. To address this, DETM is adopted to improve network transmission efficiency. Subsequently, to achieve the optimal tracking control, the HJI equation based on DETM is constructed. The solution to the HJI equation is obtained through the RL algorithm supported by critic neural network, with its weights trained using the PSO algorithm. Compared to the commonly applied gradient descent method, under the PSO algorithm, the initial weights can be randomly assigned, making implementation easier and increasing the success rate of system operation. This is of significant importance in practical applications. Besides, a simulation example illustrates the feasibility of the developed method.

This research is concerned with$H_{\infty } $security feedback control for networked singular Markovian jump systems (NSMJSs) with actuator faults and denial of service (DoS) attacks under mode-dependent switching-like adaptive event-triggered scheme. To handle energy-limited denial of service attacks and further strengthen communication efficiency, a mode-dependent switching-like adaptive event-triggered scheme (MSAETS) adopting state-dependent adaptive threshold function is introduced. By exploiting singular value decomposition (SVD) technique and establishing a mode-related discontinuous Lyapunov-Krasovskii (L-K) functional, novel$H_{\infty } $stochastic admissibility criteria for NSMJSs with DoS attacks and actuator faults are acquired, and the relationship between event-triggered parameters and DoS attacks energy is developed through the clever use of matrices/vectors norms and iterative method. Collaborative design method of event-triggered scheme and security feedback controller is proposed, which can make sure the$H_{\infty } $stochastic admissibility of NSMJSs while alleviating the communication burden and improving communication efficiency. The validity of the suggested cooperative control strategy is demonstrated via using an oil catalytic cracking process. Note to Practitioners—In actual engineering, numerous dynamic systems are usually modeled as singular systems, such as oil catalytic cracking processes, power systems, etc. Noteworthy, the investigation of singular systems is considerably complicated and more challenging than normal ones since numerous factors have to be contemplated in parallel, including stability, regularity, non-impulsiveness or causality. Most existing control results are poorly suited to these types of practical systems. Meanwhile, practical systems inevitably endure sudden changes in system structure or/and parameters, actuators may fail completely or partially during operation, and open communication environment and limited bandwidth of communication networks pose a range of challenges including packet losses, network-induced transmission delays and malicious network attacks, all of which may lead to reducing system performance, compromising system stability and eventually result in catastrophic accidents. To address the above challenges, in this work, the mode-dependent switching-like adaptive event-triggered$H_{\infty } $security feedback control scheme is designed for NSMJSs with DoS attacks and actuator faults.

As the percentage of renewable energy in the Energy Internet (EI) gradually increases, how to deal with the uncertainty of renewable energy in the economic dispatch problem (EDP) becomes an important issue. This paper proposes a digital twin (DT) assisted economic dispatch strategy for EI with information entropy. First, we leverage the storage capacity of the DT and an extensive historical data set to provide a theoretical framework for quantifying uncertainty of renewable energy. Second, a renewable energy cost function based on the maximum entropy principle, confidence interval, and penalty factor is proposed to model the renewable energy resources considering the uncertainty. Further, we design a fully distributed Newton-surplus-based optimization algorithm. This algorithm achieves fast second-order convergence to ensure the real-time performance of the DT-assisted economic dispatch framework and overcome the asymmetry caused by the directed communication network. In addition, we give theoretical proof that the Newton-surplus-based algorithm can converge to the global optimal point. Finally, simulations validate the effectiveness of the proposed algorithm.Note to Practitioners—The essence of EDP is to minimize the total costs through optimal resource allocation while ensuring compliance with all operational constraints. With the increasing penetration of renewable energy resources, their strong stochasticity and uncertainty pose challenges to achieve reliable dispatch strategy. To address this issue, this paper presents the DT-assisted economic dispatch framework, model, and method to quantify the uncertainty of renewable energy resources and achieve distributed economic dispatch with fast convergence speed for EI. Our research is beneficial for practitioners to understand how to use the DT and information entropy to deal with the uncertain of renewable energy resources. The theory and simulation results demonstrate the correctness and effectiveness of the proposed method.

This article investigates the resilient security control problem of nonlinear network systems under randomly activated deception attacks and a two-phase data transfer mechanism (TP-DTM). Initially, in order to solve the problem of high conservatism caused by the one-order free-weighting matrix (OFM) method in previous research results, this study introduces a high-order multi-mode switching free-weighting matrix (HMSFM) mechanism to establish free-weighting matrix groups under various switching modes, At the same time, sometime-varying balance matrices (TVBMs) are proposed to cooperate with HMSFM to collect proprietary features about each switching mode. Furthermore, in the context of the system subjected to deception attacks, a TP-DTM employing adaptive event-triggered mechanism (AETM) and round robin (RR) protocol is proposed to alleviate the impact of limited communication resources. Then, considering the above factors, the asymptotic stability of the augmented fuzzy system can be guaranteed under the given sufficient criteria. Consequently, a numerical example and a tunnel diode circuit example are executed to verify the advancement of the developed results. Note to Practitioners—The motivation of this paper comes from the problem that nonlinear networked control systems are vulnerable to malicious network attacks in the actual environment. In particular, malicious attacks will bring security risks such as data tampering and functional damage to the actual communication circuit system, and many state variables cannot be directly monitored due to objective conditions or financial constraints. Based on this, this paper proposes a HMSFM-based co-design mechanism for nonlinear NCSs under malicious attacks. The improved co-design scheme can deal with some difficult-to-measure state variables through observer-assisted tracking control. The main difficulty of this paper is how to reduce the conservatism of resilient control design. The improved co-design scheme can be adjusted according to the dynamic characteristics of the system by combining with TVBMs, making the constraints more relaxed and the state estimation more accurate.

This paper presents an investigation of the sliding-mode secure control for nonlinear semi-Markov jump systems in the presence of non-periodic denial-of-service attacks and false data injection attacks. First of all, we employ Takagi-Sugeno fuzzy model to describe the nonlinear semi-Markov jump control systems. In order to optimize transmission efficiency and control performance, a novel dynamic-memory event-triggered mechanism is developed by incorporating auxiliary dynamic variable and historical transmitted data. Then, a memory-based fuzzy sliding surface is put forward to attenuate the influences of stochastic cyber attacks with the aid of event-triggered state information. Moreover, by utilizing Lyapunov stability theory, sufficient conditions are derived to guarantee the exponentially mean-square stability of the system with an$H_{\infty}$performance index, even in the cases of generally uncertain and unknown transition rates. Furthermore, a memory-based sliding mode secure controller is designed to ensure the reachability of the predefined switching surface and desirable sliding motion within finite time. Finally, the efficacy of the proposed control scheme is demonstrated through a tunnel diode circuit model.Note to Practitioners—This study focuses on the issue of secure control for nonlinear semi-Markov jump systems, which holds practical significance across various domains, including applications in robotic manipulators, circuit models, and DC motors. We broaden the scope by considering more general jump parameter matrices to align more closely with the real-world system environment. Moreover, networked environments pose two primary challenges: network bandwidth constraints and the external network attacks. To tackle these issues, this paper introduces an innovative dynamic memory event triggering mechanism to enhance network transmission efficiency and optimize communication resource utilization. Meanwhile, to address cyber attacks resulting from the inherent openness of networks, the current study adopts a defensive sliding mode control strategy to provide robust protection against network attacks and disturbances. The effectiveness of the suggested approach is confirmed through a circuit system model. It is worth mentioning that the proposed method has the potential for broader application within real-world engineering scenarios, particularly those involving network-based nonlinear systems with various practical constraints.

This paper addresses the problem of global stabilization in nonlinear time-delay systems with unknown measurement sensitivity. Notably, our system allows for the unknown measurement sensitivity to be non-differentiable, coupled with unmeasurable states, which necessitates the development of observers and control input strategies based on dynamic gain. To optimize resource usage and mitigate network congestion, we introduce an event-triggering mechanism based on two events. This mechanism evaluates dynamic gain and control signals, ensuring a guaranteed positive lower bound on execution time. Moreover, the dynamic gain is designed to compensate for the impact of execution errors. The introduction of a relational sensitivity error allows the unknown measurement sensitivity to converge to a small range. By selecting appropriate Lyapunov-Krasovskii functionals, we eliminate the influence of time-delay, ultimately proving global stability of the closed-loop system. Consequently, comparative simulation results validate the effectiveness of the proposed scheme. Note to Practitioners—This paper explores event-triggered control of nonlinear systems with applications in intelligent transportation, robotics, and aerospace. Notably, we address three critical issues. Firstly, we propose methods to manage unmeasurable states, which is essential for systems like autonomous vehicles and drones where full state measurement is often not feasible. Secondly, we improve existing event-triggering mechanisms to optimize network resource usage, significantly reducing communication frequency, which is particularly beneficial in networked control systems, such as smart grids and industrial automation. Thirdly, we tackle the challenge of unknown measurement sensitivity, relevant for systems operating in uncertain environments like industrial robots and aerospace applications where sensor accuracy can vary. Comparative simulations show that our dynamic event-triggered control method effectively reduces network burden, proving its practical value in real-world applications where network bandwidth and reliability are crucial. In future research, we will also consider reducing the transmission frequency from sensor to controller to further improve system performance. Additionally, we aim to explore adaptive mechanisms to better manage uncertainties in measurement sensitivity, thereby expanding the practical applicability of our approach.

This paper presents a finite-time tracking control for PDE-ODE coupled systems with dead-zone input and actuator failures. To begin with, a novel finite-time performance function and error transformation are designed for a reaction-diffusion equation to improve the transient and steady-state performance for PDE-ODE systems. In addition, to overcome the difficulties generated by the uncertain actuator failures and dead-zone input for coupled systems, a finite-time tracking controller and the adaptive laws are designed to compensate for the drastic effect of unknown nonlinearities. By applying neural networks approximation technology, the computational complexity and difficulty of controller design are significantly reduced. Unlike the existing stability results in the PDE-ODE systems, the developed method can guarantee the given transient performance by adaptive parameter tuning and the tracking error converges to the specified region in finite time. Moreover, the boundedness and convergence of all the signals in the closed-loop coupled systems are proved. Finally, the simulation example exhibits the effectiveness of the proposed control scheme. Note to Practitioners—The PDE-ODE coupled systems in modern mechanical engineering scenarios require better transient and steady-state performance as well as more agility of adjustment method. Because of the special infinite-dimensional characteristics of coupled systems compared to single PDE or ODE systems, it is more complex to design the adaptive finite-time controller for PDE-ODE systems. The finite-time performance function and error transformation designed in this paper aim to improve the stability of the coupled systems and adjust the preassigned performance more flexible. The settling time is independent and free of the parameters and initial values of the coupled systems which can be chosen by users according to actual requirements. Meanwhile, the constraints of actuator failures and dead-zone nonlinearity are compensated simultaneously for PDE-ODE systems via the presented adaptive neural networks finite-time control scheme.

This paper centers on the distributed fault-tolerant control (DFTC) issues of time-varying delayed nonlinear multiagent systems (TVDNMASs) with switching topologies and external disturbances by considering multiple faults and event-triggered consensus strategy (ETCS). The switching topologies satisfy generally uncertain semi-Markovian switching topologies (GUSMSTs), and they contain uncertain and partially unknown semi-Markovian transition rates (TRs). In addition, the ETCS is adopted in this paper to decide the update of controllers, which alleviates the load of the correspondence network. In view of Lyapunov-Krasovskii functional (LKF), the tracking control protocols are presented to guarantee the DFTC of nonlinear multiagent systems (MASs). Moreover, the controller gain and observer gain matrices are derived through the solution of linear matrix inequalities (LMIs). Finally, a simulation example is proposed to exhibit the capability of our design technique. Note to Practitioners—Due to the complexity of engineering environment, the cooperative control of MASs has gained widespread attention. Nowadays, the MASs are generally utilized in diverse fields, such as multi-motor synchronization, drone swarm formation, and smart grids. As one of the significant research interests in cooperative control, the consensus control of MASs has become a research hotspot. However, in practical applications, due to stochastic system failures and sudden changes in the external environment, it is hard for the fixed communication topologies to cope with these unexpected situations. Therefore, the DFTC issues of delayed nonlinear MASs with GUSMSTs and external disturbances by considering multiple faults are investigated in this paper. Moreover, the mode-dependent distributed time-delay intermediate observers and active fault-tolerant consensus controllers are designed on the basis of distributed fault-tolerant control consensus protocol.

DC microgrids (DC-MGs) consist of multiple units interconnected in a network. This makes the system vulnerable to malicious cyber attacks. Malicious attacks here refer to hybrid attacks of false data injection (FDI) attacks and denial of service (DoS) attacks. The main focus of this paper is to study the state-FDI estimation and resilient control problems of nonlinear DC-MGs under malicious attacks. Since the fuzzy controller/observer based on the parallel distributed compensation method cannot obtain more relaxed satisfactory results. Methods presented in the literature will be reviewed and a method based on multi-mode fuzzy switching mechanism (MMFSM) will be developed to relax the stability analysis of these DC-MGs. Furthermore, a co-design method based on improved fuzzy switching technology is proposed. This method adopts a novel MMFSM, which makes the constraints more relaxed, the state estimation more accurate, and the conservatism of the co-design method is reduced. Finally, the effectiveness of the proposed improved co-design method is verified by comparison and analysis of simulation examples.Note to Practitioners—The motivation of this paper comes from the problem that DC-MG systems, which can realize large-scale application of new energy technology, is vulnerable to malicious cyber attacks in practical tasks. Malicious attacks (such as FDI attacks and DoS attacks) will bring security risks such as data tampering and function destruction to the system. To this end, this paper develops a MMFSM-based co-design method for DC-MGs under malicious attacks. The improved co-design method can deal with sector nonlinearity, state imperfectly measurable, FDI attacks and DoS attacks simultaneously. For this method, the main difficulty in this paper is how to reduce its conservatism. To solve this problem, we adopt a novel MMFSM. By introducing time-varying equilibrium matrix synchronously with the system dynamics of different modes, the improved co-design method can switch accordingly, thereby making the constraints more relaxed and the state estimation more accurate.

This brief describes a fast finite time adaptive control strategy for p-norm stochastic nonlinear systems (SNSs) using adding a power integrator approach. In terms of convergence speed, finite time control (FTC) offers a substantial advantage in the vicinity of the equilibrium point, but it may exhibit notably slower convergence compared to exponential convergence when the initial state is far from the origin. To overcome this problem, the Lyapunov function is skillfully constructed in this study. A method is devised based on this function, which incorporates the characteristic of adding a power integrator technique and the symbolic function to effectively tackle challenges posed by complex system structures. Then, adaptive control is utilized to deal with the mismatched uncertain nonlinear function. Subsequently, a novel fast FTC strategy is proposed for p-norm SNSs with dead-zone via the back-stepping framework, which ensures the transient performance of the closed-loop system. In comparison to existing results, this controller effectively achieves performance control for p-norm SNSs with dead-zone and mismatched uncertainties functions. Finally, the superiority of the scheme is illustrated by comparative simulations. Note to Practitioners—The FTC problem is a prominent subject in the field of control, playing a crucial role in practical applications. This is especially notable in p-norm nonlinear systems, where the dynamic behavior exhibits uncontrollable linearization characteristics near the origin, introducing complexity to control analysis. Another challenging aspect in nonlinear control is the impact from external disturbances. In practical systems, the presence of random disturbances is inevitable and frequently results in system instability. A fundamental technical barrier is the involvement of Brownian motion integral terms in stochastic nonlinear systems, along with Itô differential, which introduces not only gradients in Lyapunov analysis but also the Hessian of the Lyapunov function. Furthermore, it is observed that mismatched uncertainties and dead-zone phenomena exist in real systems. Designing fast finite-time controllers has become a focal point of controller research. To address these issues, this paper proposes a fast FTC algorithm tailored for a class of p-norm SNSs with mismatched uncertainties. The proposed approach ensures that the system state can converge to the desired region near the origin in an almost fast finite time.

This paper focuses on the problem of outlier-resistant distributed filtering under dynamic event-triggered scheme (DETS) and cyber-attacks over sensor networks. A novel distributed DETS is proposed, which allows us to minimize the data-releasing rate while simultaneously preventing abrupt data from being sent over the network. Consider the situation of measurement outliers in presence, a saturation function is used in distributed filter design to confine the contaminated signals so as to improve filtering performance. The occurrence of stochastic DoS attacks which may corrupt the measurement in the sensor networks are also considered. Sufficient conditions for the expected filter are derived while guaranteeing the asymptotically stability of the filtering error system with a guaranteed$H_{\infty}$performance index$\gamma$. A numerical simulation is given to illustrate the effectiveness of the theoretical analysis and design method.Note to Practitioners—The issue of filtering over sensor networks is subject to network impections induced by the limited communication resources and cyber-attacks. Since these imperfections may lead to performance degration or instability of the system, it is critical to take some measures to reduce unnecessary signal communication among sensor nodes and eliminate the adverse effects of cyber-attacks. Besides, the measurement outliers are frequently encountered due to sensor aging or abnormal disturbances, which may impair the accuracy of the estimation resuts. In this paper, the outlier-resistant distributed filtering problem is investigated in sensor networks subject to dynamic event-triggered schemes and DoS attacks. A co-design method of the DETS and the distributed filter is propsed which can gurantee the desired system performance.

The dynamic event-triggered (DET) bipartite consensus and attack estimation problem is investigated for multi-agent systems (MASs) under false data injection (FDI) attacks generated by exogenous systems. For the purpose of compensating for the system bias, a novel set of estimators are introduced to estimate the FDI attacks. To optimize the limited resources of the network bandwidth, a DET protocol dependant on the auxiliary variable and the local estimations is employed to regulate data transmission. By employing the designed state observer and attack observer, an novel attack tolerant event-triggered control strategy is established. Subsequently, sufficient criteria are obtained to ensure the bipartite consensus performance with$l_{2}$-$l_{\infty }$constraint. Then, by solving algebraic matrix equations and recursive linear matrix inequalities (LMI), the gains of state estimator, attack estimator and desired controller are determined, respectively. Finally, simulation examples are provided to demonstrate the validity of the derived results. Note to Practitioners—This paper discusses the secure bipartite consensus control problem for MASs subject to FDI attacks. Since the system state deviation caused by FDI attacks will bring about degradation of system performance, it is important to protect the MASs from being destroyed by designing observers to estimate the FDI attack and the system state. In view of the bandwidth constraints among the agents in MASs, optimization utilization of the network bandwidth should be taken into account seriously. Therefore, in this paper, the proposed observer-based DET controller is developed to guarantee bipartite consensus of the considered MASs while ensuring efficiency utilization of bandwidth resources. The current research provides a helpful reference for the secure bipartite consensus control of MASs with bandwidth constraints.

Due to dynamic characteristic of demand response and stochastic nature of power generation, it brings great challenge to smart energy management. In this paper, a demand response model is created with two-level dynamic pricing transaction among grid operator, service provider and customers, which also involves customers’ active participation with load shifting issue. To effectively control system load on the demand side, an improved deep reinforcement learning approach is proposed with a recursive least square (RLS) technique to deal with the dynamic pricing demand response problem, which accelerates the on-line training and optimization efficiency. On the power generation side, a probabilistic penalty-based boundary intersection (PBI) based multi-objective optimization algorithm is improved to optimize the economic cost, emission rate and statistic voltage stability index (SVSI) simultaneously with generated stochastic scenarios, which can ensure energy conservation and environmental protection, as well as system security. The case results reveal that the proposed two-level optimization strategy successfully deals with energy management with dynamic pricing demand response.Note to Practitioners—This paper is motivated by solving stochastic energy management issue of isolated power system with dynamic pricing demand response. Those existing methods merely focus on the load demand or power generation side, and the methods for demand response issue lacks efficient on-line learning ability, while this work proposes a recursive least square based deep reinforcement learning approach to tackle with the two-level dynamic pricing demand response issue, scenario based PBI multi-objective optimization is proposed to solve the power dispatch issue on power generation side, and the numerical analysis results suggest that the proposed optimization strategy can deal with the whole energy management issue well. The future work will focus on the dynamic power-load coordination in the energy management issue.

This paper presents an adaptive boundary control design for flexible riser systems with external disturbances and boundary position constraint. An integral barrier Lyapunov function (iBLF) is used to solve the boundary position constraint problem. Since the iBLF directly constrains the boundary position, this relaxes the conservative restriction on the state constraint of conventional BLF control. A new auxiliary signal is designed to offset the effect of the coupling term that cannot be eliminated. Compared to time triggering, the controller and actuator communicate less when using event triggering. Therefore, an event-triggered control scheme is designed to achieve effective suppression of riser vibration by introducing a relative threshold strategy. The Lyapunov stability theory is used to demonstrate that the flexible riser system is finally constrained. The efficiency of the control strategy is then further verified by numerical simulationsNote to Practitioners—This paper investigates the control problem of flexible riser systems with external disturbances. Since the riser needs to consider the uninterrupted marine distribution disturbance and external disturbance, the riser will inevitably distort and vibrate. So the stability of the ship is extremely challenging. The riser is regarded as an Euler-Bernoulli beam construction because of its small diameter and lengthy length. Using Hamilton’s principle, the riser is represented as a fourth-order partial differential equation and two ordinary differential equations. In contrast to the logarithmic BLF and tangent BLF, the integral BLF has direct constraints on the boundary positions, which relaxes the conservative restrictions on state constraints imposed by conventional BLF control. Event-triggered control has attracted the interest of many flexible system control researchers due to its benefits in preserving communication, cost and other resources, and is widely used in practical engineering fields. The complexity and uncertainty attributed to the PDE system itself makes the design of event-triggered strategies more difficult. Based on the original ODE event triggering, it discusses the PDE-based event-triggered strategy of flexible riser systems.

This paper investigates the dynamic event-triggered boundary control of cyber-physical flexible riser systems under spoofing attacks. It aims to dampen vibrations resulting from riser pipe deformation, alleviate the communication load, and curtail the influence of such attacks. Firstly, a novel dynamic event-triggered boundary controller is constructed by utilizing external disturbances and event-triggering strategies. This controller overcomes the complex spatio-temporal coupling phenomena in riser systems and suppresses vibrations. Secondly, a controller is developed to minimize the impact of false data injection on the cyber-physical flexible riser system due to uncertain spoofing attacks. Finally, the stability of the system is mathematically analyzed to prevent the occurrence of Zeno phenomena. The simulation results further validate the effectiveness of the proposed method. Note to Practitioners—Cyber-physical flexible risers play an important role in various marine engineering and industrial fields, such as underwater oil and gas extraction, deep-sea resource exploitation, and seabed exploration. A challenge within these domains is the effective mitigation of cyber-physical riser vibrations amidst spoofing attacks, a problem that has yet to be resolved. This paper introduces a novel dynamic event-triggered boundary control strategy aimed at dampening vibrations induced by riser deformations, reducing communication overhead, and attenuating the effects of spoofing attacks. Based on PDEs, the proposed control strategy offers a solution for the regulation of flexible riser systems in forthcoming engineering endeavors.

This paper presents an online transfer heuristic dynamic programming (THDP) control approach for a class of nonlinear discrete systems. The proposed approach integrates transfer learning with adaptive critic control. To design a robust optimal control strategy for the nonlinear discrete systems, we utilize sample data collected from a source task to acquire prior knowledge. This prior knowledge is subsequently used to guide the online control process of nonlinear systems of target tasks. To avoid negative transfer effects and conserve computational resources, we introduce a novel attenuation function with a truncation mechanism. Additionally, we develop a disturbance compensation control mechanism to address uncertainties. Furthermore, we demonstrate that the properties of the uncertain nonlinear systems under robust optimal control, as well as the weight error of neural networks, are ultimately uniformly bounded given certain conditions. Finally, two simulations are conducted to verify the performance of the proposed algorithm. Note to Practitioners—Adaptive dynamic programming (ADP) is one of the main methods to solve the Hamilton-Jacobi-Bellman (HJB) equation. However, when using neural network approximation, it often requires a long time of iteration and a large amount of computational process, wasting a lot of computational resources. For this reason, we propose an ADP control scheme with enhanced detection speed: that is, by learning a class of similar tasks to obtain prior knowledge to assist in the online control of our actual system. At the same time, this paper considers system disturbances, which means that they are more universal and robust. After simulation experiments, it has been proven that this scheme has good performance.

In this paper, the novel prescribed-time dynamic event-triggered control method of an unknown multiplayer nonzero-sum game (MP-NZSG) is designed by using adaptive dynamic programming (ADP). Firstly, a neural network-based identifier is constructed to estimate the unknown system dynamics. Subsequently, a novel ADP-based dynamic event-triggered control approach is advanced to ensure optimality and prescribed-time stability. A critic neural network (NN) is established for each player to approximate the Nash equilibrium solution of the dynamic event-triggered Hamilton-Jacobi-Isaacs (HJI) equation. This network employs a novel weight updating law, based on the experience replay technique, to alleviate the persistence of excitation condition. Furthermore, using the Lyapunov method, the uniform limit boundedness analysis of the neural network approximation error and multiplayer system is validated. Additionally, minimum inter-event time (MIET) is conclusively established to mitigate the notorious Zeno behaviour. Ultimately, the efficacy of the proposed method is rigorously substantiated through comprehensive simulation results. Note to Practitioners—Our research addresses the challenges of multi-component coordinated control, particularly in spacecraft attitude control. To handle these complexities, we propose an innovative adaptive dynamic event-triggered control approach. By integrating adaptive dynamic programming and neural networks, we effectively model and manage unknown system dynamics, enhancing the controller’s adaptability and robustness. Dynamic event-triggered policies are introduced to optimize system performance and reduce computational costs. The ADP-based prescribed time optimal control scheme prioritizes steady-state performance of nonlinear nonaffine systems, ensuring precise task completion within specified timeframes. Additionally, experience replay technology further fortifies the controller’s learning and adaptability to dynamic environments.

In this paper, we investigate the problem of prescribed-time optimal control using reinforcement learning technology. Unlike finite/fixed-time control methods that only achieve stability within specified time bounds, we propose a prescribed-time adaptive dynamic programming (ADP) control approach that ensures both optimality and prescribed-time stability. To address the challenge of solving the nonlinear Hamilton-Jacobi-Bellman (HJB) equation in finite horizon, we construct an actor-critic neural network (NN) with a time-varying activation function. The novel weight update laws are derived from the system’s terminal error and the approximate error of the HJB equation. This derivation eliminates the need for knowledge of dynamic conditions while ensuring compliance with terminal constraints. Based on the proposed prescribed time stability criterion, the control scheme is proven to satisfy prescribed time stability while also ensuring optimal system performance index and bounded weights. We apply the designed control scheme in a time-varying delay system and simulation examples validate the efficacy of the strategy.Note to Practitioners—Many industrial processes are nonlinear time-varying delay systems, which brings great challenges to solving the HJB equation of the prescribed-time control problem. Therefore, it is of great value to solve the prescribed-time control problem by using the advantages of finite time ADP in solving the time-varying HJB equation. The ADP-based prescribed-time optimal control (ADPPTC) scheme designed in this paper aims to optimize the steady-state performance of nonlinear time-varying delay systems, and because the user can prescribe the stability time, the system can accurately complete a task within a specific time range. At the same time, the prior demand for the system state can be eliminated by the proposed actor-critic neural network.

This article designs a self-triggered adaptive dynamic programming (STADP) algorithm combined with the model predictive control (MPC) mechanism to address the approximate optimal control of a nonlinear system with terminal state constraints. The MPC mechanism transforms the problem into a series of subproblems and then reduces the number of subproblems through the self-triggered mechanism (STM), thereby reducing the amount of computation. The MPC-based STADP (MSTADP) algorithm employs neural networks (NNs) to construct three key modules: the model module, the critic module, and the action module. These modules enable the identification of the unknown system, approximation of the cost function, determination of the terminal penalty, and estimation of the optimal control strategy set. Furthermore, a relaxation factor is incorporated to modulate the convergence rate of the system states online. Finally, experimental validation on two distinct systems demonstrates the algorithm’s effectiveness, and comparative experiments against the traditional HDP algorithm are performed to highlight the superiority of the proposed approach.

This article focuses on addressing the issue of asynchronous${H_\infty}$control for Takagi-Sugeno (T-S) fuzzy Markov jump systems with generally incomplete transition probabilities (TPs). The delay is assumed to vary periodically, resulting in one monotonically increasing interval and one monotonically decreasing interval during each period. Meanwhile, a new Lyapunov-Krasovskii functional (LKF) is devised, which depends on membership functions (MFs) and two looped functions formulated for the monotonic intervals. Since the modes and TPs of the original system are assumed to be unavailable, an asynchronous switching fuzzy controller on the basis of hidden Markov model is proposed to stabilize the fuzzy Markov jump systems (FMJSs) with generally incomplete TPs. Consequently, a stability criterion with improved practicality and reduced conservatism is derived, ensuring the stochastic stability and${H_\infty}$performance of the closed-loop system. Finally, this technique is employed to the tunnel diode circuit system, and a comparison example is given, which verifies the practicality and superiority of the method.Note to Practitioners—As a category of stochastic hybrid nonlinear systems driven by continuous time and discrete events, FMJSs have significant applications in practical engineering such as aircraft control systems and large-scale manufacturing systems. However, the real-time acquisition of system mode information and TPs is difficult due to technological constraints and limited resources. Moreover, the presence of periodically varying delay is prevalent in many industrial processes, resulting in degradation of dynamic system performance and instability. Therefore, it is necessary to study the FMJSs with generally incomplete TPs and periodically varying delays in asynchronous framework. Accordingly, unlike previous work, the designed LKF relies on system modes, MFs, and two looped functions for monotonic intervals. This new LKF exhibits a high degree of flexibility, fully leveraging the information of MFs and periodically varying delays, which can significantly reduce conservatism.

This paper focuses on the fault-tolerant consensus problem of multi-agent systems under an encoding-decoding framework with Markovian switching topologies. Due to the influence of complex environments, the communication network changes over time, and thus, a Markov chain is introduced to describe the random topology switching. Under the stochastic characteristics and encoding-decoding framework, Lyapunov’s second method is applied for the first time instead of the original matrix analysis method, with both uniform and logarithmic quantizers considered. To obtain the unmeasurable states and the unknown sensor faults in the form of first-order differences, augmented estimation is performed, followed by encoding-transmission-reception-decoding for controller design. Under uniform quantization, the relationship between the scaling function and the parameters in the Riccati inequality is established, enabling boundedness analysis of data transmission. Under logarithmic quantization, a quantization-dependent Lyapunov function is constructed, and its rationality is rigorously proven. Finally, numerical simulations under both uniform and logarithmic quantization are provided to demonstrate the achievement of consensus and poly-quadratically stable in mean square sense.

The problem of normalized proportional-derivative (P-D) and intermittent hybrid$H_{\infty}$control for delayed descriptor impulsive systems (DDISs) is studied in this work. The P-D and intermittent hybrid state feedback controller is designed, such that normalisation and$H_{\infty}$stabilisation of DDISs can be realised. A novel impulsive-inputs-dependent Lyapunov-Krasovskii functional based on a couple of auxiliary functions is constructed, which is continuous along the system state trajectories without imposing additional conditions on impulsive dynamics. Improved$H_{\infty}$stability criterion is proposed in the form of linear matrix inequalities by utilizing free weighting matrix technique, and the$H_{\infty}$stability criterion is described as a single condition based on a combination of discrete and continuous dynamics. Finally, the usefulness of the method set forth in this work is demonstrated by a two-loop circuit network.Note to Practitioners—This work is motivated by realizing normalized P-D and intermittent hybrid$H_{\infty}$control for delayed descriptor impulsive systems. In practical engineering, many dynamic systems have to be formulated as descriptor systems when modeling, such as circuit systems, vehicle suspension systems, and so on. It is worth pointing out that infinite dynamic modes will occur due to the algebraic constraints in descriptor systems, and can lead to internal impulsive behavior. At the same time, these systems are often accompanied by external impulsive perturbations, such as the sudden failure of a component in circuit systems, etc. The internal and external impulses can cause serious damage to the system performances and stability. Most of the existing control schemes are not well suited for such practical systems. In addition, due to the presence of time-varying delays, the delayed dynamic systems can easily collapse and cause significant damages. In this work, the P-D and intermittent hybrid$H_{\infty}$controller is designed so as to deal with the above challenges.

This article considers the problem of event-based$H_{\infty }$fuzzy control for implicit hybrid active vehicle suspension systems (IHAVSSs) embedding acceleration and Markovian jumping characteristics under random deception and denial-of-service (DoS) attacks. Aiming at conserving of communication resources, an event-triggered strategy is introduced in the communication link between sensor and controller. The accelerations of sprung, unsprung and tyre are taken into account, the active vehicle suspension systems are constructed as the implicit one. Admissibility conditions are derived under the framework of linear matrix inequalities by utilizing the piecewise Lyapunov-Krasovskii (L-K) functional. Via singular value decomposition (SVD) technique, the IHAVSSs are proved to be regular and impulse-free. By means of Takagi-Sugeno (T-S) fuzzy method and parallel-distributed compensation (PDC) technique, a mode-dependent (M-D) fuzzy feedback controller (FFC) is designed to ensure$H_{\infty }$stochastic admissibilization of IHAVSSs under random deception and DoS attacks. The validity of the results is demonstrated by using the quarter active vehicle suspension model produced by Quanser company. Note to Practitioners—The active vehicle suspension systems hold paramount significance in practical applications, effectively dampening vibrations from road surfaces and enhancing ride comfort. Concurrently, as networking advances, interconnectedness among various components within the active vehicle suspension system grows. However, the communication links are vulnerable to malicious attacks that may decrease the performance of the AVSSs, which inspires our current research. This paper delves into the$H_{\infty }$stochastic admissibilization of the AVSSs subjected to network malicious attacks, and makes full use of the dynamic variable of the system in the modeling process, that is, the accelerations of each components are selected as the system state variable. The method is applied to a platform simulation, and the stochastic admissibility of implicit hybrid active vehicle suspension systems under random deception and DoS attacks is realized.

This article investigates the event-triggered multiasynchronous dissipative sliding mode control problem for the gird-connected systems, where the coupled Inductance-Capacitance (LC) oscillators in electrical networks are subject to actuator attacks and external disturbances. To reduce the communication burden, the dynamic event-triggered mechanisms (DETMs) are introduced along with the switching mechanism for multiple topologies. Specifically, the topology switching process is further viewed as a general uncertain semi-Markov (GUSM) jumping process. This jumping process along with the DETM is thus represented by hidden Markov model (HMM). Then the distributed integral-type sliding mode controller is constructed on the top of the HMM. Sufficient conditions for the desired performance of the closed-loop synchronization error system are derived by constructing the mode-dependent Lyapunov-Krasovskii functional (LKF) with extended dissipativity analysis. The numerical simulation of LC oscillators in the single-phase photovoltagic grid interconnection process is conducted to validate the proposed method.

In this article, we consider the problem of privacy preservation in consensus control for second-order integrator multiagent systems (MASs). Specifically, we consider the setting where the initial position and velocity of each legitimate agent are both private, an internal or external adversary wants to identify them based on the information it obtains. To deal with this scenario, we propose a privacy preservation algorithm based on a position and velocity simultaneous perturbation technique. To be specific, our algorithm consists of a collaborative scrambling phase and a convergence phase. In the scrambling phase, each agent is required to produce two sets of edge-based perturbation signals that are, respectively, imposed on the local position and velocity signals before transmission, with the purpose of preserving privacy; in the convergence phase, each agent updates its state per a normal rule, aiming to achieving accurate consensus. Also, we establish a system-theoretic framework to analyze privacy performance by examining the indistinguishability of private values' arbitrary variations to adversaries, and further show that, an internal adversary cannot infer the privacy of a legitimate agent provided it has at least one legitimate in-neighbor or out-neighbor, and the privacy is leaked out once that agent exclusively connects to the internal adversary in bidirectional way. As for external eavesdroppers, they can never infer any agent's privacy if the gain parameters in the scrambling phase are not accessible to them. Finally, two simulation examples illustrate the validity of the proposed approach.

Developing model-free $H_{\infty }$ optimal control schemes in systems with unknown model parameters and unmeasurable states is challenging. In this article, an output-feedback (OPFB) suboptimal control scheme based on adaptive dynamic programming (ADP) is proposed to realize model-free $H_{\infty }$ control under uncertain disturbances. First, a free matrix is introduced to compute the suboptimal gain in the absence of an optimal OPFB gain, and a policy iterative algorithm is developed to solve for the suboptimal gain and shown to converge to a solution of the algebraic Riccati equation. In addition, a model-free ADP algorithm is proposed to realize online learning of control parameters without relying on system dynamics parameters. The Lanczos method is introduced to solve the ill-condition problem in the model-free algorithm solution. After that, the algorithm is further extended to the case where the system state is not measurable and parameterized reconstruction is performed using online input-output data. The results show that the proposed algorithm can realize model-free control with unknown parameters and unmeasurable states. The effectiveness of the proposed control scheme is simulated by an F-16 aircraft.

This article investigates the state estimation and security control problem for discrete-time dual-rate cyber-physical systems (CPSs) under denial-of-service (DoS) attacks. The asynchrony predicament between different signals of dual-rate CPSs, exacerbated by the impact of cyber attacks on the sensor-to-controller channel, substantially increases the complexity of state estimation and control processes. Based on the signal-to-interference-plus-noise ratio and two-channel probability descriptions, an improved sample-and-hold (SAH) estimator is applied to dual-rate CPSs, ensuring favorable state estimates while enduring low-frequency sampling and DoS attacks. Furthermore, to solve the performance degradation problem posed by the SAH algorithm, an alternating-sampling-prediction (ASP)-based estimation method is proposed. At each fast-update moment, the predictor generates virtual outputs. The estimator can reconstruct complete state information by alternately using incomplete sampling data and iterative predictive information. Compared with the SAH method, the proposed ASP-based approach significantly enhances the control performance of dual-rate CPSs. Building on two valid estimation methods, the corresponding security control inputs are designed, guaranteeing both ideal control performance and resilience against attacks. Using convex optimization analysis, both estimator and controller gains are calculated to realize the stochastic stability of closed-loop dual-rate CPSs. Finally, the effectiveness and intercomparisons of the two estimation methods are shown by simulating a satellite yaw-angle control system and a quadrotor landing control experiment.

To achieve low-carbon operation of a distribution network, new energy resources like photovoltaics (PVs) have been extensively integrated into it. However, this integration poses significant challenges to the supply-demand balance. Specifically, the generation of PVs is stochastic, causing power fluctuations. Additionally, the increase in power data and the open nature of the network will cause network congestion and communication disturbances. To address these issues, an active power support (APS) strategy is developed with the following innovations. First, an adaptive mutation-based generation prediction algorithm incorporating a multi-extreme learning mechanism (ELM) is proposed to optimize the prediction model and provide reliable predicted generation data for regulation. Second, a demand-driven path optimization method is proposed to prioritize critical data transmission, ensuring that regulatory service demands are met while mitigating congestion. Third, a hierarchical control strategy utilizing multifactor matching and a sliding mode controller (SMC)-based virtual leader-following consensus algorithm is designed to generate optimal control commands for PVs and suppress disturbances. Finally, adequate simulations demonstrate that the proposed method reduces the prediction error by at least 10.1% compared to existing methods, adjusts transmission paths based on data importance and service needs to mitigate congestion, and suppresses communication disturbances within 1s, thereby enabling effective APS.

Based on Petri nets (PNs), this paper tackles the problem of hybrid modeling and fuzzy control of supply chain networks (SCNs) under disruptions. First, a new fuzzy-based SCN operational model using delivery rate regulation experience is developed, which can be regarded as a fuzzy interconnected large-scale system. Then, a PN-based formal system approximation for continuous operational activities is performed, while visualizing discrete disruption events. As a result, the unified model of SCN hybrid dynamics is achieved via PNs, which has the potential advantage on facilitating the monitor of SCN changes in a general graphical and mathematical language. Furthermore, PN-based fuzzy control design criteria are derived via Lagrange and Lyapunov stability analysis on the hybrid markings. Finally, a hydrogen SCN case in the IEEE PJM 5-bus power system is provided to substantiate the effectiveness and benefits of the proposed methods.

This paper addresses the critical challenge of achieving asymptotic stability in networked control systems (NCSs) under denial-of-service (DoS) attacks, focusing on maintaining security and stability within bandwidth-constrained environments. First, we construct a practical attack model using the NSL-KDD dataset to provide a realistic representation of DoS attack dynamics, capturing key attributes such as attack duration and frequency. Then, an iterative shrinkage-thresholding algorithm (ISTA) is introduced to supervise the adaptive sampled-data controller (ADSC), dynamically optimizing the sampling period to enhance control performance while minimizing communication overhead. To further mitigate the impact of DoS attacks, we propose a novel data compression mechanism that adapts to varying network conditions, ensuring efficient bandwidth utilization and preserving critical control data fidelity. In addition, the stability of the NCS is rigorously verified through Lyapunov-Krasovskii functions (LKFs), demonstrating robust system behavior even under adverse network conditions. Finally, the effectiveness and practicality of the proposed approach are validated through experimental studies on a 2-degree-of-freedom (2-DoF) helicopter system, confirming its capability to ensure stability, optimize communication efficiency, and mitigate the effects of DoS attacks in real-world scenarios.

This paper proposes a novel co-design method of denial-of-service (DoS) attack-resilient time varying estimators/observers and controllers aimed at addressing these challenges in a discrete-time linear networked control systems (NCSs) under sensor and actuator false data injection (FDI) attacks. Our time-varying estimators have uniquely equipped to perform a joint estimation of the system state, sensor and actuator attack signals despite the presence of the intermittent DoS attacks. The main features of the developed time-varying observers are twofold: firstly, it involves time-varying gains corresponding to the DoS attack off/on transitions, and secondly, it entails augmenting the estimations of sensor and actuator FDI attacks within the piecewise observer error dynamics, thus providing a comprehensively and rigorous estimation and control methodologies. By introducing the conceptions of minimum and maximum sleeping/active durations of DoS attacks, a new time-varying DoS attack instant-dependent piecewise Lyapunov function approach is proposed to analyze theH∞stability of the augmented estimation error system and closed-loop control system under sensor and actuator FDI attacks. Based on the obtainedH∞stability analysis results, time-varying gains of state and attack observers are formulated to construct the DoS-resilient observers. Besides, the time-varying feedback gains are also obtained to construct the DoS-resilient controllers by attack compensation based on the actuator FDI attack estimations of time-varying observers, thus achieving the mitigation of sensor and actuator FDI attacks. Case studies are performed on a three-area interconnected power systems under DoS and FDI attacks to validate the effectiveness and advantages of the developed theoretical findings.

To achieve stable operation and current sharing in dc microgrids with communication networks of random packet losses, this article proposes a distributed event-triggered control (ETC) strategy based on data sampling mechanism and combined measurement. The proposed ETC consensus protocol achieves mean-square consensus of the distributed renewable power generation units (RGUs) by coupling the sampling interval, control gain, and packet loss probability. Moreover, the independent triggering of individual RGUs reduces communication burden during the control process and lowers the update frequency of converters. The proposed ETC strategy has the advantages of having fewer parameters, utilizing periodic data sampling mechanisms, avoiding the Zeno phenomenon in the control system and continuously monitoring the system state. Finally, detailed experimental tests are presented to demonstrate that the proposed distributed ETC strategy exhibits good capabilities in current sharing and robustness against random packet loss.

In this article, the security control problem of networked interval type-2 (IT-2) active suspension systems is investigated based on the multi-instantaneous fuzzy control mechanism. First, considering that the dynamic behavior of the suspension system is extremely nonlinear, a fuzzy suspension model is established according to IT-2 fuzzy rules to characterize its nonlinearity and uncertainty. Second, a multi-instantaneous fuzzy gain-scheduling control law is developed based on the normalized fuzzy weighted membership degrees (NFWMDs) of the current moment and the past moment, which is homogeneous polynomial parameter dependent. At the same time, by developing a new slack variable technique, more implicit algebraic properties of the NFWMDs can be mined, so as to reduce the conservatism of the design. Then, the exponential stability condition of the suspension system subjected to random activation network attacks is derived under the premise of satisfying the$H_{\infty }$performance index. Eventually, the performance of the proposed controller is evaluated by hardware-in-loop experiments.

This article proposes an asynchronous gain-scheduling secure control framework for nonlinear cyber-physical systems subject to complex and uncertain mode transition behaviors. To address the challenge that ideal probabilistic information is often unavailable in practical industrial environments, a dual-domain polynomial methodology is developed to enhance control performance under realistic conditions. In the structural domain, complex transition probabilities—comprising imprecise and partially unknown components—are reconstructed into a polytopic form, enabling a flexible and accurate abstraction of stochastic system dynamics. In the control design domain, homogeneous polynomial Lyapunov functions and controller structures are utilized to reduce conservatism and improve robustness. The proposed method guarantees exponential mean-square stability and desired performance under cyber attacks. Numerical simulations and hardware-in-the-loop (HIL) experiments on a nonlinear active suspension system confirm the superiority of the approach in terms of feasible design region and performance$\gamma _{\min }$optimization of at least 32.4%.

This article is devoted to studying the homogeneous polynomial parameter-dependent (HPPD)-type control strategy of active vehicle suspension systems (AVSSs) within a cyber-physical architecture that is subjected to malicious attacks. A framework based on cyber-physical systems is proposed for designing the controller parameters of an AVSS, considering the vulnerability of control signals in the transport layer to malicious cyberattacks. To address the hybrid attacks consisting of denial of service and false data injection (FDI), a resilient controller with FDI attack compensation is designed, and an augmented error system model under hybrid attacks is established. Subsequently, to further enhance handling stability and ride comfort, a homogeneous polynomial method is introduced, and a novel HPPD-type resilient controller with FDI attack compensation is devised. The co-design method for the HPPD-type controller and FDI attack observer is derived using a time-varying Lyapunov function to ensure the exponential stability of the HPPD-type augmented error system. Finally, the effectiveness of the proposed method in enhancing stability and improving comfort is verified through software simulations and hardware-in-the-loop experiments, and the superiority of the method in resisting attacks is demonstrated through comparative analysis of some performance indicators.

In this paper, an observer-based gain-scheduling tracking control scheme is designed for cyber-physical active suspension systems (ASSs) with uncertainties and external disturbances. Firstly, a fuzzy suspension model is established based on interval type-2 (IT-2) fuzzy rules to capture the nonlinearity and uncertainty of ASSs. Then, considering that it is difficult to obtain the state information of the suspension system in the complex environment, a co-design method based on the high-order free-weighting gain-scheduling (HFG) control law is proposed. At the same time, a class of Lyapunov functions and slack variable techniques, which are homogeneous polynomial parameter-dependent, are designed to simplify the stability analysis of ASSs. Furthermore, under the premise of satisfying the$H_{\infty }$performance index, the exponential stability of the augmented error system under randomly activated network attacks is realized. Finally, the performance of the proposed control scheme is evaluated by numerical and hardware-in-loop (HIL) tests.

This article presents a cryptography-based event-triggered resilient distributed charging scheduling method for plug-in electric vehicles (PEVs), addressing non-ideal factors such as privacy leakage, DoS attacks, and constraints on communication and computational resources. The proposed approach addresses two key challenges: first, integrating an edge-event-triggered mechanism (EETM) into the scheduling algorithm to reduce the communication and computational overhead caused by the cryptography-based confidential communication protocol (CCP), whose execution significantly increases transmitted data size and requires substantial computational resources; second, ensuring that the EETM-based regulation algorithm meets the following functional requirements in charging scheduling task: 1) CCP-compatibility, 2) sampled-data-based implementation, 3) resilience to DoS attack. Theoretical analysis demonstrates that the proposed method optimizes the charging strategy for each PEV while effectively handling the above non-ideal factors. Simulation results further confirm that under the constraints of minimizing system cost and maintaining an acceptable convergence rate, the execution count of CCP is reduced by 68% and 78% compared to the existing node-event-triggered mechanism and periodic sampling mechanism, respectively, which implies the superior communication and computational-resource efficiency of the proposed EETM framework.

In this article, an adaptive predefined accuracy control issue is addressed for vehicle platoon control system (VPCS) with time delay and deception attacks. Two nonnegative switched functions are employed to handle the predefined accuracy control problem. Some radial basis function neural networks (RBF NNs) are applied to estimate uncertain functions. Different from the existed reports on the VPCS, by combining with the switched functions and the Nussbaum functions, an adaptive distributed controller is designed for the VPCS to overcome the influence of time delay and deception attacks so that the spacing errors gather to a preset vale. At last, some simulation results are used to test the correctness of the proposed scheme with predefined accuracy value 0.2. In order to emphasize that the proposed scheme is independent of parameters, we also get a simulation result with an accuracy of 0.1. And some simulation results are also obtained under the strength of time-delays and deception attacks to highlight the valid of the presented method.

This article is focused on the secure consensus of multi-agent systems (MASs) with Euler-Lagrange (EL) dynamics and multiple DoS attacks. First, a new model of the multiple DoS attacks is built, which is based on discrete sampled-data communication and considers the joint impact of the multiple DoS attacks. Second, under multiple DoS attacks, two new technical results are proposed, which lay a good foundation for consensus analysis. Then, by designing an adaptive distributed control (DC) protocol combining with two new auxiliary systems, secure consensus results are derived for MASs with EL dynamics and multiple DoS attacks. Finally, simulations based on networked two-linked robot manipulators are presented to show the effectiveness of the theoretical results.

In this article, a novel adaptive critic learning (ACL) framework is constructed for a class of nonzero-sum (NZS) differential games problem of unknown continuous-time (CT) nonlinear systems with state constraints. First, generalized fuzzy hyperbolic model (GFHM)-based identifiers are established to reconstruct the unknown system dynamics. Then, under the ACL framework, a critic network with secure finite-time experience replay turning law is developed for each player to acquire the Nash equilibrium point solution in finite time while the finite-time stability is guaranteed via Lyapunov analysis. Meanwhile, the persistence of excitation (PE) condition is no longer needed in this work, by introducing an easy-to-check rank condition. Furthermore, by incorporating the immediate cost function associated with each player and the control barrier function (CBF), the algorithm ensures that the system states evolve in a secure environment. Finally, two numerical examples are presented to demonstrate the validity of the developed scheme.

From the perspective of industrial production reliability, a robust event-triggered (ET) control strategy is presented for uncertain continuous stirred tank reactor (CSTR) system with asymmetric input constraints. To begin with, we propose a nonquadratic performance function to transform the robust control issue by constructing the relevant auxiliary dynamics. For effectively mitigating the pressure of data transmission and controller execution, a dynamic ET scheme (DETS) with an adjustable threshold function is adopted. Subsequently, we formulate the DETS-based Hamilton–Jacobi–Bellman (DET-HJB) equation according to optimality theory. In addition, a DETS-assisted reinforcement learning algorithm with a unique critic neural network can efficiently tackle the derived DET-HJB equation. Meanwhile, the corresponding critic weight is regulated on the basis of gradient descent technique and experience replay approach. By presenting a rigorous analysis under two situations, the uniform ultimate boundedness of auxiliary dynamics and weight approximation error can be ensured. Eventually, the feasibility of the proposed algorithm is demonstrated by experimental results of CSTR system.

In this article, the problem of data-driven control for Markovian jump systems (MJSs) under aperiodic sampled-data (ASD) control is studied. By constructing a loop-based Lyapunov functional (LBLF), the stability criterion of MJSs based on the model is established. Combining this model-based condition with data-based representations, two distinct stability conditions are formulated. ASD controllers are subsequently designed based on these conditions. The proposed approach is validated by modeling an aircraft system as an MJS, with flight test data showing that the controller effectively stabilizes the system, whether the system matrices are known or unknown. Furthermore, a numerical example highlights that the proposed approach achieves a larger upper bound for the sampled-data period.

This study considers a dynamic event-triggered fuzzy${\mathcal {H}}_{\infty }$consensus problem for multiagent systems (MAS) characterized by parameter uncertainties and external disturbances in interval type-2 (IT2) fuzzy form. The proposed control strategy aims to minimize data transmission by triggering control events dynamically. Stability analysis is conducted by Lyapunov stability theory, and more mathematical tools are introduced to relax the sufficient condition and demonstrate the${\mathcal {H}}_{\infty }$consensus. The developed control scheme ensures the consensus among agents, enhancing the overall system performance in the presence of uncertainties and disturbances. Finally, three examples exhibit the validity of the suggested controller.

The security problem plays a critical role in managing the operation of cyber–physical systems (CPSs). This article investigates state estimation, attack reconstruction and attack detection for uncertain CPSs with unknown but bounded (UBB) noise. First, uncertain CPS dynamics are characterized using Takagi–Sugeno fuzzy logic. To address critical modeling challenges arising from complex non-Gaussian stochastic processes, the UBB processes are systematically analyzed. Within this framework, false data injection (FDI) attacks on actuators or sensors are regarded as unknown inputs that can compromise the integrity and authenticity of the system information. Second, a new switching-type zonotopic unknown input observer (SZUIO) is proposed to enhance estimation accuracy while mitigating attack impacts. This observer handles system uncertainties and partial unknown inputs through a switching mechanism that activates multiple operational modes, thereby relaxing state estimation constraints and reducing conservatism. Moreover, the optimal SZUIO for each time step is selected from a set of candidate observers, based on the dynamic information of MF. Third, to enhance proactive defense against attacks, an integrated framework is proposed for state estimation, attack reconstruction and detection in uncertain CPSs. Finally, the feasibility of the proposed method is demonstrated through examples.

This article investigates the$H_{\infty } $optimal output-feedback control problem of heterogeneous multiagent systems. First, a hierarchical control scheme is designed to reduce the algorithm’s complexity and the expected global performance constraints can be ensured by designing compensation input indicator. Second, a relaxation parameter is introduced to derive the optimal solution under output feedback. Additionally, a policy iteration algorithm and vectorization method are presented to determine local and collaborative control gains. This relaxation parameter serves to ease the design conditions for performance indicator. In addition, adaptive dynamic programming (ADP) is introduced and reversible datasets are designed to obtain optimal parameters with unknown drift dynamics. This design achieves model-free control of optimal output feedback for heterogeneous multiagent systems. Finally, the effectiveness of the control schemes is validated using F-16 aircraft and 4-wheel autonomous vehicles as examples.

This article investigates the mean-square stabilization problem of nonlinear semi-Markov jump systems (SMJSs) subject to time-varying transition rates (TRs). To accommodate TRs variations across different operating conditions, a piecewise homogeneous embedded Markov chain (EMC), varying across intervals but time-invariant within each interval, is introduced. Considering partial states unobservability and real-time requirements, a mode-dependent fuzzy dynamic output feedback controller is developed, operating across multiple homogeneous Markov chain levels for real-time performance control. By incorporating richer sojourn-time information and membership function (MF) characteristics, elapsed-time term and the homogeneous polynomially parameter-dependent (HPPD) method are integrated into Lyapunov functions (LFs), enabling relaxed stability conditions. Furthermore, different utilization efficiencies of available semi-Markov kernel (SMK) information are discussed, with extended exploitation of partial information covering existing conservative results. Finally, numerical simulations of a tunnel diode circuit model (TDCM) and hardware-in-the-loop (HIL) tests of a suspension system are presented to demonstrate the superior control performance of the proposed method compared to existing methods.

This article investigates the stabilization problem of fuzzy Markov jump systems (F-MJSs) with incomplete transition probability (TP) information. Existing methods for handling partially unknown TPs often introduce excessive conservatism using scaling techniques that may violate the fundamental stochastic constraints. To address this issue, we propose a novel polynomial-based gain-scheduling control framework that integrates a polytopic probability reconstruction strategy. This strategy rigorously preserves the stochastic completeness of TP matrices (TPMs) while reducing conservatism in controller design. By leveraging homogeneous polynomial theory, we further establish a codesign methodology for both polynomial Lyapunov functions and fuzzy controllers, significantly expanding the feasible solution space. Theoretical analysis demonstrates that the proposed method achieves substantially reduced conservatism compared with conventional aggregated approximation approaches. Numerical simulations reveal the improvement compared with classical aggregated treatment approaches. Hardware-in-the-loop (HIL) experiments on active suspension systems validate the effectiveness and robustness of the designed control strategy, especially γminachieved a reduction optimization of 87.5%.

In this article, we concentrate on the stability and stabilization issues for the discrete-time Takagi-Sugeno (T-S) fuzzy semi-Markov jump systems (FS-MJSs) with incomplete transition probabilities (TPs). Since the statistical properties of mode transitions are frequently hard to get in practice, the system is built on the assumption that the information of TPs is partly accessed. Then, by making use of the incompletely discrete-time semi-Markov kernel, we offer the sufficient requisites for FS-MJSs mean square stability (MSS). We emphasize the impact of TPs on FS-MJSs by utilizing known TPs and introducing them into sufficient conditions for MSS. Numerically testable stability criteria for FS-MJSs in the sense of MSS are provided. The existence criteria are suggested to design the controller to guarantee the MSS of the closed-loop FS-MJSs. At the same time, a homogeneous polynomial technique is developed to reduce conservatism. The numerical examples demonstrate the effectiveness of our method.

Cyberattacks significantly compromise the security of sensor networks, which largely hinder the accuracy and privacy of the information interaction process. However, it is tough to identify the attacks with unknown statistical models by a traditional detection scheme. This article is concerned with the resilient set-membership estimation for 2-D systems over sensor networks subject to cyberattacks and unknown-but-bounded noises. First, using the dynamic watermarking (DW) technique, a novel attack detection method is proposed to guarantee the security of information transmission among sensors. Compared to existing results on attack detection, the developed mechanism is capable of adapting to the ellipsoid-dependent set-membership estimation framework that incorporates the set ideas. Second, a group of scalable resilient set-membership estimators are derived for large-scale sensor networks. Each sensor has access to an ellipsoidal estimation set containing the true state of the system, in which the proposed design procedure is independent of global information about the network topology. Third, a set of parameter optimization algorithms is introduced in a recursive manner, which allows the sensor network to obtain a satisfactory estimation performance utilizing the designed estimation gain and detection mechanism. Lastly, a simulation example is shown to evaluate the availability and superiority of the proposed technique.

In this study, an event-driven fuzzy adaptive control strategy is introduced to address the tracking control problem in a class of stochastic nonstrict-feedback systems under conditions of input delay, unknown control directions and full-state constraints. First, a model for a class of stochastic nonlinear control systems is established based on a ship maneuvering system. Subsequently, the system model is generalized further to obtain more complex nonstrict-feedback systems with unknown control directions. Next, the system is preprocessed to facilitate the design of control strategy. Through the introduction of an intermediate variable, Pade approximation principle is employed and the impact of input delay is eliminated. Subsequently, a nonlinear mapping approach is employed to transform the issue of full-state constraints into an unconstrained problem. This circumvents the complexities caused by the utilization of barrier Lyapunov functions effectively. Furthermore, the principles of fuzzy approximation and adaptive control theory are introduced. Based on the properties of the exponential function, an event-triggered control strategy is designed meticulously to ensure the semiglobal boundedness of all signals in the closed-loop system.

This study focuses on the prescribed performance practical fixed-time control problem for nonlinear uncertain multiagent systems with input saturation and external disturbances. Unlike existing practical fixed-time consensus approaches, we propose an adaptive dynamic surface design scheme to mitigate computational complexity in the backstepping procedure. In addition, fuzzy logic systems are adopted to approximate uncertainties. To reduce the frequency of controller updates, an event-triggering mechanism is introduced. Using the backstepping technique and Lyapunov stability theory, we design a real adaptive distributed fuzzy controller that can guarantee consensus errors remain within prescribed performance in a fixed time. Ultimately, emulate results express the effectiveness of the presented strategy.

The article designs a secure co-estimation approach for nonlinear systems with false data injection (FDI) attack and network bandwidth limitations, which is described by interval type-2 (IT2) fuzzy system. For mitigating communication load and avoiding network data collision, an event-triggered weighted try-once-discard protocol is implemented to adjust the data transmission frequency. Given the unknown system state and FDI attacks, both of the state observer and the attack observer are put forward. Besides, a new attack compensation controller is proposed under co-design of the observer of the state and FDI attack. The asymptotical stability of the augmented system can be realized by the proposed sufficient conditions for the existence of the fuzzy observer and controller gains, while the prescribedH∞performance requirement can be met. Then the secure controller design method is given accordingly. Finally, the validity of the attained results are provided by simulation examples.

In this article, an unscented Kalman filter (UKF)-based multistep heuristic dynamic programming (MsHDP) optimal control algorithm is developed for nonlinear discrete-time (DT) systems with uncertainty and asymmetric input constraints. The Hamilton–Jacobi–Bellman (HJB) equation is solved by the UKF-based MsHDP algorithm, which has the advantages of faster convergence speed and handling unknown disturbances in the system. The convergence of the developed algorithm is proved under certain conditions, and the system stability is guaranteed. To reduce the communication needs, a dynamic event-triggering mechanism is designed. Then, an event-based EC structure is proposed to implement the UKF-based MsHDP algorithm, where the UKF is used to estimate the future state of uncertain systems and the critic neural network (NN) is used to approximate cost function. Finally, simulation results are provided to verify the effectiveness of the developed algorithm.

A novel adaptive constraint control approach is proposed for flexible riser systems characterized by uncertain parameters and external disturbances, aimed at achieving the desired transient performance. By combining Hamilton’s principle with partial differential equations (PDEs), the physical model is transformed into a dynamic model. Considering the boundary position constraint, a boundary controller is built using the tangent barrier Lyapunov function (BLF) to mitigate vibrations. In order to ensure the convergence of the boundary position error at a predetermined rate, the control approach incorporates a performance function to attain the necessary transient performance. An auxiliary term is defined to counteract the impact of coupling terms that remain during the decoupling process of PDEs. Finally, the above scheme is further validated through MATLAB simulations.

The microgrid, capable of providing flexible and controllable means to integrate distributed renewable energy sources (DRESs), has long been seen as a most promising solution to convert DRESs into the electrical power. However, the intermittent power output of DRESs, together with the unexpected load perturbations, challenges the frequency stability of microgrids. In this context, the work proposes a robust distributed load frequency control (DLFC) method for multi-area wind energy-dominated microgrids, in which way all interconnected areas can work cooperatively to confront the unbalanced power occurring in partial areas. Considering the flexibility for large-scale deployment, the wind energy is taken as the DRES, while the thermal power plant is chosen as the base power generation. To mitigate the fluctuation of wind power output caused by uncertain wind speed, a sample-based stochastic model predictive control approach is presented. For the high-level DLFC of multi-area microgrids, robust performance index is incorporated in stability analysis and control synthesis. Moreover, temporary phasor measurement unit (PMU) failures are considered in DLFC design and are modeled by random Bernoulli variables to quantitatively analyze their impacts on frequency dynamics. Validations on a four-area microgrid verify the efficacy of the proposed robust DLFC method under different PMU failure probabilities.

This article addresses the secure finite-time tracking problem via event-triggered command-filtered control for nonlinear time-delay cyber physical systems (CPSs) subject to cyber attacks. Under the attack circumstance, the output and state information of CPSs is unavailable for the feedback design, and the classical coordinate conversion of the iterative process is incompetent in relation to the tracking task. To solve this, a new coordinate conversion is proposed by considering the attack gains and the reference signal simultaneously. By employing the transformed variables, a modified fractional-order command-filtered signal is incorporated to overcome the complexity explosion issue, and the Nussbaum function is used to tackle the varying attack gains. By systematically constructing the Lyapunov–Krasovskii functional, an adaptive event-triggered mechanism is presented in detail, with which the communication resources are greatly saved, and the finite-time tracking of CPSs under cyber attacks is guaranteed. Finally, an example demonstrates the effectiveness.

This paper addresses the problem of event-based distributed set-membership estimation for complex networks with unknown but bounded (UBB) disturbances. To reflect the compromised data transmissions in cyber security, deception attacks are taken into consideration. Meanwhile, a novel estimation model is proposed against UBB disturbances. In order to schedule the signal transmissions between nodes and remote estimators, a novel decentralized dynamic periodic event-triggered mechanism (DPETM) with a time-varying threshold is developed for each node of the complex networks, which reduces the waste of communication resources and the complexity of computation. Thereafter, a series of distributed set-membership estimators are designed, whose parameters are explicitly determined in terms of the resolution of a particular linear matrix inequality (LMI) related to the information of the communication topology. An optimized ellipsoid estimation set is obtained by applying a recursive optimization algorithm. Finally, the simulation results are shown to demonstrate the viability of the proposed method.Note to Practitioners—This paper is motivated by set-membership state estimation problem of complex networks in practical missions, such as military, environment, industry, etc. The set-membership estimation of complex networks provides a reliable confidence region for each system node. Event-triggered control is an effective method for the design of set-membership estimator. But the common results require the systems to monitor the measurements point-to-point, which leads to the huge consumption of calculation and communication resources. For this reason, this paper originally extends the DPETM to the discrete-time version from the field of continuous-time systems. Meanwhile, this paper considers the deception attacks in communication channels, and the generic framework established earlier can tackle simultaneously sector-bounded nonlinearity, UBB disturbances, and deception attacks. The main difficulty of this paper lies in the analysis for the sawtooth constraint of periodic samplings. For this difficulty, we introduce a piecewise auxiliary function, which is similar with the loop-function in the field of continuous-time systems. Together with recursive optimization algorithm, the detailed analysis method is proposed for the reliable confidence regions of each set-membership estimator.

This paper studies group synchronization tracking problem for a class of high-order multi-agent systems (MASs) with nonidentical and unknown direction faults (NUDFs) under multiple cyber attacks (i.e., denial-of-service (DoS) attacks and false data injection attacks (FDIAs)). Be motivated by this, a fully distributed hierarchical (cyber layer and physical layer) Zeno-free event-triggered (ET) intrusion-and fault-tolerant controller is presented based on Nussbaum-type gain technique, where a positive inter-event time exists in the state-dependent asynchronous ET mechanism (ETM). The constructed virtual cyber layer realizes the interaction among different agents so as to avoid the interaction in physical processes and thus reduce the error propagation. This two layer controller greatly increase the flexibility of the controller design compared with single-layer control strategies. In addition, a novel Nussbaum function stability lemma (Lemma lem4lem4) is developed for the first time. Based on this lemma, the fully distributed adaptive controller can adjust the direction of the input to match the fault direction with the help of Nussbaum function. Finally, a robotic manipulator example demonstrates the effectiveness and merit of the proposed control scheme.Note to Practitioners—In industrial processes, NUDFs and cyber attacks often occur in many different systems, which usually lead to performance degradation or even serious accidents. Typically, NUDFs affect the performance of chemical and industrial processes, circuits, and sensors. Meanwhile, in driverless vehicle platoon, attackers change the control signal through the wireless network, and then issue emergency braking commands, etc. Therefore, this paper designs a fully distributed hierarchical ET intrusion-and fault-tolerant scheme for high-order MASs that are usually used to model ship dynamics, robotic manipulators, and quarter-car active suspension. The control scheme gives solutions to the problem of NUDFs, multiple cyber attacks, and network bandwidth limitations at different layers, and effectively integrates the physical and cyber layers to achieve group synchronization. Meanwhile, a new event-triggered mechanism under the framework of group synchronization is developed to save communication resources. Robotic manipulator simulation studies verify the validity of the proposed scheme.

This paper investigates the optimal decentralized control issue for a class of networked interconnected systems (NISs) under communication and control constraints. First of all, the decentralized optimal control problem for NISs is transformed into the optimal control issue for nominal systems. And then the event-triggered Hamilton-Jacobi-Isaac (HJI) equations are derived with optimal control theory based on the constructed cost function and adopted adaptive event-triggered mechanism (AETM). Furthermore, a Reinforcement Learning (RL) based event-triggered optimal control algorithm with actor-critic networks is proposed to obtain numerical solutions of the HJI equations and the Uniformly Ultimately Bounded (UUB) stability of NISs is proved to be guaranteed with Lyapunov stability theorem. Eventually, a simulation experiment is conducted to verify the effectiveness of proposed RL-based optimal decentralized algorithm with AETM.Note to Practitioners—Actually, the limitation of communication resource is one of the key factors leading to performance degradation of NISs. It is crucial to cope with this issue in the control of NISs. Employing proper communication protocol is an effective way to diminish the adverse effects of undesirable phenomena, such as data loss and out-of-order. In addition, given the scale is gradually expanded and the structure is gradually complex for NISs, the operation cost is a problem that cannot be ignored in the control process of NISs. Thus, it is significant and challenging to minimize the operation cost on the basis of ensuring system stability. In view of the communication constraints and optimization problem, the HJI equations based on AETM are derived to model the decentralized optimal control problem for NISs. Moreover, a RL-based iterative algorithm is proposed to derive the numerical solutions to HJI equations and further effectively stabilize the targeted control constrained NISs in the sense of UUB.

This paper investigates the prescribed-time control for nonlinear systems with sensor faults and unknown control directions. Firstly, the prescribed-time control is realized based on scale function and descending power coordinate transformation. Then, effective nonlinear terms are designed in the controllers to compensate for state pollution caused by sensor faults. Furthermore, the Nussbaum gain function is introduced and it can be proven that the derivative of its variable is bounded, which is of significance to analyze the invariant set. The proposed control scheme guarantees that system states converge to zero within the specified time in advance and all signals of the closed-loop system are bounded. Finally, a numerical simulation and a practical simulation based on the Nomoto ship model intuitively show the feasibility of the scheme.Note to Practitioners—This study is motivated by achieving the prescribed-time control for nonlinear systems with sensor faults and unknown control directions. With the improvement of automation, the prescribed-time control that the convergence time can be arbitrarily specified in advance has been applied to many time-critical fields, such as missile guidance, emergency braking, and so on. It is noted that hypersonic weapons, uncalibrated visual servo control, and other practical models have the characteristic of unknown control direction, and most of the existing prescribed-time control schemes are not suitable for these practical systems. In addition, since the hovercraft power systems and aircraft systems are in a harsh environment for a long time, it can easily lead to sensor faults resulting in major accidents. In this study, based on the descending power coordinate transformation, the prescribed-time controllers with unique nonlinear terms are designed to deal with the above challenges.

The inductive power transfer (IPT) technology, as one of the main wireless power transfer methods, has been prevalent in both industrial and commercial applications. However, the circuit parameter perturbations and communication delays will deteriorate the transfer performance, including output fluctuation and efficiency drop. To deal with the above mentioned issues and maximize the transfer efficiency, a boost converter is first cascaded after series-series IPT topology, then a novel control strategy is proposed to fulfill the constant power output with maximum efficiency tracking (MET). In the proposed strategy, the MET condition can be derived regardless of coupling coefficient and load resistance through elaborate design. Next, the stability of nonlinear IPT systems subjected to communication delays is modeled and described based on the concept of Takagi-Sugeno (T-S) fuzzy models. Furthermore, an event-triggered$\bm{H_{\infty}}$fuzzy controller is designed to improve the robustness (against perturbations of coupling coefficient, loads and communication delay), and reduce the computation and transmission burden. Finally, the effectiveness of the suggested strategy is shown using the simulation results.Note to Practitioners—Maintaining a constant output power and high transmission efficiency remains a challenging task in IPT technology due to parameter variations, communication delays and model nonlinearity, especially in the charging scenarios of drones and electric vehicles. Therefore, an event-triggered$\bm{H_\infty}$fuzzy controller is proposed to cope with aforementioned situations such that the constant output power with high efficiency is guaranteed. Even in the presence of communication delays, the proposed strategy can still maintain stable output with high efficiency. In addition, the proposed method is equipped with the event-triggered mechanism to reduce the frequency of controller updates and transmission burden while maintaining the transient performance. The outcome of this paper provides a simple but useful MET condition and controller design procedure that can be employed to maintain the reliable and stable operation of IPT systems and optimize their transfer efficiency.

In this article, the exponential stability (ES) and fuzzy control problem is addressed for DC microgrid (DC-MG) system based on T-S fuzzy model under denial-of-service (DoS) attacks. Considering that the time scale of networked T-S fuzzy model and parallel distributed compensation (PDC) fuzzy control rules is asynchronous, the T-S fuzzy model of the DC-MG system is established. More importantly, in order to reflect the effect of DoS attacks, a time-constrained DoS attack (TCDA) model, which only characterizes the duration of DoS attacks, is established compared with the classic DoS attack model. Then, a switched DC-MG fuzzy system model based on state-feedback control law and TCDA model is established. Furthermore, the time-varying Lyapunov function related to attack parameters is used to ensure the ES of the system. Besides, a fuzzy-dependent switching control strategy is designed in terms of linear matrix inequalities (LMIs). Finally, through a simulation example, the effectiveness of the proposed control strategy is verifiedNote to Practitioners—As a typical example of cyber-physical systems, nonlinear DC-MG system is vulnerable to malicious cyber attacks (such as DoS attack). The existing DoS attack models are usually characterized by the duration and frequency of attacks. In this paper, we adopt a new approach to describe the DoS attack model using only attack duration characteristics. This makes the DoS attack model more general. We then propose a switching fuzzy control algorithm subject to intermittent DoS attacks and derive sufficient conditions for tolerable duration of attack. This can allow practitioners to know under what conditions the ES of the attacked system can still be guaranteed. The effectiveness of theoretical analysis results is verified by simulation experiments. In the future research, we will address the design of fuzzy control algorithms for DC-MG under various cyber attacks.

This paper investigates the${H}_{\infty}$tracking control problem for the series-parallel (SP)-inductive power transfer (IPT) system with coil misalignment. To describe the nonlinear characteristic caused by large-scale coil misalignment, a Takagi-Sugeno (T-S) fuzzy modeling approach is successfully applied to the SP-IPT system. By introducing an integrator related to the error between the actual and the reference system output signals, an augmented T-S fuzzy-based SP-IPT system model is established. Then an${H}_{\infty}$parallel distributed compensation (PDC) fuzzy control strategy with a valid event-triggering scheme (ETS) is put forward to guarantee desired tracking control performance and decrease unnecessary packet transmission at the same time. To ensure the asymptotic stability of the augmented T-S fuzzy-based SP-IPT system and the disturbance suppression index, sufficient conditions are employed by utilizing an extended Lyapunov functional method. Finally, a simulation example with regard to the SP-IPT system is developed, which demonstrates that the event-based${H}_{\infty}$PDC fuzzy control strategy proposed in this paper can maintain the constant output voltage of the SP-IPT system while saving communication resources.Note to Practitioners—For IPTs, the coil misalignment phenomenon unavoidably affects their desired performance, such as constant voltage and current output, constant power output, maximum efficiency tracking, and so on. Therefore, the corresponding tracking controllers have brought wide attention in the power transmission research. The proposed control strategies have been utilized to suppress the negative influence caused by coil misalignment, whereas it is difficult for these strategies to ensure the robustness and the stabilization under large-scale coil misalignment. To deal with this problem, this paper is devoted to design a T-S fuzzy-based${H}_{\infty}$control strategy with an ETS to guarantee the stabilization of practical inductive power transfer systems. It is worth mentioning that the proposed robust control strategy is proposed based on the IPT system with T-S fuzzy rules and the ETS, which can simultaneously guarantee desired tracking control performance and decrease unnecessary packet transmission in real applications. In this paper, only constant voltage tracking control are considered for the IPT system with coil misalignment, but some other tracking performance still need to be researched in practice. Therefore, we will take the tracking performance indexes of constant current and constant power into account in the future research.

Distributed control of DC microgrid is becoming more and more important in modern power system. An important control goal is to ensure voltage stability and current sharing of DC bus. In the presence of constant power loads and uncertainties, a novel distributed quadratic optimum control technique based on reinforcement learning (RL) is developed in order to ensure correct current sharing and adequate performance. Firstly, the system model with power coupling is established and transformed into a linear heterogeneous multi-agent system (MAS) with unknown disturbances. Subsequently, a neural network (NN)-based adaptive model-free observer is developed. Since not all followers have direct access to the leader’s information, a distributed cooperation performance index with discount component is created by fusing the dynamics of the observer and the follower. The$Q$-learning technique is applied to obtain the optimal control strategy to achieve voltage stabilization and current sharing without using system dynamics. Finally, simulation and experimental results show the effectiveness of this strategy.

This study investigates a fuzzy consensus problem for nonlinear multi-agent systems (MASs) with parameter uncertainties via dynamic event-triggered mechanism. The interval type-2 (IT2) fuzzy systems are used to model MASs, and a dynamic event-triggered fuzzy controller is presented. A Lyapunov-Krasovskii functional is constructed in which the sampling property is included, based on which the sufficient condition is determined for dynamic event-triggered fuzzy controller, while all agents are guaranteed to be consensus exponentially. Finally, the MASs of tunnel diode circuit and one-link manipulator are used to verify the efficiency of the presented control method, respectively.

In this paper, the issue of finite-time fault-tolerant tracking control via event-triggered strategy is investigated for a general class of non-affine systems with a semi-bounded structure. The differentiable condition imposed on the non-affine terms is removed. A new model transformation method is used to transform the non-affine system into a pseudo-affine one, which generates an uncertain model with the undesired overflowed variables. We utilize the neural networks to approximate the uncertain functions and separate the overflowed variables to guarantee the solvability of virtual controllers in the iterative design. In addition, the tracking error is limited to a specified range within a finite time by the introduced prescribed performance. By considering the actuator fault and the limited communication resources, an event-triggered fault-tolerant control scheme is proposed, which not only ensures finite-time tracking, but also avoids the Zeno behavior and reduces the waste of communication resources. Finally, the proposed method is used for the microgrid systems.

This study investigates the synchronization control of discrete-time complex dynamical networks (CDNs) under discontinuous network communication. A dual-event-driven control scheme is proposed based on periodic detection, which combines a centralized event-driven intermittent mechanism and a decentralized event-driven mechanism. The centralized event-driven intermittent mechanism is utilized to determine the working/rest time of controller, which realizes fine control of the working/rest intervals by responding quickly to system states. Furthermore, the decentralized event-driven mechanism is employed to decide whether the control signal is updated. Compared with existing results, this scheme eliminates the constraints and assumptions related to the interval length, avoids the successive measurements of signal, and reduces the frequency of controller updates. In addition, the piecewise Lyapunov function is constructed for flexible adjustment of the sampling period. Sufficient criteria for realizing discrete-time CDNs synchronization are derived under the proposed control scheme. Finally, several simulation examples are given to verify the validity of the obtained results.

This paper is concerned with noisy sampled-data networked control systems with stochastic network-induced delays and noisy sampling intervals using a stochastic discrete integral quadratic constraint (DIQC) approach. Initially, the noisy sampled-data networked control system is discretized into a stochastic discrete-time system. This system is then transformed into a feedback interconnected system with zero initial conditions. Next, a stochastic DIQC method is developed to obtain a novel stability condition for the noisy sampled-data networked control system. Based on this criterion, a two-stage algorithm is presented to design suitable controllers to ensure the closed-loop system under study is uniformly exponentially stable. Finally, a numerical examples and a fourth-order interleaved flyback modular integrated converter circuit are given to validate the efficiency of the proposed results.

This paper investigates the problem of stability analysis for aperiodic sampled-data load frequency control system with multiple time-varying delays. A discrete-time model of the load frequency control system including both generation units and energy storage systems is constructed firstly. Then, the form of feedback interconnection composing of nominal linear system and uncertainty is bulit, where uncertain operators are found to describe the aperiodic sampled-data interval and time-varying delays. Next, a uniformly exponential stability criterion is developed utilizing integral quadratic constraint analysis. Based on the stability criterion, algorithms are presented to obtain more accurate delay margins and maximum allowable sampled-data intervals. Finally, case studies are conducted to demonstrate the validity and benefits of proposed stability criterion.

This paper proposes a novel dynamic event-triggered mechanism (DETM) of a switched linear DC microgrid with intermittent denial-of-service (DoS) attacks. In a switched linear system based on DETM, the subsystem mode is immediately updated along with the occurrence of switching signals, while the controller mode is updated after a successful event-triggering. This means both communication interruptions and periodic sampling may cause asynchronous switching situations, which together pose a challenge for stability analysis. To this end, a multiple Lyapunov function that can simultaneously describe subsystem mode and controller mode is adopted, and a new DETM based on acknowledgement character technique (ACK) is studied to ensure input-to-state stability (ISS) of the system. Meanwhile, the maximum allowed DoS duration is first studied to further analyze the relationship between DoS parameters, event-triggered parameters, and system stability. By utilizing ACK, the system can detect the end of the DoS attack and remain ISS under dynamic event-triggered control. Finally, simulation verification is conducted in a switched DC microgrid.

This paper investigates the T-S fuzzy-based bipartite quasi-synchronization of fractional-order heterogeneous coupled reaction-diffusion neural networks. In the considered neural networks, interactions between adjacent neurons are time-varying, cooperative, and competitive, and heterogeneity and T-S fuzzy system rule are simultaneously introduced to characterize the parameter uncertainty arising from complexity and ambiguity in the real world. A new time-varying graph-theoretic Lyapunov function is given for time-varying coupled reaction-diffusion neural networks. Meanwhile, a more general fractional-order derivative law is provided to estimate the derivative of this function, which includes the existing fractional-order derivative laws. Based on a fuzzy-based aperiodically intermittent control, some sufficient conditions are offered for the bipartite quasi-synchronization under a time-varying graph-theoretic Lyapunov function, and the allowable error bound is given. Finally, we carry out some simulations numerically to show the validity of the theory.

This article addresses adaptive optimized tracking control problem for strict-feedback cyclic switched nonlinear output constrained systems with average cyclic dwell time (ACDT). Different from most of the existing results on optimized control of switched nonlinear systems, a new mode-dependent reinforcement learning (RL) algorithm of identifier-critic-actor architecture is designed. Technically, with the help of neural networks (NNs) switched state observer, the virtual and actual optimal controllers are developed by solving the Hamilton-Jacobi-Bellman (HJB) equation. Meanwhile, to reduce the impact of systems switching on the overall optimization control, the information of the switching signal is considered into the optimal performance index functions. In an attempt to settle the output constraints, a nonlinear output-dependent time-varying function is used to ensure that the system output never transgresses the prescribed regions. More importantly, by combining the improved ACDT method and Lyapunov stability theorem, a novel adaptive optimized control scheme is put forward which ensures that the boundedness of all signals in the closed-loop system. Finally, the effectiveness of the proposed optimized control algorithm is verified by numerical as well as practical simulations.

In this paper, the adaptive intelligent control problem for a class of nonlinear switched stochastic cyber-physical systems (CPSs) with output constraint under deception attacks is studied. The output-dependent function is introduced to convert the system into an unconstrained system. In order to eliminate the effects caused by the attacks, the attack gains are introduced into the coordinate transformations and then the Nussbaum function technology is used to deal with the unknown attack gains. Based on the new coordinate transformations, the corresponding controllers are designed for each subsystem using the compromised states. Furthermore, a switching event-triggered mechanism (ETM) is proposed, which can not only resolve asynchronous switching problem without any strict restrictions, but also effectively save communication resources. Meanwhile, a segment constant variable is introduced into the ETM, which is helpful to find a strict positive lower bound for two consecutive triggering intervals to obtain the absence of Zeno behavior. It is shown from the Lyapunov stability theory that all signals in the closed-loop system are bounded in probability under arbitrary switching. Finally, the simulation results validate the effectiveness of the proposed method.

In this paper, the distributed secondary voltage and frequency restoration problem is addressed in AC microgrid systems subjected to hybrid false data injection (FDI) and denial-of-service (DoS) attacks. Firstly, a new distributed resilient iterative estimator based on the k-step estimation method is proposed that can accurately estimate the FDI attack signals as well as the voltage and frequency of each distributed generation (DG) even under the impact of DoS attacks. Then, based on the mean value of the attack estimation signal, a distributed resilient secondary controller is designed to compensate for the considered hybrid attacks. Compared with existing researches on resilient control of AC microgrids under hybrid attacks, the voltage and frequency regulation errors of the microgrid system converge to zero for the first time. Finally, the precise convergence of voltage and frequency in the AC microgrid system under the proposed method is verified through a real-time controller-hardware-in-the-loop experiment in OPAL-RT.

This article addresses the problem of finite-time asynchronous switching control for fuzzy Markov jump systems (FMJSs) using polynomial membership functions. Firstly, a Lyapunov-Krasovskii functional (LKF) is designed, incorporating both system modes and polynomial membership functions. This LKF contains more information about the membership functions, closely aligning with the characteristics of FMJSs, and effectively reducing conservatism. Based on the polynomial matrices switching rule, a practical asynchronous switching controller is introduced. The objective is to ensure finite-time boundedness of the closed-loop FMJSs while satisfying a$H_{\infty } $performance index. Furthermore, the average dwell time method is applied to handle the switching signal, eliminating the predefined assumptions that switching numbers are finite or that system states are constrained to a specific region. Ultimately, the validity and practicability of the obtained results are verified through three examples.

This article investigates the issue of distributed dual-terminal adaptive event-triggered admissible consensus tracking for linear leader-following descriptor multi-agent systems (DMASs) against asynchronous denial-of-service (DoS) attacks. Due to the various off/on moments and durations of consecutive asynchronous DoS attacks on different edges, the communication topologies of DMASs are considered to be randomly switched according to different types of DoS attacks, and the switched topologies are governed by Markov chains. To mitigate dispensable information transmission, a novel dual-terminal adaptive event-triggered protocol is put forward, which excludes the Zeno behavior in addition to flexibly adjusting the inter-event interval. Then, a local estimator based on state reconstruction is designed in a triggered way to exactly estimate agents’ states between two successive triggered moments. Additionally, by constructing a modified mode-dependent Lyapunov-Krasovskii functional and employing singular value decomposition technique, the frequencies and durations of DoS attacks are analyzed and the admissible consensus tracking conditions are acquired for DMASs when frequencies and durations of DoS attacks satisfy bounded conditions. Lastly, multiple transistor electrical circuit systems are employed to demonstrate the validity of the proposed strategy.

This article investigates the practical fixed-time synchronization of uncertain coupled neural networks via dual-channel event-triggered control. Contrary to some previous studies, the bipartite synchronization of signed graphs representing cooperative and antagonistic interactions is studied. The communication channel is introduced into deception attacks, which are described by Bernoulli's stochastic variables. Based on the concept of two channels, event-triggered mechanisms are designed for sensor-to-controller and controller-to-actuator channels to reduce communication consumption and controller update consumption as much as possible. Lyapunov and comparison theories are used to derive synchronization criteria and explicit expression of settling time. An example of Chua's circuit system is presented to demonstrate the feasibility of the obtained theoretical results.

In this note, a novel prescribed fixed-time adaptive tracking control scheme is developed to cope with the fixed-time tracking control issue for a category of constrained MIMO nonlinear cyber-physical systems (CPSs) with exogenous perturbations, which suffer from deception attacks started in controller-actuator (C-A) channel. Distinguished from the conservative dynamic surface control (DSC) schemes with a linear filter, a novel nonlinear filter is designed in our strategy, which can tackle the intrinsic issue of explosion of computational complexity and promote the system performance. Besides, a new barrier Lyapunov function (BLF) is designed to ulteriorly enhance the tracking performance on the basis of the prescribed performance function (PPF) approach. Prominently, the proposed control strategy could accommodate the exogenous interferences and deception attacks simultaneously. Furthermore, we have substantiated that the developed approach can not only make certain that all the tracking errors of the resulting closed-loop system, including output tracking errors and virtual tracking errors, enter a prespecified small region near equilibrium point with fixed-time convergence rate, but also guarantee them obey the corresponding constraints throughout the entire control operation, where the regulation time and the tracking accuracy level keep prior known and could be prespecified arbitrarily. Finally, the validity and effectiveness of the proposed control scheme are illustrated through a representative application instance.

This article studies an event-based two-step transmission mechanism (TSTM) in the control design for networked T-S fuzzy systems. The transmission task is achieved in two steps. Consecutive triggering packets are relabeled in the first step by applying a traditional event-triggered mechanism (ETM). Then a probabilistic approach is employed to determine which packet is a real release packet (RRP) in the second step. This event-based TSTM is particularly suitable for scenarios in which traditional ETMs are unable to determine which packets are redundant. By discarding most of the unnecessary data packets, especially when the system is tending toward stability, the burden on the network bandwidth is reduced. To establish a control strategy for T-S fuzzy-based nonlinear systems with random uncertainties, a new timing analysis technique is proposed. Additionally, the necessary conditions for a nonlinear system's mean-square asymptotic stability (MSAS) are derived. Finally, two practical applications demonstrate the effectiveness of the suggested transmission mechanism in networked T-S fuzzy systems.

This article investigates the event-triggered leaderless consensus control problem for fractional-order multiagent systems (FOMASs), where both the agent-to-agent communication channel and the controller-to-actuator communication channel are based on the events. A filter is introduced to transform the original high-order system into a first-order one, greatly simplifying the complexity of controller design compared to the traditional backstepping. Further, the convergence of filtered output signals is proved to be consistent with that of the outputs of agents themselves. Superior to the traditional event-triggered scheme, two dynamic variables are designed for the triggering conditions of the communication among agents and the controller update, respectively. Via elaborately constructing the dynamic variables, zero-error leaderless consensus can be achieved instead of only ultimately uniformly bounded result. It is proved that the proposed control strategy can guarantee better control performance of leaderless consensus under limited communication resources, and Zeno behavior is excluded. Finally, two examples are provided to verify the effectiveness of our proposed control approach.

To enhance system robustness in the face of uncertainty and achieve adaptive optimization of control strategies, a novel algorithm based on the unscented Kalman filter (UKF) is developed. This algorithm addresses the finite-horizon optimal tracking control problem (FHOTCP) for nonlinear discrete-time (DT) systems with uncertainty and asymmetric input constraints. An augmented system is constructed with asymmetric control constraints being considered. The augmented problem is addressed with a DT Hamilton-Jacobi-Bellman equation (DTHJBE). By analyzing convergence with regard to the cost function and control law, the UKF-based iterative adaptive dynamic programming (ADP) algorithm is proposed. This algorithm approximates the solution of the DTHJBE, ensuring that the cost function converges to its optimal value within a bounded range. To execute the UKF-based iterative ADP algorithm, the actor-estimator-critic framework is built, in which the estimator refers to system state estimation through the application of UKF. Ultimately, simulation examples are presented to show the performance of the proposed method.

In this article, the novel adaptive neural networks (NNs) tracking control scheme is presented for nonlinear partial differential equation (PDE)-ordinary differential equation (ODE) coupled systems subject to deception attacks. Because of the special infinite-dimensional characteristics of PDE subsystem and the strong coupling of PDE-ODE systems, it is more difficult to achieve the tracking control for coupled systems than single ODE system under the circumstance of deception attacks, which result in the states and outputs of both PDE and ODE subsystems unavailable by injecting false information into sensors and actuators. For efficient design of the controllers to realize the tracking performance, a new coordinate transformation is developed under the backstepping method, and the PDE subsystem is transformed into a new form. In addition, the effect of the unknown control gains and the uncertain nonlinearities caused by attacks are alleviated by introducing the Nussbaum technology and NNs. The proposed tracking control scheme can guarantee that all signals in the coupled systems are bounded and the good tracking performance can be achieved, despite both sensors and actuators of the studied systems suffering from attacks. Finally, a simulation example is given to verify the effectiveness of the proposed control method.

This article focuses on the issue of novel dynamic event-triggered consensus control of multiagent systems (MASs) with denial-of-service (DoS) attacks. Different from the conventional Markovian switching topologies, the generally uncertain semi-Markovian (GUSM) switching topologies with partially unknown elements and time-dependent uncertainties are constructed for the leader-following MASs by considering the equipment performance and external uncertain environment influence. To save communication resources, the novel dynamic memory event-triggered strategy (DMETS) is presented to decrease the frequency of communication between agents. Some secure consensus control criteria are established for the MASs with GUSM switching topologies and DoS attacks due to the potential system communication disruption caused by attackers. Finally, two physical system examples are designed to prove the effectiveness of the presented method.

This article is concerned with the security problems for networked Takagi–Sugeno (T–S) fuzzy systems with asynchronous premise constraints. The primary objective of this article is twofold. First, a novel important-data-based (IDB) denial-of-service (DoS) attack mechanism is proposed from the perspective of the adversary for the first time to reinforce the destructive effect of the DoS attacks. Different from most existing DoS attack models, the proposed attack mechanism can utilize the information of packets, evaluate the importance degree of packets, and only attack the most “important” ones. As such, a larger system performance degradation can be expected. Second, corresponding to the proposed IDB DoS mechanism, a resilient$H_{\infty }$fuzzy filter is designed from the defender’s point of view to alleviate the negative effect of the attack. Furthermore, since the defender does not know the attack parameter, an algorithm is designed to estimate it. In a word, a unified attack-defense framework is developed in this article for networked T–S fuzzy systems with asynchronous premise constraints. With the help of the Lyapunov functional method, sufficient conditions are successfully established to compute the desired filtering gains and ensure the$H_{\infty }$performance of the filtering error system. Finally, two examples are exploited to demonstrate the destructiveness of the proposed IDB DoS attack and the usefulness of the developed resilient$H_{\infty }$filter.

This article investigates internal interaction-based dynamic learning control (LC) for uncertain discrete-time strict-feedback systems. On the basis of predict technology, the original system is converted into a common n -step-ahead input-output predict model. The predict model causes every estimated neural weight to converge to n different constants using the existing control framework. To solve such a problem, the predict model is further decomposed into n one-step-ahead subsystems, which can be viewed as n independent agents. Subsequently, the distributed cooperative weight adaptive laws are designed by introducing an undirected and connected interconnection topology among subsystems. By constructing the variable relationship between the subsystems and the n -step-ahead predict model, a new internal weight interaction-based neural dynamic LC framework is proposed for the whole closed-loop system, in which estimated weights at different times share their weight knowledge. The proposed framework ensures the ultimately uniform boundedness of the closed-loop system and achieves the excellent control performance. By combining the consensus theory and a cooperative persistent excitation condition, every estimated weight along the neural input orbit is verified to exponentially converge to a close vicinity of a unique ideal constant, rather than n different constants. Consequently, the developed LC framework facilitates constant weights storage, saves the knowledge storage space, and improves the robustness of knowledge utilization. These characteristics are verified by simulation results.

This article presents an event-triggered neural-network (NN) tracking control scheme, capable of ensuring transient performance for switched nonlinear systems. A mode-dependent event-triggered communication mechanism (MDETCM) is designed, and this significantly saves communication resources without limiting the number of switches between two consecutive triggering instants. Meanwhile, to solve the impact of asynchronous switching on system performance, the information of the switching signal is considered into the event-triggered mechanism (ETM). Also, by introducing a normalized function transformation and a tan-type barrier function, the transient performance is regarded as a tracking error constraint without considering the initial conditions of system output and reference signal required in traditional prescribed performance bound (PPB) control. At the same time, the improved admissible edge-dependent average dwell time (AED-ADT) method is cleverly connected with adaptive backstepping control, and a state-feedback tracking algorithm is proposed, under which all closed-loop signals are bounded and the transient performance of the controlled plant is ensured. Finally, the superiority of the proposed scheme is demonstrated through numerical studies, and the control scheme is available for a single-link robot.

-gain for positive impulsive Takagi-Sugeno (T-S) fuzzy systems are further studied in this article. Different from the Lyapunov function in the literature, where the Lyapunov matrices are time-invariant or only linearly dependent on the impulse interval, in this article, a novel polynomial impulse-dependent (ID) copositive Lyapunov function (CLF) is constructed by using the polynomial impulse time function. In addition, the binomial coefficients are applied to derive new finite linear programming conditions. Less conservative results are obtained since the polynomial ID CLF contains more impulse interval information. Three examples demonstrate the influence of the polynomial degree on the results and the effectiveness of the developed new results.

In this technical correspondence, the resilient fuzzy stabilization is enhanced in the direction of elevating the feasible stabilization region as large as possible while the same alert threshold is chosen as the recent one. To do this, the switching-type fuzzy state-feedback controller is designed with a set of switch modes so that more groups of gain matrices can be introduced to enhance the degree of freedom. What is far more important is that a novel augmented time-variant matrix approach is proposed in order to collect the proprietary features of normalized fuzzy weighting functions with regard to each switch mode. Then, all the obtained augmented time-variant matrices are split into a set of positive/negative matrices, which can be elaborately assigned into different monomials of our designing conditions under the framework of homogeneous polynomials. Therefore, less conservative results of resilient fuzzy stabilization are obtained even if some higher alert thresholds are chosen for probably ensuring the establishment of the involved precondition. Finally, the superiority of our approach is validated by giving some detailed comparisons on the benchmark example.

This article focuses on an adaptive dynamic surface tracking control issue of nonlinear multiagent systems (MASs) with unmodeled dynamics and input quantization under predefined accuracy. Radial basis function neural networks (RBFNNs) are employed to estimate unknown nonlinear items. A dynamic signal is established to handle the trouble introduced by the unmodeled dynamics. Moreover, the predefined precision control is realized with the aid of two key functions. Unlike the existing works on nonlinear MASs with unmodeled dynamics, to avoid the issue of "explosion of complexity," the dynamic surface control (DSC) method is applied with the nonlinear filter. By using the designed controller, the consensus errors can gather to a precision assigned a priori. Finally, the simulation results are given to demonstrate the effectiveness of the proposed strategy.

This study mainly investigates the adaptive leader-following consensus tracking control problem for a class of nonlinear multiagent systems (MASs) subjected to unknown control directions, external disturbances, and sensor deception attacks. To start with, an equivalent MAS with known control directions is obtained by introducing a linear state transformation. For the purpose of estimating the unavailable system states caused by malicious attacks, a quantization-based fuzzy state observer is designed, and the fuzzy-logic system (FLS) is utilized to approximate nonlinear functions. Moreover, a dynamic uniform quantizer with scaling function is established to reduce information transmission. With the help of coordinate transformation and available compromised states, a novel compensation mechanism is designed to offset the influence of filter errors while avoiding the problem of "explosion of complexity" in the backstepping design process. In addition, the Nussbaum-type function is considered to eliminate the design obstacle of unknown control gains resulting from the attacks. Under the constructed consensus protocol, it is proved theoretically that the consensus tracking error converges to an adjustable small neighborhood of the origin, and all signals in the closed-loop system are bounded. Finally, the feasibility of the provided secure control scheme is verified through two simulation examples.

Due to cyber-physical fusion and nonsmooth characteristics of energy management, this article proposes a security event-trigger-based distributed approach to address these issues with developed smoothing technique. To tackle with nonconvex and nondifferentiable issue, a randomized gradient-free-based successive convex approximation is developed to smooth economic objective function. Due to resilience ability against security issue, a security event-triggered mechanism-based distributed energy management is proposed to optimize social welfare, which coordinately controls both power generators and load demand. The security event-triggered mechanism is designed to reduce power system security risks, and relieve communication burden caused by smoothing calculation, the convergence of proposed distributed algorithm is also properly proved. According to those obtained results on both IEEE 9-bus and IEEE 39-bus systems, it reveals that the proposed approach can achieve good convergence performance and have less security risks than other alternatives, which also proves that the proposed approach can be a viable and promising way for tackling with energy management issue of cyber-physical isolated power system.

For the flexible riser systems modeled with partial differential equations (PDEs), this article explores the boundary control problem in depth for the first time using a dynamic event-triggered mechanism (DETM). Given the intrinsic time-space coupling characteristic inherent in PDE computations, implementing a state-dependent DETM for PDE-based flexible risers presents a significant challenge. To overcome this difficulty, a novel dynamic event-triggered control method is introduced for flexible riser systems, focusing on optimizing available control inputs. In order to save computational costs from the controller to the actuator, a dynamic event-triggered adaptive boundary controller is designed to effectively reduce boundary position vibrations. Additionally, considering external disturbances, an adaptive bounded compensation term is incorporated to counteract the influence of external disturbances on the system. Addressing boundary position constraints, a new integral barrier Lyapunov function (iBLF) tailored specifically for flexible riser systems is introduced, thereby alleviating conservatism in the controller design of flexible risers modeled by PDEs. At last, the validity of the proposed method is demonstrated through a simulation example.

In this paper, the distributed fuzzy tracking control problem is investigated for high-order fuzzy nonlinear multiagent systems (MASs) under denial-of-service attacks. The proposed method is distinct from existing approaches in that it can accommodate scenarios where the model parameters of the reference systems are unknown, and the MAS is high order and nonlinear. Specifically, a data-driven algorithm is first introduced to learn the unknown reference system matrix. Based on the learned matrix, a distributed resilient observer and an improved observer are, respectively, designed to guarantee that both observers can observe the reference system state and that the high-order derivative of the improved observer state exists. By using the improved observer state and its high-order derivatives, a decentralized adaptive fuzzy controller is designed for each agent based on the backstepping technique. It is shown that the distributed resilient tracking can be achieved by the proposed method. Finally, a simulation example is proposed to show the effectiveness of the developed method.

This paper is concerned with the attack detection problem of T–S fuzzy systems with unknown but bounded (UBB) noise subject to malicious attacks via the set-membership estimation and a switching multi-mode high-order free-weighting matrix (SMHFM) method. Initially, the SMHFM is developed to address the so-called conservatism problem caused by the one-order free-weighting matrix (OFM) method. To solve this problem, the homogeneous polynomial technique is employed to introduce groups of free-weighting matrices for different switching modes. As a result, the SMHFM is synchronized with the working modes and possesses a high-order feature. Additionally, a switching multi-mode mechanism is implemented to enable the SMHFM to exhibit multiple modes. Time-variant balanced matrices are introduced for different switching modes to adjust the relevant matrix terms. This adjustment allows for obtaining more relaxed conditions, leading to smaller constraint sets and higher accuracy in state estimation. Furthermore, a zonotope-based set-membership (ZS) attack detection algorithm is introduced for T-S fuzzy systems, which is capable of detecting various types of attacks. By utilizing the proposed SMHFM method for attack detection, the level of conservatism in state estimation can be reduced. Finally, two simulation examples are given and some comparisons are made to validate the effectiveness of the proposed methods.

In this paper, we study the cooperative optimization problem (COP) for fuzzy nonlinear multi-agent systems (MASs) subjecting to denial-of-service (DoS) attacks. Unlike the existing cooperative optimization results, both fuzzy nonlinear systems and DoS attacks are considered in this paper. To solve the problem, a hierarchical equivalence mechanism is first introduced to transform the COP into an equivalent one consisting of both a distributed optimization problem (DOP) and a decentralized tracking problem (DTP). By introducing an optimal distributed algorithm, a customized virtual signal is devised to minimize the optimization function and simultaneously mitigate the effects of DoS attacks. To construct a bridge between solving the COP and the DTP, a local reference generator, which includes the characteristics of existing high-order derivatives, is designed utilizing the Hermite interpolation method. Subsequently, the backstepping technique is employed to create a decentralized fuzzy adaptive controller. It is illustrated that the proposed method is capable of achieving the cooperative optimization objective. Finally, the theoretical results are successfully applied to show the efficiency of the proposed method.

In this paper, the prescribed-time cooperative resilient fuzzy tracking control problem is addressed for thirdorder nonlinear cyber-physical vehicle systems (CPVS) under denial-of-service (DoS) attacks. Different from the existing results on cooperative resilient fuzzy tracking control, the developed method can achieve the cooperative resilient fuzzy tracking control objective within the prescribed time. To begin with, a data-driven-based online learning algorithm is introduced for learning the unknown and switching matrix of the reference signal. Based on the learned matrix, novel distributed resilient cooperative observers are designed to achieve prescribed-time observation by introducing an asynchronous observing method. To further improve the smoothness of the observation signal, a new improved smooth second-order prescribed-time observer is designed. Furthermore, leveraging the states of the smooth observer, a fuzzy controller is proposed to achieve precise tracking within the prescribed time, independent of initial conditions using the scaling error method and the backstepping technique. Finally, a simulation example is included to illustrate the effectiveness of the proposed methodology

This article studies the cooperative resilient tracking control problem for nonlinear multiagent systems (MASs) under denial-of-service (DoS) attacks and time delays. In comparison to the existing distributed control results based on the output observability condition, a joint output observability condition, which is a more universal one, is considered in this article. Based on this, a novel cooperative resilient observer is designed to estimate the state of the reference system subjected to DoS attacks and time delays in the communication topology. Then, a new observed variable with high-order derivatives is constructed by designing a novel chain of low-pass filters. Furthermore, with the help of the newly constructed variables, a fuzzy controller is proposed by using the adaptive method and backstepping technology to ensure the semiglobally uniformly ultimately boundedness for tracking errors. Finally, a simulation example is included to showcase the effectiveness of the proposed method.

This article addresses the fuzzy filtering problem for nonlinear systems based on the interval type-2 fuzzy model. To make better use of the constrained resources for communication, a novel event-triggering weighted try-once-discard protocol (ET-WTODP) is proposed. Different from the existing diverse protocols, ET-WTODP only allows a portion of components with relatively greater deviation to transmit at each triggering moment. The fuzzy filter is constructed with imperfectly matched membership functions and mode-dependent parameters. Denial-of-service (DoS) attacks frequently occur in communication networks are also considered. The overall fuzzy filtering error system (OFES) model is established taking into account ET-WTODP and DoS attacks. The sufficient conditions for the OFES to be asymptotically stable with a preset$H_{\infty }$performance level are identified by using the Lyapunov stability theory to obtain the desired asynchronous filter. Finally, numerical simulations are presented for verification that the proposed filtering approach is feasible and valid.

This article is concerned with the secure event-triggered (ET) control issue for interval type-2 (IT-2) fuzzy networked systems under stochastic communication (SC) protocol and random false data injection attacks. On account of the realistic physical sensor constraint, a saturation function is utilized in the measured output. In an effort to mitigate the network burden and reduce the incidence of data collision, a novel dynamic ET SC protocol is proposed by integrating with the major merits of the dynamic ET strategy and SC protocol. Moreover, the fuzzy observer-based controller in the presence of different membership functions is constructed. Subsequently, some sufficient design conditions are put forward for satisfying the asymptotically stable performance of the augmented closed-loop IT-2 fuzzy model. In addition, the gain parameters of fuzzy observer and controller can be obtained by virtue of solvable sufficient criteria without nonlinear terms. Eventually, the effectiveness of the theoretical secure fuzzy control scheme is verified by a numerical example.

In this article, a decentralized event-triggered (ET) regulation problem is tackled for networked interconnected systems (NISs) with control constraints and unmatched interference. Foremost, the decentralized regulation issue is converted into the optimal control problems for the associated auxiliary subsystem. In confronting the unavailability of system dynamics, the utilization of generalized fuzzy hyperbolic models-assisted identifier provides a novel perspective to devise the efficacious control policy for the constrained NISs. For the sake of mitigating the communication workload, a new dual threshold functions-based adaptive ET scheme (DTAETS) is put forward by incorporating the current data and latest ET signal. Moreover, we present a data-driven decentralized reinforcement learning algorithm to acquire the solution of DTAETS-boosted Hamilton–Jacobi–Isaacs equation. Then, the uniformly ultimately bounded stability of auxiliary subsystem and the weight estimation error is assured. Ultimately, a numeral experiment is conducted to substantiate the validity of the theoretical results.

This paper investigates the dynamic memory eventtriggered (DMET) fuzzy optimized consensus control for nonlinear multi-agent systems (MASs) with quantized reference signal. To alleviate the communication burden, a dual communication channels DMET scheme is proposed, which encompasses eventdriven communication for interactions among followers and communication between controllers and actuators. In comparison to the traditional dynamic event-triggered (DET) scheme, the devised DMET scheme incorporates historical information of the dynamic variable, resulting in longer triggering time intervals. Note that the problem of non-differentiability in backstepping method is generated by the event-triggered communication and quantization. To address this challenge, a smooth signal generator is introduced to reconstruct the step signals into the differentiable new one. Meanwhile, a reinforcement learning (RL) approach is employed to optimize the controllers, which utilizes an identifiercritic-actor architecture with fuzzy logic system (FLS) approximations at each step of backstepping method. The effectiveness of the proposed control method is demonstrated through simulations, confirming its capabilities in achieving optimized consensus control while mitigating communication loads.

This paper focuses on the observer-based event-triggered(ET) scheme issue for interval type-2(IT-2) fuzzy systems under the multiple cyber attacks including false data injection (FDI) attacks and denial-of-service (DoS) attacks. Considering both intermittency of DoS attacks and unmeasurable of partial systems, a switched observer-based nonlinear systems in the form of interval type-2 (IT-2) fuzzy models is established. An adaptive event-triggered (AET) scheme that can modulate the threshold value is proposed for better saving the communication resources. Considering the impact of stochastic FDI attacks, a switched AET controller is designed. Then, Lyapunoval analysis method is developed such that the augmented error IT-2 fuzzy systems is mean square exponentially stable with$H_\infty$performance. Finally, a practical example is employed to reflect the validity of the approach.

This article mainly addresses the stabilization issue of discrete-time interval type-2 fuzzy (IT-2F) semi-Markov jump systems in the presence of denial-of-service attacks by means of homogeneous polynomial approach. By employing the IT-2F technique, nonlinear features, such as possible uncertainties and unknown perturbations, are effectively expressed, and the corresponding membership functions of the fuzzy rules facilitate the application of subsequent polynomial method. A homogeneous polynomially parameter-dependent (HPPD) control law and a type of homogeneous polynomial-based fuzzy functions are designed for enlarging feasible parameter space as well as reducing the conservatism of the conditions, which are both HPPD on membership functions. Moreover, the conclusions concerning nonpolynomial controller and partial unavailable semi-Markov kernel are covered. It is also exemplified that the larger the degree of polynomial matrices, the less energy consumed by the controller. Finally, two examples of quarter-car suspension model and tunnel diode circuit model are provided to support the effectiveness of the presented results.

This article focuses on the security tracking control problem of nonlinear autonomous ground vehicles (AGVs) under denial-of-service (DoS) attacks. In order to resist DoS attacks and other external disturbances, a new security control scheme is proposed. First, the Takagi–Sugeno (T-S) fuzzy system is established to represent the nonlinear AGV system under DoS attacks. In particular, in order to improve the flexibility of control and reduce the impact of DoS attacks on tracking control, a novel controller with a specific switching mechanism is designed. The switching mechanism relies on fuzzy membership functions, which can make better use of nonlinear vehicle speed information. Second, the sufficient conditions to ensure global exponential stability of the T-S fuzzy-based switched system are given by using the Lyapunov function method. Finally, the simulation platform built by Carsim and MATLAB/Simulink is used to verify the effectiveness of the proposed control scheme.

In this article, we propose a novel fuzzy control scheme to enhance the ride comfort of active vehicle suspension systems (AVSSs). To begin, Takagi–Sugeno fuzzy theory is employed to address uncertainty in AVSSs. Second, a novel fuzzy controller based on the homogeneous polynomially parameter-dependent (HPPD) technique is developed, which can operate using an effective switching mechanism. The combination of the HPPD technique and switching greatly enhances the flexibility of fuzzy controllers. On this premise, the Lyapunov function with HPPD matrices is employed to provide an enhanced control strategy, which effectively improves the ride comfort performance of the AVSSs. Finally, the proposed scheme's effectiveness is demonstrated by the simulation and hardware-in-the-loop experiments.

This article is focused on the problem of adaptive event-triggered-based security controller construction for nonlinear networked control systems under multiple network attacks, which are represented by interval type-2 fuzzy models. First, in an attempt to mitigate the communication load, an enhanced adaptive event-triggered mechanism is utilized for determining the signals' transmission order, which is capable of adjusting the threshold dynamically with the signals probabilistically subjected to occurring malicious attacks. In addition, the observer is constructed under unfathomable premise variables, and then the controller with imperfect matching membership functions is created based on the estimated states, which is homogenous polynomially parameter-dependent. Moreover, the observer-based controller is obtained for the asymptotic stability with an$H_{\infty }$performance index via the Lyapunov stability theory. Then, sufficient conditions for the appropriate observer and controller gain matrices are given based on the linear matrix inequality method. Subsequently, the reliability of the proposed observer-based security fuzzy control design approach is demonstrated by two numerical simulation examples.

In this article, we investigate the problem of security control for T-S fuzzy Markov jump systems (FMJSs) under actuator faults and deception attacks, while introducing a cooperative event-triggered mechanism (CETM). In order to enhance the efficiency of communication resources, we develop the CETM in the forward channel, which operates concurrently on sensor-to-observer (STO) and observer-to-controller (OTC) channels utilizing a united event generator. Additionally, we design an attack-compensating controller to eliminate the impact of nonlinear malicious injection information generated by deceptive attacks on the system, where the compensation signal is generated by approximating the attack signal using radial basis function neural network (RBFNN) technology. Furthermore, using the Lyapunov function, sufficient conditions for ensuring that T-S FMJSs are mean square exponential ultimate bounded (MSEUB) are derived. Finally, the effectiveness of our proposed approach is demonstrated through a simulation example.

This article presents an adaptive fuzzy bipartite consensus tracking control scheme for nonlinear multiagent systems (MASs) with dead-zone inputs and actuator faults. The consensus problem for unbalanced communication topology of the MASs is difficult to deal with. First, the hierarchical algorithm is introduced to transform the consensus tracking problem for multiagents into the tracking problem of the single agent. Then, the novel error transformation and coordinate transformation are proposed based on the hierarchical design theory, leading to the condition of global Laplacian matrix information unnecessary so that the computational difficulty and communication burden are significantly reduced. Besides, the control performance would be seriously affected by the input constraints such as dead-zone and faults. There is a balance between the input constraints and the output constraints for MASs, but these two constraints are handled independently in the most existing works. Thus, a flexible performance function is developed to balance the system performance and the stability requirements by flexible signal switching. The proposed adaptive fuzzy control scheme ensures that not only the influence of the dead-zone and various types of actuator faults is eliminated, but also the preassigned finite-time tracking performance is achieved. Finally, the simulation experiment is conducted to verify the effectiveness of the established control scheme.

This article addresses a novel optimal fuzzy control scheme for a category of nonlinear Markov jump singularly perturbed systems with mixed zero-sum (MZS) game. First, a Takagi–Sugeno fuzzy structure is employed to describe the nonlinear plant. On this basis, two types of value functions for multiplayer MZS game are developed and a series of fuzzy controllers are designed. Subsequently, a hybrid iteration (HI) approximation learning framework is constructed for approaching the solutions of the fuzzy game coupled algebraic Riccati equations. The HI eliminates initial admissible control dependencies and has a desirable learning iteration rate, in contrast to the traditional policy iteration and value iteration. We present a novel model-based HI scheme and further develop it to a model-free version. The model-free HI scheme uses only online data collected along the system trajectories for controller design, and it eliminates the traditional model-dependent issues, which is more suitable for practical applications. Finally, the validity and flexibility of the proposed algorithm are verified by a simulation example.

Till now, most of the results on Takagi–Sugeno (T-S) fuzzy Markov jump systems are synchronous and independent of the analysis of membership functions (MFs), which leads to conservatism. Therefore, it is significant to study the MFs-dependent Lyapunov–Krasovskii functional (LKF) while considering asynchrony. This article investigates the${H_\infty }$control issue of T-S fuzzy Markov jump systems with time-varying delay. First, delay-product-type terms and MFs are introduced to design a new LKF, which fully utilizes the information of time-varying delay and MFs simultaneously. Moreover, based on a hidden Markov model, the controller mode is assumed to operate asynchronously with the system mode, and an asynchronous switching fuzzy controller is proposed by employing the switching approach. Thus, a more practical and less conservative stability criterion is obtained to ensure that the closed-loop system is stochastically stable with${H_\infty }$performance. Finally, three examples are provided to illustrate the superiority and practicability of the presented method.

This paper aims to develop a dynamic-memory event-triggered mechanism (DMETM) for Takagi-Sugeno (T-S) fuzzy switched systems under denial-of-service (DoS) attacks. Persistent dwell-time (PDT) is used to describe the characteristics of both DoS attacks and switching behaviours. The usage of PDT allows high-frequency switching and attacking phenomenon during certain intervals. Meanwhile, the DMETM is designed to screen for more effective triggering instants and reduce signal transmission frequency. The dynamic triggering conditions vary based on both the latest triggering data and historical triggering data simultaneously. By combining the DMETM and the acknowledgement character technique (ACK), the system can detect the initial and end instants of DoS attacks to improve control performance. Besides, a dual Lyapunov function is constructed and sufficient conditions for input-to-state stability (ISS) of nonlinear switched systems (NSSs) are derived. Finally, simulation verification is conducted in a nonlinear DC microgrid, illustrating feasibility and effectiveness of the DMETM.

This article studies the tracking control problem of uncertain Euler–Lagrange systems. Despite receiving widespread attention in recent years, the problem remains unresolved to a large content when considering response quality, optimality, robustness, and conservatism. The main challenge lies in how to integrate performance constraints into adaptive dynamic programming (ADP) algorithm and achieve a balance between robustness and conservatism within this framework. To that end, this study proposes a new performance constraint-handling sliding mode manifold, a new prescribed performance function, and a new ADP-oriented observer disturbance observer. The above theoretical findings, together with the fuzzy logic system-based ADP algorithm, realize the convergence of tracking errors to a prespecified residual set within a finite-time setting in an optimal manner, enhance robustness, and reduce conservatism. The proposed controller facilitates the practical application of tracking control for Euler–Lagrange systems. Simulations on an autonomous underwater vehicle demonstrate the effectiveness and benefits of the proposed method.

This article explores the design of switched fuzzy controllers for interval type-2 (IT2) fuzzy systems with a fuzzy-rule-dependent adaptive event-triggered mechanism (AETM). First, a novel fuzzy-rule-dependent AETM is proposed for the studied system, which takes into consideration both the information of membership functions (MFs) and fuzzy rules. The corresponding AETM for each fuzzy rule can effectively conserve the limited communication bandwidth by adaptively adjusting the triggering parameter based on the state evolution trends and MF information. Second, an appropriate switched IT2 fuzzy controller is designed that can be switched according to the values of the MFs. Compared to the existing works, the proposed switched IT2 fuzzy controller achieves superior control performance. Subsequently, relaxed stability conditions are developed by considering the information of both the lower and upper MFs, and introducing some slack matrices to cope with parameter uncertainties. The proposed stability condition can stabilize the state of the resulting closed-loop system despite the AETM. Finally, a practical mass–spring–damper example is presented to demonstrate the validity of the presented method.

Numerous previous findings on the synchronization of fractional-order networks have been conducted through event-triggered control (ETC) or intermittent control (IC), separately. Motivated by the benefits of IC and ETC, this article designs an effective event-triggered intermittent control (ETIC) to investigate the bipartite synchronization of fractional-order fuzzy signed networks. The system dynamics are constructed to describe the nonlinear signed networks via the fuzzy logic and the short-memory performance. Notably, this article represents the first attempt to design the ETIC for fractional-order networks in the sense of exponential convergence. This approach avoids the constantly updating states of IC and the uninterrupted input of ETC. By employing the Lyapunov method, some sufficient conditions for the synchronization of the considered networks are obtained. In addition, the Zeno phenomenon is eliminated so that the infimum of interval length is positive, which ensures the feasibility of the designed controller. Finally, two numerical experiment examples of the fractional-order Chua's circuits model and the fractional-order power system without load disturbance are carried on to illustrate the effectiveness and practicability of our theoretical analysis.

This note proposes a novel weighted memory$H_\infty$controller for time-varying delayed Takagi–Sugeno fuzzy systems via a distributed delay method. In contrast to the traditional memory controller based on instantaneous historical data, the continuous historical information over a given period is utilized to construct the fuzzy-based memory controller, in which a weighting function is employed for the first time to describe the importance of historical information. Then, the weighted historical information is expressed as a distributed delay and the weights are represented as delay kernel. By using a less conservative integral inequality with respect to the weighted historical information, original sufficient conditions are deduced to solve the fuzzy weighted memory$H_\infty$controller gains. Finally, simulations are carried out to reveal the merits of the presented controller.

In this article, the adaptive fuzzy optimized tracking control problem of uncertain cyclic switched stochastic nonlinear systems with actuator faults and prescribed performance is studied under average cycle dwell time. For achieving a better optimal control strategy, the information of the switching signal is taken into account by the reinforcement learning algorithm of the identifier-critic-actor architecture. Meanwhile, a novel mode-dependent event-triggered optimized mechanism for subsystem is proposed to resolve the impact of asynchronous switching on system performance, which not only does not have strict assumptions but also reduces the communication burden. Moreover, to eliminate the impact caused by actuator failures, fault-tolerant compensation scheme depending on the switching signal is designed. By presenting Lemma 3 and using the coordinate transformation technique, it is proven that the choice of the performance index function still conforms to the control protocol under the prescribed performance control framework. In the optimized backstepping control design, the proposed controller is able to ensure that all signals in the closed-loop system are bounded in probability and tracking error meets performance. Finally, both numerical and practical simulations are given to illustrate the effectiveness of the proposed optimization scheme.

This article studies the co-design of new fuzzy switching-type state-FDI estimation and attack compensation control for dc microgrid (dc-MG) systems under hybrid attacks of denial of service (DoS) and false data injection (FDI). First, for networked nonlinear dc-MG systems, a co-design system model under hybrid attacks is established based on the time-constrained DoS attack model with sleep/active period ranges of attack signal and an FDI attack compensation controller. Then, using the time-varying Lyapunov function method that depends on attack parameters, the exponential stability criterion of dc-MG system under hybrid attacks is derived, which realizes the decoupling of co-design. More importantly, a co-design method of fuzzy state-FDI estimation and attack compensation control based on convex optimization technique is proposed. Furthermore, a set of switching modes are designed according to the fuzzy membership functions. Different gain matrices of attack compensation controller and state observer are designed under specific modes to reduce the conservatism of the co-design method. Finally, an example is given to verify the validity of two different theoretical results.

This article adopts a novel homogeneous polynomial parameter-dependent (HPPD) codesign method to deal with the security control problem of the Takagi–Sugeno fuzzy system of cyber-physical dc microgrid under hybrid attacks. A new fuzzy control scheme and state estimation scheme, i.e., a function whose homogeneous polynomial parameters depend on the fuzzy membership function normalized at the current time, is proposed to achieve the combined goal of relaxed control and accurate estimation. Relaxed exponential stability conditions are then derived with less conservatism than the existing conditions. In addition, an HPPD codesign method is further proposed. The effectiveness and superiority of the results in this article are illustrated through simulation examples.

This article focuses on an adaptive output feedback control for nonlinear multi-agent systems (MASs) with input quantization and unknown control gains by applying a predefined accuracy approach. Unlike the existing predefined accuracy control (PAC) approaches, a predefined accuracy scheme of the output feedback control (OFC) for nonlinear multi-agent systems is studied for the first time in this article. Moreover, the issues of input quantization and unknown control gains are introduced for the presented method, which can be addressed depending on the Nussbaum function. To reduce the problem of computational complexity, a dynamic surface technique is applied with a nonlinear filter. By employing the backstepping methodology and fuzzy logic systems, a distributed fuzzy controller can be established to ensure the tracking errors converge to a prespecified precision. Finally, some simulation results expound the accuracy of the presented control method.

This article investigates the relaxed resilient fuzzy stabilization problem for discrete-time Takagi–Sugeno (T–S) systems based on a new switching mechanism. First, a multimode switching fuzzy controller is constructed, which covers all the possible working modes of system dynamics. For the purpose of reducing conservatism, additional groups of gain matrices are introduced corresponding to different switching modes such that the switching controller switches along with the working modes. Then, the resilient fuzzy stabilization can be accomplished by the proposed controller when the condition of alarm threshold is satisfied. Second, regarding controller design, few groups of time-variant balanced matrices (TVBM) coping with different switching modes are introduced to update the linear matrix inequality (LMI) conditions for system stabilization. Thereby, the feasibility of LMI conditions can be enhanced by using the TVBMs to adjust the related matrix terms in the framework of the homogeneous polynomial technique. Therefore, larger feasible region and less conservatism can be attained by the developed switching mechanism than before even if the alarm threshold is assigned larger values. Finally, a benchmark example is provided to testify the effectiveness and superiority of the proposed method.

This paper proposes a novel approach to model predictive control (MPC) for Takagi-Sugeno (T-S) fuzzy systems by combining the homogeneous polynomial technique and a switching mechanism. Aiming at improving the overall system performance by dynamically switching between different controllers according to system dynamics changing, the proposed switching MPC (SMPC) scheme formulates a group of optimization problems to determine the optimal switching strategy and corresponding control actions. To be specific, the optimization problem is solved at each moment to generate a control sequence that optimizes the gain matrices to achieve the minimized performance index. Building upon the traditional MPC structure, the proposed SMPC method forms a new framework by reducing the conservatism of controller design in the solving process based on linear matrix inequality (LMI) conditions via introducing the homogeneous polynomial method. As a result, the proposed SMPC method enhances the feasibility of controller solving, improves control performance and expands the domain of attraction by utilizing the switching mechanism to handle the system dynamics more freely. Finally, the effectiveness and superiority of the proposed method are validated through different examples.

The motivation of this study is to solve the challenges posed by the nonstrict feedback structure and multiple timedelays factors in stochastic systems, which significantly complicate the structure of system structure and make the procedure of controller design more difficult. Firstly, a new LyapunovKrasovskii function is constructed in this study. A method is devised based on this function, which incorporates the characteristic of kernel functions in fuzzy logic systems and the concept of variable separation to effectively tackle challenges posed by complex system structures and time-delay factors, as well as reducing the burden of updating dynamic gains. Additionally, the application of the Nussbaum function technique efficiently resolves the issue of unknown control direction while ingeniously leveraging the distinctive properties of the Nussbaum function and the stochastic Barbalat's lemma. This approach provides a complete theoretical proof of the boundedness of the system signals and guarantees the asymptotically stable in probability. Ultimately, the proposed approach is validated by the exceptional performance of the simulation results for an electromechanical control system.

This paper focuses on the issues of region stability/stabilization andH∞control for discrete-time impulsive Takagi-Sugeno fuzzy systems (DTIT-SFSs). Firstly, a more accurate asymptotic stability criterion is proposed by introducing the definition of region stability. It offers a more precise estimation of convergence speed and damping response for DTIT-SFSs compared to conventional stability criteria in terms of dynamic performance. Secondly, a fuzzy controller is designed based on the aforementioned region stability analysis, which can effectively control the convergence rate to the equilibrium state and ensure the desired damping response of DTIT-SFSs. Furthermore, a novelH∞fuzzy controller is designed, ensuring both a certain level ofH∞performance of DTIT-SFSs and constraint on the convergence speed and damping response of DTIT-SFSs. Finally, the functionality of this technique is validated through numerical calculations and an inverted pendulum control example

This article extends the finite-time adaptive tracking control to stochastic nonlinear systems with multiple uncertainties, including output constraints, unknown parameters, unmodeled dynamics, and external disturbances. Most relevant results in literature have two main restrictions: 1) uncertainties and unknown items in the systems; 2) the matter of “explosion of complexity.” By integrating an improved technique of adding fuzzy logic systems to estimate unknown parameters with a bounded command filter method, a systematic tracking control scheme is developed that eliminates both of the above restrictions. To alleviate the serious uncertainties caused by the constraints, a quartic asymmetric time-varying barrier Lyapunov function is utilized when the control coefficient is known. Subsequently, an event-triggered controller is constructed that enables boundedness and finite-time convergence of all closed-loop signals. Eventually, to validate the effectiveness of the proposed adaptation strategy, this new method is applied to ship maneuvering systems that encounters multiple uncertainties arising from disturbances, such as wind, waves, and ocean currents.

This paper is concerned with the reinforcement learning-based tracking control problem for a class of networked systems subject to denial-of-service (DoS) attacks. Taking the effects of DoS attacks into consideration, a novel value function is proposed, which considers the cost of the control input, external disturbance and tracking error. Then, using the structure of the value function, the tracking Bellman equation and Hamilton function are defined. By employing the Bellman optimality theory, the optimal control strategy and the game algebraic Riccati equation (GARE) are solved with the Hamilton function. Next, the desired tracking performance is guaranteed as the solution of the GARE is found. Furthermore, an attacks-based Q-learning algorithm is projected to find the solution to the optimal tracking problem without the system dynamics and the convergence of the Q-learning algorithm is given. Finally, the F-404 aircraft engine system is given to verify the effectiveness of the proposed control strategy.

In this article, the outlier-resistant (OR) observer-based secure control problem is investigated for nonlinear networked systems under randomly activated denial-of-service (RADoS) attacks and stochastic communication (SC) protocol. In virtue of zero-order holder (ZOH) technique, an attack compensation scheme is adopted to alleviate the adverse effects brought by RADoS attacks. By introducing multiple internal dynamic variables (MIDVs), a novel multi-variable event-triggered stochastic communication (MVET-SC) protocol is put forward to enhance the design flexibility and prevent the occurrence of data conflicts. Moreover, the non-fragile fuzzy controller is applied due to the inaccuracies in practical applications. Comprehensively taking the above factors into account, the asymptotic stability of the augmented fuzzy system can be ensured under the presented sufficient criteria. Meanwhile, the parameters of the OR observer-based secure controller are derived according to the obtained design conditions. In the end, a simulation example of mass-spring-damping system (MSDS) demonstrates the validity of the non-fragile secure control approach with OR observer.

This paper investigates fault detection and robust security control of implicit Markovian jump (IMJ) systems affected by random false data injection (FDI) attacks and packet loss under memorized output-perceptive event-triggered protocol (MOETP). In order to harmonize control performance and communication efficiency, a mode-dependent MOETP is proposed by designing an output-dependent threshold function and introducing weight parameters. Fault detector and feedback controller incorporating random FDI attacks and packet loss information are cooperatively designed to detect the occurrence of system faults and achieve robust security control for IMJ systems. Considering the property that the derivative of “time-varying delay” function is 1 and the definition of error in MOETP, a novel mode-delay-related Lyapunov-Krasovskii functional is constructed so as to derive the strict linear matrix inequality criteria of$H_{\infty }$stochastic admissibility as well as the expected gains of fault detector and security controller based on free-weight matrix method and matrix transformation technique. The validity of the presented co-design methodology is confirmed by a tunnel diode circuit system.

In this article, the matter of aperiodic sampled-data$H_{\infty }$control of a quarter vehicle active suspension system with time-varying delay is investigated based on an uncertain discrete-time model. This article mainly solves three problems based on the theory of integral quadratic constraints. First, the system is discretized by resorting to lifting technique, the uncertainties of the discrete-time model are embodied by the operators related to sampled-data and time delay, in this process, a new norm upper bound estimation of operator is given. Second, based on the multipliers of the operator, the conditions for the improved$H_{\infty }$performance constraints are given. Third, with regard to controller design, the difficulties posed by the nonlinear coupling terms for solving the matrix inequalities are addressed by an iterative algorithm. Finally, the simulation platform and a practical example show that the proposed method is effect and can obtain more optimized results.

This article addresses the lateral control problem of nonlinear autonomous ground vehicles (AGVs) with time-varying velocities. A novel solution is provided for making nonlinear AGVs drive smoothly along a predetermined path in the presence of external disturbances. First, a new controller based on the homogeneous polynomial technique is designed to improve the control flexibility so as to enhance the control effect of the vehicle facing the change in road curvature. Second, a more relaxed stability criterion is derived by using convex optimization techniques and relaxation techniques to ensure the exponential stability of the closed-loop vehicle system. Finally, the MATLAB/Simulink-CarSim co-simulation platform is used to verify the proposed control strategy's effectiveness.

The integration of large-scale distributed generators into active distribution networks (ADNs) will aggravate voltage fluctuations, which can affect the secure operation of power grids seriously. In this article, we investigate a cooperated voltage regulation problem of ADNs. Specifically, we first formulate a two-timescale voltage regulation problem considering the coordination of various hybrid devices while reducing the power loss of the whole ADNs. Given that the aforementioned problem is challenging to solve directly, we reformulate it as bilevel Markov games. Then, we propose a hierarchical multi-agent attention-based deep reinforcement learning algorithm to solve them. To be specific, the upper level Markov game is solved by a discrete multi-actor-attention-critic (MAAC) algorithm, and the lower level Markov game is solved by a continuous MAAC algorithm. In addition, the two-timescale coordination between upper level and lower level agents is implemented through the information exchange of rewards during the training process. Simulation results show that the proposed algorithm has good effectiveness, robustness, and scalability in voltage regulation.

This article lays the spotlight on embedded-adaptive-observer-based$H_\infty$integrated fault estimation and memory fault-tolerant control for a nonlinear delayed implicit robotic arm. To tackle the nonlinearity of the system, a prototypical Takagi–Sugeno fuzzy method is deployed. An embedded adaptive proportional–integral observer program is proposed to implement$H_\infty$simultaneous estimation of the original system states, sensor faults, and actuator faults via the fault-embedded technique, embedding the sensor faults into the original system states and allowing them to be transformed into new substates. The development of a fresh fuzzy Lyapunov–Krasovskii functional with time delays, Markov jump modes, and fuzzy information creates a firm groundwork for the outcome of the fuzzy delayed implicit jump system meeting with stochastic admissibility and$H_\infty$performance metrics. Novel observer-based memory-aware fault-tolerant controller is engineered by taking the form of linear matrix inequalities to compensate the impact of time delays, perturbations, and faults. To illustrate the validity of the method put forward, a single-link robotic arm device is offered as an example finally.

This paper addresses the challenge of distributed adaptive platooning control of connected vehicles with randomly switching topologies. A linearized longitudinal vehicle platoon dynamic model is investigated, which simultaneously considers the bounded external disturbances and leader control input. By representing the switching topologies model in terms of a continuous-time Markov process, a distributed adaptive control scheme is developed such that follower vehicles can synchronize their velocities and accelerations with the leader while preserving the intended distance. The outstanding feature of the proposed distributed adaptive control scheme is that it avoids acquiring global information associated with communication topology. Besides, the design procedure is scalable since the control gain can be derived by only solving a linear matrix inequality offline related to the vehicle dynamics parameters, which means that the method remains applicable when the platoon size changes. Finally, the efficacy of theoretical findings is substantiated through the utilization of simulations.

This paper addresses the problem of adaptive memory-event-triggered control for intelligent vehicle transportation systems (IVTSs). Unlike the existing methods for modeling IVTSs, the acceleration information is introduced in the desired distance to achieve better distance control performance of IVTSs. The information between vehicles interacts over a wireless network. In order to further reduce the amount of data transmission, a novel adaptive memory-event-triggered mechanism (METM) is developed, in which historical information is utilized. In addition, the proposed METM threshold is designed to vary with the system state of each autonomous vehicle to adjust the data-releasing rate adaptively. Under the adaptive METM, a distributed tracking controller with historical information is put forward to guarantee uniformly ultimately bounded (UUB) stability using the Lyapunov stability theory and linear matrix inequality (LMI) technique. Finally, simulation results are given to verify the superiority of the proposed method.

A belief propagation (BP) based cooperative integrity monitoring (BP-CIM) algorithm is proposed in this work. BP is widely adopted as the cooperative positioning (CP) estimator, however, the corresponding integrity problem is not solved which restricts its practical application. To guarantee the reliability of a BP-based CP system, our proposed BP-CIM can detect the faulty observations in a distributed approach. Meanwhile, error analysis for BP is performed to derive the CP estimation error bound, which is subsequently used to determine the protection level (PL) of BP-CIM. The simulation and experimental results show that BP-CIM outperforms many existing fault-tolerant CP algorithms in the sides of accuracy and robustness, and the calculated PL can provide a conservative error bound for the estimated CP states. BP-CIM framework can be further extended to many other multi-sensor CP systems to improve the system reliability.

In this article, a learning-based resilient fault-tolerant control method is proposed for a class of uncertain nonlinear multiagent systems (MASs) to enhance the security and reliability against denial-of-service (DoS) attacks and actuator faults. With the framework of cooperative output regulation, the developed algorithm consists of designing a distributed resilient observer and a decentralized fault-tolerant controller. Specifically, by using the data-driven method, an online resilient learning algorithm is first presented to learn the unknown exosystem matrix in the presence of DoS attacks. Then, a distributed resilient observer is proposed working against DoS attacks. In addition, based on the developed observer, a decentralized adaptive fault-tolerant controller is designed to compensate for actuator faults. Moreover, the convergence of error systems is shown by using the Lyapunov stability theory. The effectiveness of our result is examined by a simulation example.

This article explores the quasi-synchronization of discrete-time-delayed heterogeneous-coupled neural networks (CNNs) via hybrid impulsive control. By introducing an exponential decay function, two non-negative regions are introduced that are named time-triggering and event-triggering regions, respectively. The hybrid impulsive control is modeled by the dynamical location of Lyapunov functional in two regions. When the Lyapunov functional locates in the time-triggering region, the isolated neuron node releases impulses to corresponding nodes in a periodical manner. Whereas, when the trajectory locates in the event-triggering region, the event-triggered mechanism (ETM) is activated, and there are no impulses. Under the proposed hybrid impulsive control algorithm, sufficient conditions are derived for quasi-synchronization with a definite error convergence level. Compared with pure time-triggered impulsive control (TTIC), the proposed hybrid impulsive control method can effectively reduce the times of impulses and save communication resources on the premise of ensuring performance. Finally, an illustrative example is given to verify the validity of the proposed method.

The primary purpose of this article is to design an intelligent false data injection (FDI) attacks detection, isolation, and mitigation scheme for a class of complex microgrid systems with electric vehicles (EVs). First, a networked microgrid with an EV model is well established, which takes load disturbance, wind generation fluctuation, and FDI attacks into account so as to truly reflect the operation process of the complex system. Then, an intelligent hyper basis function neural network (HBF-NN) observer is designed to accurately estimate the state of the microgrids, learn, and reconstruct the possible attack signal online. Subsequently, a novel HBF-NN-based${\mathcal {H}}_{\infty}$controller is skillfully designed to mitigate the negative impact of FDI attacks online, so as to ensure the normal operation of the complex systems in an unreliable network environment. Finally, a two-stage integrated intelligent detection and maintenance algorithm is summarized and one simulation is presented to provide tangible evidence of the feasibility and superiority of the proposed FDI attacks detection, isolation, and mitigation methodology.

This article studies bipartite consensus of multiagent systems (MASs) with input saturation and denial-of-service (DoS) attacks over weighted directed networks. First, a distributed control protocol is proposed by using low-gain technology to address the input saturation constraint. Then, an estimator is introduced to design a dynamic event-triggered communication protocol, which avoids continuous communication between agents. In addition, sufficient conditions for realizing bipartite security consensus are obtained under insecure communication networks with DoS attacks. Moreover, the dual-channel concept is considered to further save resources. An event-triggered controller protocol and a dynamic event-triggered communication protocol are designed in the communication channel and the controller–actuator channel, respectively. By considering an exponential threshold, the event-triggered controller protocol can operate stably when the control signal is minute. Thus, a novel dynamic event-triggered communication protocol is obtained to implement bipartite security consensus and exclude Zeno behavior. Finally, a practical example is presented to show the effectiveness of our design method.

This article is concerned with the static output feedback stabilization problem of T-S fuzzy systems by developing a novel switching sequence convex optimization (SSCO) algorithm. First, the time-varying relaxation matrix with time-varying properties is introduced, which combines the membership functions and the constructed switching mechanism to adjust the positive and negative terms of the inequality conditions, thereby improving the relaxation quality of stability conditions. To compute bilinear matrix inequalities (BMIs) with complex time-varying relaxation matrix structures, the developed SSCO algorithm employs a more flexible switching-type optimization variable and an inner approximation strategy capable of linearizing all concave sections. As a result, a sequence of linear matrix inequalities (LMIs) are obtained without introducing any additional constraint and with better approximation level than existing solving methods. The superiority of the proposed method includes two aspects: more relaxed solving conditions are gained by using the time-varying relaxation matrix technique to facilitate controller design; the proposed SSCO algorithm is of faster convergence rate, which means less computational time for practical implementation. Finally, the proposed relaxed switching control method is validated by simulation comparison.

In this article, the exponential stability and controller design of large-scale networked control systems with prediction-based controller are addressed. A matrix dimension transformation method is proposed, which solves the problem of matrix dimension mismatch due to the complex structure. First, a new Lyapunov–Krasovskii functional (LKF) is introduced under the condition of the backstepping-based partial differential equation (PDE) method, and stability criteria with less conservatism are obtained with the help of free-weight matrixes and the inequality deflation technique. Second, combining with the reduction-based ordinary differential equation (ODE) method, by constructing the two-sided mode-dependent loop-based LKF, the information of sampled-data intervals can be utilized more sufficiently. Meanwhile, with the help of the proposed matrix dimension transformation method, controller design algorithms based on the two prediction methods are given, respectively. Finally, the effectiveness of theoretical analysis are demonstrated by using two coupled cart-pendulum systems, where the proposed method can obtain larger upper bounds of the allowable time delay and sampled-data intervals.

Synchronization control is an important issue in complex networks (CNs), but the specific realization is generally influenced by many factors. In this article, by taking into accounts of the coupling effect and cyber attacks, we dedicate to design an efficient synchronization control approach for discrete-time CNs. Given that the coupling among nodes in CNs inevitably introduces the internode data exchange, round robin (RR) protocol is adopted to prevent data collision caused by the limitation of communication resources. Moreover, a probabilistic interval model is employed to capture the characteristics of the coupling delay, i.e., the delay of the internode data transmission. The deception attacks launched on the multichannel-enabled communication network between controllers and actuators of nodes in CNs are also considered. Then, a synchronization error model is established to describe the concerned synchronization control problem. By defining appropriate Lyapunov–Krsasovskii function, the sufficient conditions for the stability of the envisioned synchronization error system are obtained, and the design method for controllers is proposed subsequently. Simulations are finally conducted to demonstrate the validity of the work.

This article addresses a security control issue for discrete-time networked control systems (DTNCSs) with uncertainty under stochastic communication protocol (SCP) characterizing a class of networked systems, such as autonomous dynamics. Specially, in order to properly take account of the constructed system in practical application, the time-varying uncertainty with norm-bounded parameter is adopted in DTNCSs. To avoid data conflict in the communication network with limited bandwidth, SCP modeled by discrete-time Markov chain is introduced to schedule the transmitted signals, which are subjected to deception attacks described by a random process. In addition, the mode-dependent observer and controller are utilized in line with the scheduling situations led by SCP. Moreover, the stochastic stability of the augmented dynamics is ensured by the presented sufficient condition. Meanwhile, the corresponding gain parameters of the observer and controller can be computed. Ultimately, two simulation experiments are utilized to validate the availability of the proposed security control strategy.

This article investigates the FlexRay (FR) protocol-based dynamic event-triggered (DET) secure filtering problem with the high-rate communication (HRC) network for the interval type-2 (IT-2) fuzzy networked system. For fear of data collisions and preempting limited communication resources, a novel DET-FR (DETFR) protocol is adopted to schedule sensor nodes. Different sensors are employed for distinct protocols and data-holding strategies to reinforce the efficiency of network transmission. Moreover, considering the random occurrence of cyber attacks and fading measurements in the HRC channel, the attack parameters are represented by the Bernoulli process, and measurement attenuation coefficients are expressed by the random variables of equidistribution on a fixed interval. Based on this, to ensure that the error dynamics meet the disturbance attenuation level, several sufficient conditions are given. Subsequently, the DETFR protocol-based secure filtering algorithm is developed to acquire the fuzzy filter parameters. Eventually, the validity of our designed secure filtering algorithm is proved through two examples.

This article investigates the privacy-preserving consensus control and containment control for strict-feedback multiagent systems (MASs). For the agents possessing sensitive state information that needs safeguarding, an output mask function is employed, which ensures that the true state value remains indiscernible to the other agents during the process of information interaction. However, the introduction of mask function increases the complexity of the cooperative control design for MASs, given the untrustworthiness of the received state information from other agents. To address this challenge, an adaptive backstepping-based control algorithm is proposed, relying on the masked states of neighboring agents. Simultaneously, a dynamic event-triggered control with the reset mechanism is introduced to save communication resources, in which the dynamic of the additional variable is determined by the preset conditions. Based on the proposed event-triggered privacy-preserving control method, it is ensured that the initial state value of each agent remains undisclosed, and the tracking errors can converge to a residual set around zero. Similar results are extendable to the privacy preservation containment control for MASs. Finally, the efficacy of the proposed control method is validated through two illustrative examples.

This article further investigates the tracking control problem of flexible-joint robot systems. Compared with existing results, all states are assumed to be quantized by a uniform quantizer, which results in discontinuous quantized signals. To address this issue, a new adaptive controller is proposed by introducing a command filter, in which the quantized virtual controller is used as input to obtain continuous signals. Thus, the discontinuity problem is avoided and the quantization influence is further compensated. It can be proven that all signals in the closed-loop system are bounded and tracking errors can converge to an arbitrarily small neighborhood of the origin. Finally, a simulation result is given to verify the practicability of the proposed method.

This article focuses on the adaptive stabilization control of high-order strict-feedback systems (SFSs) with unknown control directions. It addresses the challenge of dealing with unknown control directions in the fully actuated theory. To overcome this challenge, the Nussbaum gain technique and tuning functions directly based on the high-order fully actuated system (FAS) method are proposed to deal with the unknown control directions and system uncertainties, while avoiding the phenomenon of overparameterization. Additionally, a relative threshold event-triggered strategy is utilized to effectively avoid continuous controller updates, which helps conserve network resources used for signal transmission. The proposed controller guarantees the convergence of all system state variables to zero and ensures that all signals within the closed-loop system remain bounded. To validate the effectiveness of this approach, a numerical simulation and a practical example using the Nomoto ship model are conducted. Overall, this study contributes to the FAS field by providing a solution for adaptive stabilization control in high-order SFSs with unknown control directions.

This article investigates the distributed constrained optimization problem with event-triggered communication over time-varying weight-unbalanced directed graphs. A more generalized network model is considered where the communication topology may be variable and unbalanced over time, the information flows across agents are subject to time-varying communication delays, and agents are not required to know their out-degree information accurately. To address the above challenges, we propose a novel discrete-time distributed event-triggered delay subgradient algorithm. To facilitate convergence analysis, a consensus-only “virtual” agent technique is employed, dynamically adjusting its state (active or asleep) to ensure a delay-free information flow among agents. Additionally, an augmentation approach is proposed to ensure that the augmented time-varying weight matrix is row-stochastic. It is shown that the agents’ local decision variables converge to the same optimal solution, in the case of reasonable communication delays and event-triggering thresholds. Numerical examples show the efficiency of the proposed algorithm.

The concept of reachable set and state space ellipsoid is used in this article to determine the optimal safe range of the truck-trailer driving by allowing the constrained variables to move freely within a given range. A method of returning the truck to the desired position is proposed by analysing the movement trajectory of the truck. Two results are certified. The first result considers the issue of reachable set estimation (RSE) for the multirate sampled-data (MRSD) system in the aperiodic sampled-data framework based on the model knowledge. By constructing loop-based Lyapunov functional (LBLF), we obtain the sufficient condition that all the state trajectories are confined to target ellipsoid. This article also provides a computational method for an MRSD controller considering RSE. The second result provides the data-driven control tactics for the unknown sampled-data system to consider the RSE problem for the aperiodic sampled-data system, using only the noisy data. In addition, this article extends the data-driven control scheme to the design of MRSD controllers and ensures the stability of the system in agreement with the measured data. Simulation results show that the MRSD controller under both the model-driven method and the data-driven method is valid and achieves better control effect compared to the single-rate sampled-data (SRSD).

A fast finite-time adaptive fuzzy tracking control algorithm is proposed for stochastic nonlinear systems (SNSs) under an event-triggered mechanism. Unlike the traditional finite-time control of SNSs, for this article, the drift and diffusion terms can be completely unknown. First, a fuzzy-logic system has been implemented to approximate the uncertain functions of SNSs. Second, a novel theorem of a fast finite-time adaptive control mechanism of deterministic systems is presented by revamping the fast finite-time stability in the mean square. Next, the complex explosion issue caused by the backstepping technique is effectively avoided based on command filtering feedback control. Compared with the standard backstepping technique, which has avoided the analytical computations of the derivatives of virtual control functions and has dramatically reduced the computational burden. Finally, an example of the one-link manipulator with motor dynamic systems is provided to verify the theoretical analysis.

This article explores the state estimation problem of memristive neural networks (MNNs) with mixed delays subject to multichannel round-robin protocol (MRRP) and multimodal injection attacks (MIAs). MRRP allows for multichannel-enabled signal transmission between sensors and remote estimators, thereby significantly mitigating network congestion. Different types of attacks are supposed to be encountered during the sensor data transmission via network. Both the impacts of the MRRP and the attacks are reflected in modeling the addressed system. The purpose of this article is to design an estimator capable of constraining the estimation error within an ellipsoidal region in the presence of noise interference, mixed delays, MRRP, and MIAs. Using recursive matrix inequality (RMI) techniques, sufficient conditions are derived for achieving the desired performance and the expected state estimator gains are derived by minimizing the constrained ellipsoid region. Ultimately, the efficacy of the developed estimate strategy is demonstrated through numerical simulation.

To address the false data injection (FDI) and denial of service (DoS) attack, this article proposes an event-trigger-based resilient distributed energy management approach for cyber–physical system of smart grid. Here, an event-trigger-based resilient consensus algorithm (ERCA) is proposed with the attack identification and compensation mechanism. The event-triggered mechanism is improved within distributed optimization combined with reliable acknowledgment (ACK) signals technique to mitigate the impact of data loss or transmission delay, and trust nodes-based compensation approach is proposed during resilient coordinated optimization for state correction to ensure the stability and security of power grid system. The optimality and convergence of the proposed method are proved theoretically that the proposed method can approximate to optimal solution well and achieve consensus by ensuring the proactive involvement of all participants under coordinated cyber attack. According to those obtained simulation results, it reveals that the proposed algorithm can effectively solve the energy management issue under coordinated DoS and FDI attack.

This article addresses the optimal containment problem of heterogeneous multiagent systems (MASs) with dynamic leaders via reinforcement learning (RL), where the dynamics of all agents are all completely unknown. A distributed model-free observer is constructed for each follower to estimate the leaders’ dynamics and the output trajectories inside the convex hull formed by the leaders. Based on the designed observers, the optimal containment problem is formulated as an optimal tracking control issue. Then the discounted performance functions are introduced to obtain algebraic Riccati equations (AREs). And a model-free RL algorithm is developed to learn the AREs online. To implement this algorithm, we design a single critic neural network structure for each follower to approximate Q-function, and estimate optimal control policy and worst-case adversarial input policy. Finally, a numerical simulation is provided to demonstrate the effectiveness of the proposed algorithm.

This article addresses the issue of adaptive event-triggered${H_{\infty} }$control for Markov jump systems based on the Takagi–Sugeno (T–S) fuzzy model. First, a new double asynchronous switching controller is presented to deal with the problem of the mismatch of premise variables and modes between the controller and the plant, which is widespread in real network environment. To further reduce the power consumption of communication, a switching adaptive event-triggered mechanism is adopted to relieve the network transmission pressure while ensuring the control effect. In addition, a new Lyapunov–Krasovskii functional (LKF) is constructed to reduce conservatism by introducing the membership functions (MFs) and time-varying delays information. Meanwhile, the invariant set is estimated to ensure the stability of the system. And the disturbance rejection ability is measured by the optimal${H_{\infty} }$performance index. Finally, two examples are presented to demonstrate the effectiveness of the proposed approach.

This work addresses the issue of$H_{\infty }$adaptive sliding-mode control (SMC) for nonlinear delayed singular systems (NDSSs) under impulsive attacks (IAs). The NDSSs subjected to IAs are modeled as fuzzy delayed singular impulsive systems (FDSISs), and a neoteric fuzzy integral sliding surface function is constructed based on the piecewise auxiliary functions method, which is continuous on$(0,+\infty)$without any other additional conditions. Then, a suitable SMC law and an adaptive SMC law are designed, such that the state trajectories of FDSIS can be driven to the predetermined sliding surface in finite time. In addition, an improved impulse-time-dependent Lyapunov-Krasovskii functional containing characteristics of IAs and time delays is designed, and it is demonstrated to be continuous along the FDSIS trajectories. Improved conditions are put forward in the form of strict linear matrix inequalities via congruent transformation technology, which can guarantee that the singular sliding-mode dynamics under IAs fulfills$H_{\infty }$stochastic admissibilization. Finally, the practicability of the approach presented is attested and the effects of IAs on convergence time are testified by the networked truck-trailer system.

This paper investigates the stability analysis and controller design issues for aperiodic sampled-data networked control systems with time-varying delays. Three main results are obtained. Firstly, the discretized model with delay is constructed as an feedback interconnected system formed by a structural uncertainty operator and a linear time-invariant system. Secondly, an exponential decay rate is introduced as a performance index of the system through model transformation, an equivalent stability condition for the system is also obtained, further, the conclusion is extended to systems with arbitrary initial states. On this basis, the exponential stability conditions with minimal computational complexity are given under an integral quadratic constraint. Thirdly, an iterative algorithm for the solution of the controller is given to deal with the effects of non-linear coupling terms. Finally, two numerical examples and an application example of an interleaved flyback modular integrated converter are used to illustrate the effectiveness and computational simplicity of the stability criterion and the controller design algorithm of this paper.

The proportion of distributed resources connected to the distribution network is gradually increasing. But in most scenarios, resources operate in passive response mode and cannot give full play to their active regulation potential. To awaken the regulation capability of distributed resources for active support of system frequency stability, a transmission and decision-making co-designed architecture is studied in this paper when a local supply-demand imbalance in the distribution network causes frequency instability. The architecture contains “data module”, “transmission module”, and “decision-making module”. Firstly, in the “data module”, based on the theory of multi-extreme learning machines and power flow calculation, the generation prediction of energy sources is performed to provide the data basis for generating regulation commands. Secondly, in the “transmission module”, through the nodal current equation-based sliding mode control and fast path reconstruction, the response strategy of the communication disturbance problem is proposed to provide the transmission support for generating regulation commands. Finally, based on the theory of “multiple factors matching” and “source-load interaction”, the source and load-side regulation commands are generated in the “decision-making module” by combining the transmitted data. Related case studies are carried out to verify the effectiveness of the proposed strategies.

This article investigates the event-triggered synchronization control problem of discrete-time neural networks (DNNs) in the case of periodic sampled-data. A discrete-time periodic event-triggered mechanism is adopted to evaluate the measurements, which avoids formulating the triggering function in a continuous manner and saves energy consumption. Under this framework, an event-triggered dynamic output-feedback controller is designed to achieve the goal of synchronization. A piecewise Lyapunov functional is constructed to analyze the sawtooth-like pattern of sampled-error signals. Thereafter, the synchronization criteria are formulated for the considered DNNs. The co-designed issue is further discussed for the control gains and triggering parameter. Finally, a simulation example is presented to show the effectiveness of the proposed method.

This article reports the synchronization control of discrete-time complex networks using an event-triggered method. The main contributions are twofold: 1) a discrete-time scenario of the dynamic periodic event-triggered mechanism is developed to schedule the transmissions of measurements. The proposed mechanism monitors the synchronization error in a periodic manner, which is beneficial to reduce the calculation resources of sensors. Simultaneously, the proposed mechanism increases the triggering threshold so that it contributes to enlarging the average interevent interval and 2) a new Lyapunov functional is developed to deal with the periodic samplings. On the one hand, the proposed functional involves a delay-dependent term, which is convenient to formulate the synchronization criterion by the delay analysis technique. On the other hand, the functional takes the sawtooth constraint of periodic samplings into consideration by introducing a piecewise functional. Finally, a succinct criterion is derived such that the considered networks are synchronized with a predetermined error level. A simulation example is provided to show our advantages in comparison with the existing approaches.

This article is concerned with developing a featured multi-instant Luenberger-like observer of discrete-time Takagi-Sugeno fuzzy systems with unmeasurable state variables, that is, not only to reduce the conservatism but also (at the same time) to alleviate the computational complexity over the recent approach reported in the literature. Contrary to previous approaches, an enhanced gain-scheduling mechanism is proposed for constructing much abundant working modes by online evaluating the updated variation information of normalized fuzzy weighting functions across two adjacent sampling instants and, thus, a different group of observer gain matrices with less conservatism is designed in order to employ the exclusive features for each working mode. Moreover, all the redundant terms containing both surplus and unknown system information are discriminated and removed in this study and, thus, the required computational complexity is reduced to a certain extent than the counterpart one. Finally, numerical examples are provided to illustrate the superiority of the developed approach.

In this study, the event-triggered problem of networked control systems (NCSs) is investigated, and a novel information transmission scheme is established. Under this scheme, the segment-weighted information (SWI) in a sliding historical window (SHW) is calculated and then sampled. Compared with the traditional direct sampling method, in this approach, the control input includes historical information in the SHW, thereby leading to less information loss due to sampling. This study also emphasizes on designing an SWI-based event-triggered mechanism (ETM) for scheduling network transmission. Different from most of the existing ETMs, the proposed SWI-based ETM leverages historical information to determine which data are necessary for the whole control system. Our approach can greatly reduce the number of unexpected triggering events of a control system with stochastic disturbances owing to the introduction of the SWI in the ETM. Moreover, Zeno phenomena are prevented thanks to periodic sampling. Sufficient conditions are derived based on the Lyapunov functional approach, and a numerical simulation example is provided to demonstrate the effectiveness of the proposed method.

In this article, a networked fault detection (FD) problem is investigated for interval type-2 T–S fuzzy systems. A novel adaptive memory-event-triggered mechanism (METM) is proposed by introducing historical information of the measured output in a prescribed sliding window. The current measured output in the traditional event-triggered mechanism is replaced by a weighting function-based historical information. As a result, the data releasing rate can be effectively reduced and maltriggering events aroused by unknown abrupt disturbance or measurement noise can be avoided as well. Meanwhile, an adaptive threshold depending on the historical information is utilized to further adjust the data releasing rate. The FD filter is designed and derived in terms of linear matrix inequalities to guarantee the$H_{\infty }$performance of fault detected systems. Finally, a hardware-in-loop simulation experiment platform is built to manifest the effectiveness of the proposed METM-based FD method.

This article focuses on the distributed robust fault estimation problem for a kind of discrete-time interconnected systems with input and output disturbances. For each subsystem, by letting the fault as a special state, an augmented system is constructed. Particularly, the dimensions of system matrices after augmentation are lower than some existing related results, which may help to reduce calculation amount, especially, for linear matrix inequality-based conditions. Then, a distributed fault estimation observer design scheme that utilizes the associated information among subsystems is presented to not only reconstruct faults, but also suppress disturbances in the sense of robust$H_{\infty }$optimization. Besides, to improve the fault estimation performance, a common Lyapunov matrix-based multiconstrained design method is first given to solve the observer gain, which is further extended to the different Lyapunov matrices-based multiconstrained calculation method. Thus, the conservatism is reduced. Finally, simulation experiments are shown to verify the validity of our distributed fault estimation scheme.

This article addresses the adaptive fuzzy control problem for switched nonlinear systems with state constraints. The unified barrier function (UBF) is introduced to solve the time-varying state constraints, which removes the feasibility conditions. By integrating command filter into backstepping control to avoid the "explosion of complexity." In addition, a novel event-triggered strategy is designed to deal with the asynchronous switching between subsystems and controllers without limiting the maximum asynchronous time, and mitigate the communication burden. Also, a new threshold function is introduced to overcome the difficulty of discontinuous triggering error at the switching instants. Then, by combining the improved admissible edge-dependent average dwell-time (AED-ADT) method with Lyapunov stability analysis, it is proved that all system signals are bounded and do not violate the predefined constraints under given switching rule. Finally, the numerical simulation results verify the superiority of the proposed algorithm, and the algorithm is applied to a ship maneuvering system.

The problem of enhancing the robust performance of nonlinear fault estimation (FE) is addressed by proposing a novel real-time gain-scheduling mechanism for discrete-time Takagi-Sugeno fuzzy systems. The real-time status of the operating point for the considered nonlinear plant is characterized by using these available normalized fuzzy weighting functions at both the current and the past instants of time. To achieve this, the developed fuzzy real-time gain-scheduling mechanism produces different switching modes by introducing key tunable parameters. Thus, a pair of exclusive FE gain matrices is designed for each switching mode on the strength of time-varying balanced matrices developed in this study, respectively. Since the implementation of more FE gain matrices can be scheduled according to the real-time status of the operating point at each sampling instant, the robust performance of nonlinear FE will be enhanced over the previous methods to a great extent. Finally, considerable numerical comparisons are implemented in order to illustrate that the proposed method is much superior to those existing ones reported in the literature.

The problem of relaxed state estimation of discrete-time Takagi-Sugeno fuzzy systems is studied by constructing a novel multi-instant gain-scheduling fuzzy observer. First, a multi-instant gain-scheduling mechanism with a single adjustable parameter is given for the first time in order to produce more reasonable switch modes over previous results reported in recent literature. Second, for every switch mode, a batch of specified observer gain matrices is determined by developing an efficient balanced matrix approach so that the updated values of adjacent normalized fuzzy weighting functions can be flexibly exploited. Since the implied information of each specific switch mode is capable of being absorbed and utilized more thoroughly by the aid of the refined higher-order balanced matrices, the conservatism can be prominently reduced at the price of consuming extra computational burden within the allowable range. Finally, two benchmark examples are provided to test and verify the progressiveness of our proposed approach.

This study is devoted to event-triggered fuzzy load frequency control (LFC) for wind power systems (WPSs) with measurement outliers and transmission delays. Due to the integration of wind turbine (WT) with nonlinearity, the T–S fuzzy model of WPS is established for stability analysis and controller design. To mitigate the network burden, a new sampled memory-event-triggered mechanism (SMETM) related to historical system information is presented. It has the following two merits: 1) the utilization of continuous memory outputs over a given interval is useful to reduce the information loss in the period of samples and the redundant triggering events induced by disturbances and noises and 2) an extra upper constraint is added in the triggering condition to generate a new event only when the error signal belongs to a bounded range, thus, the false events caused by measurement outliers can be differentiated out and then be dropped. By representing the memory signal with transmission delay as a time-varying distributed delay term, a T–S fuzzy time-varying distributed delay system is built up to model the$H_{\infty}$LFC WPS. With the help of the Lyapunov method and the integral inequality relying on distributed delay, some criteria are derived to solve the triggering matrix and fuzzy controllers. Finally, the merits of the proposed SMETM are tested by simulation results.

This article focuses on designing a novel stochastic data-based denial-of-service (DoS) attack strategy that can intercept measurements and reduce the quality of remote state estimation in interval type-2 (IT2) T–S fuzzy systems. The new proposed DoS attack strategy has two main characteristics. First different from most of the existing DoS models, it is data-based, which mainly attacks the packets playing important roles in the system performance. Therefore, compared with the existing indiscriminate DoS attack approaches, the data-based DoS attack is more intelligent and can cause larger disruptions. Second, the proposed attack strategy is random, which has better concealment than the periodic or consecutive DoS attack models. Then, by using a stochastic method, the relationship among attack effect, attack probability, and attack parameter are analyzed and shown in Theorem1. Furthermore, if the attacks are energy-constrained, the relation between the attack rate threshold and the upper bound of the attack parameter is expressed analytically, which is shown in Theorem2. Simulation results demonstrate that, compared with some existing DoS models, the proposed stochastic data-based DoS attack strategy brings about greater destructiveness to the estimation quality of the systems, which demonstrates the effectiveness of the proposed attack strategy from the attacker’s perspective.

This article focuses on the fault reconstruction and fault-tolerant control problems of switched fuzzy systems with actuator and sensor faults, where the faults may be fast time-varying and unbounded. The multiple coordinate transformations are introduced, then the reduced-order observer based fault reconstruction method is considered, which can reconstruct the system state, actuator, and sensor faults, simultaneously. For the case that there is no disturbance, the LMI conditions are achieved to ensure that for any switching signal, the error dynamics can be exponentially stable. Utilizing the estimated fault information, the fuzzy dynamic output feedback fault tolerant controllers are designed to compensate the fault effect and stabilize the systems. The root-mean-square gain is considered to reduce the disturbance influence on fault estimation and fault-tolerant control, in which the zero initial condition is not needed. Finally, simulations are conducted to demonstrate the effectiveness of the considered techniques.

This article is concerned with the observer-based security fuzzy control problem for a class of nonlinear networked systems with imperfectly matched membership functions (MFs) under weighted try-once-discard (WTOD) protocol. The nonlinear networked system is constructed based on interval type-2 Takagi–Sugeno model, which can properly handle parameter uncertainties via lower and upper MFs. To mitigate the communication load, WTOD protocol is exploited to schedule the transmission order of the signals, in which those signals may be subjected to randomly occurring deception attacks. The observer is constructed under immeasurable premise variables, and then the controller with imperfect matching MFs is designed according to the estimated states. Moreover, the observer-based controller is derived with Lyapunov stability theory such that the stochastic stability of the augmented closed-loop system with predefined disturbance attenuation performance can be guaranteed. Subsequently, sufficient conditions are provided for the desired observer and controller gain matrices based on linear matrix inequalities technique. Numerical simulation example demonstrates the validity of the proposed observer-based security fuzzy control design scheme.

This article researches$H_{\infty }$asynchronous admissibilization for nonlinear singular delayed hybrid hydraulic turbine governing systems with impulsive perturbations. By exploiting Takagi–Sugeno fuzzy technique, the fuzzy singular delayed hybrid hydraulic turbine governing system with impulsive perturbations is built, which cannot only accurately and concisely describe the dynamic behaviors of the pipeline, but also resist damages for the hydraulic turbine system caused by sudden reasons. Then, the asynchronous fuzzy state-feedback controller (FSFC) is designed by using parallel distributed compensation technique, and the asynchronous mechanism between the modes of FSFC and the modes of controlled plant is depicted by a hidden Markovian model. By constructing an improved timer-dependent Lyapunov–Krasovskii functional, the new criteria about$H_{\infty }$admissibilization for fuzzy singular delayed hybrid hydraulic turbine governing systems with impulsive perturbations can be acquired. The gains of asynchronous FSFC are expressed by solving linear matrix inequalities. Impulsive operators are successfully generalized and extended from$\mathbb{R}$to$\mathbb{R}^{n\times n}$, which makes the approach presented in this article more universal. Finally, the simulation results prove the correctness and availability of the method provided in this article.

This article studies the$\mathcal{l}_{1}$filtering problem for positive Takagi–Sugeno fuzzy systems. A pair of filters is sought to assure the stability and positivity of filtering error systems with guaranteed$\mathcal{l}_{1}$performance indices. For this purpose, a pair of linear copositive Lyapunov functions that capture the positivity characteristics of filtering error systems is adopted to derive sufficient conditions for the existence of filters, which boils down to the bilinear programming problem. To solve this dilemma, we propose a convex approximation strategy, and thus, a sequence of convex surrogates is developed to reasonably replace the nonconvex constraints, based on which a successive linear programming algorithm is constructed. Therefore, the filters can be achieved by solving a battery of linear programming. Finally, the efficiency of the designed filtering scheme is justified by simulation validations.

This article is focused on the adaptive event-based interval type-2 (IT-2) fuzzy security control problem for networked control systems with multiple network attacks. In order to save the network resources, this article proposes an improved adaptive event-triggered model, which can adjust the threshold dynamically according to the change of current signal and previous triggering signal. In addition, due to the change of external environment, the impact of randomly occurring output bias is considered in the systems. Taking the effects of multiple network attacks and adaptive event-triggered scheme into consideration, a class of augmented error fuzzy system model is established. Next, some sufficient conditions are obtained for the stochastic stability with an$H_{\infty }$performance index via the Lyapunov stability analysis method. The corresponding parameters of the IT-2 fuzzy controllers and observers are also derived by some linear matrix inequalities. Finally, two simulation examples are given to support the advantages of the proposed method.

This article presents a novel finite-time adaptive fuzzy event-triggered control strategy for stochastic nonlinear systems in nonstrict feedback structure, where time-varying output constraints and input delay are considered. To deal with the output constraints, a stochastic nonlinear mapping is developed to transform the original system into an equivalent one without output constraints. Furthermore, the Pade approximation method is applied to address the input delay by introducing a new intermediate variable. Then, a novel adaptive event-triggered mechanism is proposed to reduce the number of data transmissions and mitigate the effects of tracking error. The stability analysis shows that the closed-loop signals are semiglobal finite-time stable in probability, while the tracking performances are well and satisfy the output constraint condition. Finally, simulation results demonstrate the effectiveness of the developed approach.

The constrained Takagi–Sugeno fuzzy systems with local nonlinear models (N-TS fuzzy systems) are much more practical than the conventional T–S fuzzy models, but their applications are seriously affected by either the great conservatism or the heavy computational burden. In this short article, an enhanced local stabilization of constrained N-TS fuzzy systems is investigated with the purpose of not only reducing conservatism but also relieving computational burden. To do this, a new class of threshold functions are established in order to achieve real-time online assessment of the variation of the normalized fuzzy weighting functions (NFWFs) at different sampling instants, i.e., the one-step-past one and the current one. Thus, a key alternative is proposed for eliminating all the involved terms containing the one-step-past NFWFs while their main information is retained. Since our obtained design criteria are merely dependent on the current NFWFs, the conservatism can be reduced at the expense of lighter computational burden. The benefits of our proposed results are validated by implementing several objective comparisons with those recent results.

In this article, we study the design of fuzzy synchronization controller of Takagi–Sugeno (T–S) fuzzy neural networks with distributed time-varying delay and probabilistic network communication delay. Compared with the existing model of neural networks with distributed time-varying delay without kernel, a more general model containing a distributed delay kernel is considered. By utilizing the probability distribution of random communication delays, a distributed but deterministic delay model is established. In this model, the delay probability density function is treated as the distributed delay kernel. By developing a new Lyapunov–Krasovskii functional related to the distributed delay kernels and using an integral inequality, new sufficient conditions for the existence of a synchronization controller are presented. Finally, a numerical simulation and an application of encrypting the image are carried out to illustrate the effectiveness of the developed strategy.

This article proposes a new multiobjective optimization approach for designing a self-generated interpretable fuzzy logic system (FLS). The types of fuzzy sets (FSs) can be constructed automatically by self-organizing method, so as to form a hybrid fuzzy system. Different from the existing evolutionary type-1 fuzzy system, which is full of type-1 FSs, and the evolutionary interval type-2 fuzzy system, which is full of interval type-2 FSs, there are both type-1 FSs and interval type-2 FSs in the hybrid fuzzy system. A new transparency-oriented objective function is defined, and the constraint of the footprint of uncertainty of the interval type-2 (IT2) FS is considered for the first time. A new FS merging criterion focusing on the proximity of the cores of FSs is proposed, which is easy to calculate and maintains the characteristics of classical similarity measures. Combined with the new merging criterion, the online cluster and FS updating algorithm is employed to initialize the reference rule base and the type of FS, as it is assumed that no training data are collected in advance. Based on the reference rule base, the advanced multiobjective front-guided continuous ant colony optimization algorithm is introduced to optimize all the free parameters of the FLS. With the operation mentioned above, the self-generated FLSs achieve a good balance between interpretability and performance. The effectiveness of the proposed method is verified by three nonlinear system tracking problems.

Cyber security of modern power systems has become increasingly significant due to their open communication architecture and expanding network connectivity exposed to malicious cyber attacks. Resilient control represents an effective means to preserve the survivability of the power system under cyber attacks. In this paper, we address the resilient load frequency control (LFC) design for multi-area power systems under a new class of time-constrained denial-of-service (DoS) attacks. First, different from the widely-explored duration- and frequency-constrained DoS attack models, we consider a general time-constrained DoS attack model where only the attack durations are confined into some bounds, which represents less a priori knowledge of an attacker’s actions. Second, instead of using a traditional yet conservative time-invariant Lyapunov function (TILF), we develop an attack-parameter-dependent time-varying Lyapunov function (TVLF) approach to enable a resilient LFC design without jeopardizing the desired closed-loop system stability and performance. Furthermore, we provide a formal stability and performance analysis condition as well as a design criterion for the desired DoS-resilient output feedback LFC controller. We also show that the minimum allowable sleeping period and the maximum allowable active period of the attacked LFC system can be explicitly disclosed. Finally, we present two simulation case studies on a two-area LFC system and a three-area LFC system to demonstrate the effectiveness of the obtained results.

An accurate and comprehensive risk assessment in a distribution cyber-physical system (DCPS) is essential to ensure its smooth operation, effective control, and exposure of hidden dangers and security implications. Unfortunately, prior risk assessment methods are mostly limited in two aspects. First, the current studies do not respect the complex network topology and intertwined devicewise dependencies, thereby failing to delineate and model the risk propagation mechanism in DCPS accurately. Second, the prior work tends to focus on gauging the risks underlying physical systems independently, overlooking the quantification of risk impact on physical systems incurred by the cyberattack. To fill the gap, in this article, we propose a unified risk assessment model that gauges the comprehensive security implication of DCPS in a Bayesian regime, in which the three key components, namely, the prior probability, posterior probability, and minimum load-loss ratio, are calculated via the cumulative densities, epidemic model, and optimal load shedding, respectively. We benchmark our proposed model on a public testbed, IEEE 39-bus system, with extensive experiments. The results substantiate the viability and effectiveness of our model and suggest that the vulnerability of DCPS is positively correlated with the three components in our Bayesian modeling. We hope this finding can shed some light on future research by providing a plausible apparatus for measuring the security implications of physical systems in DCPS under cyberattacks.

In traditional leak location methods, the position of the leak point is located through the time difference of pressure change points of both ends of the pipeline. The inaccurate estimation of pressure change points leads to the wrong leak location result. To address it, adaptive dynamic programming is proposed to solve the pipeline leak location problem in this article. First, a pipeline model is proposed to describe the pressure change along pipeline, which is utilized to reflect the iterative situation of the logarithmic form of pressure change. Then, under the Bellman optimality principle, a value iteration (VI) scheme is proposed to provide the optimal sequence of the nominal parameter and obtain the pipeline leak point. Furthermore, neural networks are built as the VI scheme structure to ensure the iterative performance of the proposed method. By transforming into the dynamic optimization problem, the proposed method adopts the estimation of the logarithmic form of pressure changes of both ends of the pipeline to locate the leak point, which avoids the wrong results caused by unclear pressure change points. Thus, it could be applied for real-time leak location of long-distance pipeline. Finally, the experiment cases are given to illustrate the effectiveness of the proposed method.

This article is concerned with distributed resilient load frequency control (LFC) for multi-area power interconnection systems against jamming attacks. First, considering uncertainties and high dimension nonlinearity, the model-free adaptive control (MFAC) model is adopted for the power system, in which only input and output (I/O) data are used. Second, jamming attacks are modeled in a stochastic process, and a multistep predictive compensation algorithm is developed to mitigate the impact of jamming attacks. Then, the distributed MFAC protocol with predictive compensation algorithm is designed such that the frequency tracking errors under the predictive compensation algorithm of multi-area power interconnection systems converge consensually into a small neighborhood of origin in the mean square sense. Simulation results show the effectiveness of the approach.

This article focuses on designing an event-triggered impulsive fault-tolerant control strategy for the stabilization of memristor-based reaction-diffusion neural networks (RDNNs) with actuator faults. Different from the existing memristor-based RDNNs with fault-free environments, actuator faults are considered here. A hybrid event-triggered and impulsive (HETI) control scheme, which combines the advantages of event-triggered control and impulsive control, is newly proposed. The hybrid control scheme can effectively accommodate the actuator faults, save the limited communication resources, and achieve the desired system performance. Unlike the existing Lyapunov-Krasovskii functionals (LKFs) constructed on sampling intervals or required to be continuous, the introduced LKF here is directly constructed on event-triggered intervals and can be discontinuous. Based on the LKF and the HETI control scheme, new stabilization criteria are derived for memristor-based RDNNs. Finally, numerical simulations are presented to verify the effectiveness of the obtained results and the merits of the HETI control method.

With consideration of false data injection (FDI) on the demand side, it brings a great challenge for the optimal defensive strategy with the security issue, voltage stability, power flow, and economic cost indexes. This article proposes a Takagi-Sugeuo-Kang (TSK) fuzzy system-based reinforcement learning approach for the resilient optimal defensive strategy of interconnected microgrids. Due to FDI uncertainty of the system load, TSK-based deep deterministic policy gradient (DDPG) is proposed to learn the actor network and the critic network, where multiple indexes' assessment occurs in the critic network, and the security switching control strategy is made in the actor network. Alternating direction method of multipliers (ADMM) method is improved for policy gradient with online coordination between the actor network and the critic network learning, and its convergence and optimality are proved properly. On the basis of security switching control strategy, the penalty-based boundary intersection (PBI)-based multiobjective optimization method is utilized to solve economic cost and emission issues simultaneously with considering voltage stability and rate-of-change of frequency (RoCoF) limits. According to simulation results, it reveals that the proposed resilient optimal defensive strategy can be a viable and promising alternative for tackling uncertain attack problems on interconnected microgrids.

This article concentrates on optimal tracking control for a class of nonlinear networked systems subjecting to limited network bandwidth and unmatched disturbance. Given the models of the control and reference systems, the considered optimal tracking control issue is initially formulated as a minimax optimization problem. Then, with the introduction of an event-triggered mechanism used for saving bandwidth, the formulated problem is transformed into solving an event-based Hamilton-Jacobi-Isaacs (HJI) equation by recurring to the Bellman optimality theory. Based on the HJI equation, we demonstrate that the stability of the concerned system in the sense of uniformly ultimately bounded (UUB) can be guaranteed with the envisioned optimal control and worst disturbance policies. Here, the disturbance policy can be varied periodically while the control policy can only be updated at event-triggering instants, which differs from the existed researches. Furthermore, we propose a reinforcement learning (RL)-based algorithm to handle the constructed HJI equation and thus settle the studied tracking control problem. The effectiveness of the algorithm is finally validated by both theoretical analysis and simulations.

This article considers the control synthesis for positive nonlinear systems modeled by Takagi–Sugeno (T–S) fuzzy characterizations. A fuzzy static output feedback (SOF) controller is sought to assure the closed-loop stability and positivity with a guaranteed$\mathcal {l}_{1}$performance level. The favorable positivity enables us to adopt a linear co-positive function as the Lyapunov candidate, and we construct the essential conditions for the existence of fuzzy SOF controllers in the form of bilinear programming (BP) problem. To provide a direct and generic algorithm for solving the BP problem, we propose a vital approximation strategy by which the general bilinear constraints are replaced with a sequence of convex surrogate ones. Recognizing the fact that a fundamental promise of the proposed successive linear programming algorithm is a feasible initial solution, we also develop an iterative procedure to calculate an initial controller gain. Finally, we clarify the applicability of the developed scheme with two examples.

This article mainly focuses on the problem of resilient$H_{\infty }$filtering for cyber–physical systems (CPSs) subject to denial-of-service (DoS) attacks and sensor saturation. A new event-triggered mechanism (ETM) considering both DoS attacks and limited network bandwidth is put forward to guarantee the secure performance of the filter. Under this mechanism, inherent periodical transmission attempts are generated during DoS active periods, by which the latest measurement output of the system can be successfully transmitted to the filter after the end of the DoS attack; while during DoS sleep periods, the ETM degenerates into a traditional one. Furthermore, a valid DoS attack model is proposed to further characterize the following two scenarios occurring between adjacent sampling instants: 1) the end of the DoS attack and 2) both the start of the DoS attack and the end of the DoS attack. Sufficient conditions for designing the secure filters of CPSs against DoS attacks are achieved by using the piecewise Lyapunov–Krasovskii functional approach. Finally, the validity of our designed approach is manifested by an illustration of quarter-vehicle suspension systems (SSs).

This article considers the distributed resilient cooperative control for photovoltaic generators (PVs) suffered from two types of denial-of-service (DoS) attack, where the global DoS attack jams all the communication channels and the distributed one jams each of the channels independently. The proposed control method realizes the fair utilization of all PVs, and restore the active power flow across certain transmission line and the voltage of the critical bus to their reference values. The self-triggered mechanism is introduced to ensure the control performance under the DoS attack and reduce the data flow in the communication network simultaneously. In addition, the parameter selection guidance for the resilient control method with fluctuation range, triggering frequency, and stabilization time is provided. The effectiveness of the theoretical result is verified by simulation.

In this article, a distributed-delay-dependent method is proposed to deal with the stabilization for interval type-2 Takagi–Sugeno fuzzy systems subject to stochastic network delay and actuator saturation. To deal with the stochastic feature of network-induced delays, their probability density function is utilized to establish the distributed delay model, which is more practical than the traditional time-varying network delay model. Meanwhile, in order to enlarge the estimation of the domain of attraction, a polytopic strategy composed of a state vector and a distributed-delay-dependent vector is proposed to treat the saturation nonlinearity. By constructing a distributed-delay-dependent Lyapunov–Krasovskii functional, new and less conservative conditions are achieved to guarantee the stability of the established closed-loop system. Additionally, two simulation examples are carried out to illustrate the advantages of the proposed strategy.

This article aims to a predefined tracking precision consensus control issue for nonlinear uncertain multiagent systems (MASs) with disturbance and input saturation. Unlike the existing results of prespecified accuracy for MASs, the phenomenon of unknown control gains is solved in this article. A saturation model based on the Gaussian error function is applied due to the appearance of input saturation. The unknown disturbance is considered which can be solved by a disturbance observer. Also, to handle the problem of an unknown coefficient for the controller, the Nussbaum function is employed. Moreover, the radial basis function neural networks (RBF NNs) are utilized to estimate unknown nonlinear functions. On account of the Lyapunov stability method and backstepping technique, adaptive laws are created and the desired distributed controller is designed which guarantees that the consensus errors can converge to prescribed values. Finally, several simulation examples demonstrate the valid of the proposed method.

The synchronization in probability of reaction-diffusion neural networks (RDNNs) with stochastic sampling is studied in this article. By introducing a stochastic switching parameter, a new switching system protocol is proposed for stochastic sampling control systems. The switching system protocol effectively improves the existing methods. By the protocol, the stochastic switching sampled-data controller is designed, and the considered system is transformed into a switching system. Different from the existing sampled-data controllers with determined control gains, the stochastic switching sampled-data controller is with switching gains, which is more elastic. Then, by constructing a new stochastic switching Lyapunov–Krasovskii functional (LKF), using the law of large numbers and the Lagrange mean value theorem, new synchronization in probability criteria are established for RDNNs. In the mean time, the wanted stochastic switching sampled-data controller gains are obtained. Moreover, the synchronization in probability issue is also studied for NNs with stochastic sampling. Finally, the effectiveness of the proposed results are verified by two numerical examples.

The asymptotical synchronization in mean square of reaction–diffusion neural networks (RDNNs) with random delays is studied in this article. By sampling on both the time domain and spatial domain, a time–space sampled-data controller (TSSDC) is designed, which can efficiently save the network communication resources for RDNNs. A new processing method for the TSSDC is provided. Compared with the existing methods, the processing method here can capture more sampling information and is more concise. An extended Poincaré–Wirtinger inequality is proposed, which is in matrix form and less conservative. Then by constructing a sampling-dependent LKF, using the extended Poincaré–Wirtinger inequality and Hölder inequality, new mean square asymptotical synchronization criteria are set up for RDNNs with random delays, and the desired TSSDC gain is obtained. At length, a numerical example is given to verify the effectiveness and superiority of the obtained results.

In this article, relaxed local stabilization criteria of constrained N-TS fuzzy systems are provided by developing a weighted ranking protocol. Different from the recent criteria reported in the literature, a set of operating modes is produced by employing the weighted ranking information of the available normalized fuzzy weighting functions. With regard to each enabled operating mode, its proprietary boundary information constraint is fully considered by means of introducing a class of cascade-type free variables, and thus the conservatism can be reduced to a large extent than before. More importantly, the applied variable weights for adjusting the range of different operating modes play an important role in further enlarging the estimated attraction regions. Finally, the superiority of the proposed approach is tested and verified by giving several comparisons on two key indicators for the same benchmark example.

In this paper, the adaptive fuzzy control of switched stochastic nonlinear systems with set-time prescribed performance based on event-driven mechanism is studied. The creative part of this paper is that based on the set-time performance function, a modified event-triggered strategy that considers asynchronous switching to deteriorate system performance without strict assumptions is presented, which avoids Zeno behavior and saves communication resources. Then, by using backstepping recursive design technique, It$\hat {o}$’s differential lemma and mode-dependent average dwell time (MDADT) method, a novel adaptive performance control scheme is proposed, which can ensure that all the variables in the system are semiglobally uniformly ultimately bounded (SGUUB) in probability and the tracking error gets into prescribed boundary no later than an arbitrarily adjusted setting time. Finally, the proposed algorithm is applied to a RLC circuit and its practicability is verified via simulation results.

The problem of robust nonlinear fault estimation for discrete-time Takagi-Sugeno fuzzy systems is investigated by proposing a depth partitioning approach. Compared with those existing results, the working space spanned by the updated normalized fuzzy weighting functions can be partitioned into any number of non-overlapping subspaces in a systematic way and thus a new gain-scheduling fault estimation observer is developed with proprietary gain matrices concerning the current operating mode. More importantly, the conservativeness will become less and less if the prescribed number of non-overlapping subspaces varies from small to large. In other words, it provides a chance to achieve much better performance of fault estimation while a smaller degree of the homogenous matrix polynomial can be chosen, which is very important for practical applications of theoretical results. Finally, the given depth partitioning approach is applied to deal with the fault estimation of the tunnel diode circuit and its advantages are validated via simulation comparisons.

The heuristic dynamic programming (HDP) ( λ )-based optimal control strategy, which takes a long-term prediction parameter λ into account using an iterative manner, accelerates the learning rate obviously. The computation complexity caused by the state-associated extra variable in λ -return value computing of the traditional value-gradient learning method can be reduced. However, as the iteration number increases, calculation costs have grown dramatically that bring huge challenge for the optimal control process with limited bandwidth and computational units. In this article, we propose an event-triggered HDP (ETHDP) ( λ ) optimal control strategy for nonlinear discrete-time (NDT) systems with unknown dynamics. The iterative relation for λ -return of the final target value is derived first. The event-triggered condition ensuring system stability is designed to reduce the computation and communication requirements. Next, we build a model-actor-critic neural network (NN) structure, in which the model NN evaluates the system state for getting λ -return of the current time target value, which is used to obtain the critic NN real-time update errors. The event-triggered optimal control signal and one-step-return value are approximated by actor and critic NN, respectively. Then, the event trigger-based uniformly ultimately bounded (UUB) stability of the system state and NN weight errors are demonstrated by applying the Lyapunov technology. Finally, we illustrate the effectiveness of our proposed ETHDP ( λ ) strategy by two cases.

Due to the high resistance/reactance (R/X) ratio of a low-voltage microgrid (LVMG), virtual complex impedance-based P-· V/Q-ω droop control is adopted in this article as the primary control (PC) technique for stabilizing the system. A distributed event-triggered restoration mechanism (ETSM) is proposed as the secondary control (SC) technique to restore the output-voltage frequency and improve power sharing accuracy. The proposed ETSM ensures that neighboring communication happens only at some discrete instants when a predefined event-triggering condition (ETC) is fulfilled. In general, the design of the ETC is the crucial challenge of an event-triggered mechanism (ETM). Thus, in this article, a static ETM (SETM) is proposed as the ETC at first, where two static parameters are utilized to reduce the triggering frequency. Bounded stability is ensured under the SETM, which means that the output-voltage frequency is restored to the vicinity of its nominal value, and close to fair utilization of the distributed generators (DGs) is achieved. To further improve the power sharing accuracy and accelerate the regulation process, a dynamic ETM (DETM) is then introduced. In the DETM, two dynamic parameters that converge to zero in the steady state are designed, which promises asymptotic stability of the system. Besides, Zeno behavior is excluded in both mechanisms. An LVMG consisting of four DGs is constructed in MATLAB/Simulink to illustrate the effectiveness of the proposed methods, and the simulations correspond with our theoretical analysis.

filtering for Takagi-Sugeno fuzzy-model-based nonlinear networked systems with multisensors. A weighted fusion approach is adopted before information from multisensors is transmitted over the network. A novel event-triggered mechanism is proposed, which allows us not only to reduce the data-releasing rate but also to prevent abnormal data being potentially transmitted over the network due to sensor measurement or other practical factors. The problem of denial-of-service (DoS) attacks, which often occurs in a communication network, is also considered, where the DoS attack model is based on an assumption that the periodic attack includes active periods and sleeping periods. By employing the idea of the switching model for filtering error systems to deal with DoS attacks, sufficient conditions are derived to guarantee that the filtering error system is exponentially stable. Simulation results are given to demonstrate the effectiveness of the theoretical analysis and design method.

In daily pipeline inspection, it is significant to ensure good network communication and security. With the development of drone technology, it is possible to apply drones as air routers to collect information from pipeline networks and transmit it to pipeline inspectors. It is also crucial to achieve optimal drone deployment in pipeline networks. This article proposes a two-phase evolution optimal 3-D drone layout algorithm to deploy drones in pipeline networks. First, a 3-D pipeline graph model is designed to represent the possible projection position of drones, and the objective function is proposed for optimal drone deployment. Then, in the first phase, based on the features of the 3-D pipeline graph, the drone flight rules and constraint conditions are presented to calculate the number of drones and the initial layout sequence. In the second phase, according to the objective function and the above results, every drone is continuously moved in a small area to achieve a tradeoff between signal coverage and interference. Moreover, the key parameters of the objective function can be discussed to further optimize drone deployment. Simulation results are presented to illustrate the effectiveness and advantages of the proposed algorithm.

The microgrid with the high proportion of renewable sources has become the trend of the future. However, the negative features, such as renewable energy perturbation, nonlinear counterpart, and so on, are prone to causing the low-power quality of the ac microgrid. To deal with these problems, this article proposes an event-triggered consensus control approach. First, the nonlinear state-space function regarding the ac microgrid is built, which is further transformed into the standard linear multiagent model by using the singular perturbation method. It provides indispensable preprocessing for the direct application of advanced linear control approaches. Then, based on this standard linear multiagent model, the secondary consensus approach with the leader is designed to compensate for the output voltage deviation and achieve accurate power sharing. In order to decrease the communication among various distributed generators, the event-triggered communication method is further proposed. Meanwhile, the Zeno behavior is avoided through the theoretical proof. Finally, simulation results are presented to demonstrate the effectiveness of the proposed approach.

This article investigates the issue of observer-based security control for the interconnected semi-Markovian jump systems with completely unknown and uncertain bounded transition probabilities (TPs). Considering the limited bandwidth of communication network in each subsystem, an adaptive event-triggered mechanism (AETM) is developed to relieve more network burden than the conventional event-triggered mechanism (ETM), where the designed adaptive law can dynamically adjust the triggering threshold. In addition, two Bernoulli distributed variables are utilized to describe the influence of denial-of-service (DoS) attacks and false-data injection (FDI) attacks in the proposed observer-based security control strategy. Moreover, some sufficient criterions are derived for the stochastic stability with an$H_{\infty }$attenuation level of augmented systems. Meanwhile, the observer and controller gain matrices can be attained simultaneously with the help of linear matrix inequalities (LMIs). Finally, we provide a practical example to demonstrate the effectiveness of theoretical results.

This article is concerned with the problem of the$H_{\infty }$output feedback control for a class of event-triggered networked systems subject to multiple cyber attacks. Two dynamic event-triggered generators are equipped at sensor and observer sides, respectively, to lower the frequency of unnecessary data transmission. The sensor-to-observer (STO) channel and observer-to-controller (OTC) channel are subject to deception attacks and Denial-of-Service (DoS) attacks, respectively. The aim of the addressed problem is to design an output feedback controller, with the consideration of the effects of dynamic event-triggered schemes (DETSs) and multiple cyber attacks. Sufficient condition is derived, which can guarantee that the resulted closed-loop system is asymptotically mean-square stable (AMSS) with a prescribed$H_{\infty }$performance. Moreover, we provide the desired output feedback controller design method. Finally, the effectiveness of the proposed method is demonstrated by an example.

In terms of pipeline leak detection, the unavoidable fact is that existing data could not provide enough effective leak data to train a high accuracy model. To address this issue, this article proposes mixed generative adversarial networks (mixed-GANs) as a practical way to provide additional data, ensuring data reliability. First, multitype generative networks with heterogeneous parameter-updating mechanisms are designed to explore a variety of different solutions and eliminate the potential risks of instable training and scenario collapse. Then, based on expert experience, two data constraints are proposed to describe leak characteristics and further evaluate the quality of generated leak data in the training process. Through integrating the particle swarm optimization algorithm into generative model training, mixed-GAN has better generation performance than the conventional gradient descent algorithm. Based on the above-mentioned contents, the proposed model is able to provide satisfactory leak data with different scenarios, contributing to data quantity expansion, data credibility enhancement, and data variety enrichment. Finally, extensive experiments are given to illustrate the effectiveness of the proposed generative model for pipeline network leak detection.

This article investigates the problem of resilient secure control of cloud-aided 5-DOF active semivehicle suspension systems (SVSSs). A novel joint model considering both the event-triggered mechanism (ETM) and Denial of Service (DoS) attacks is established. Under such a model, during the active period of DoS attacks, periodic transmission attempt is made to ensure the control system can receive the control information at the earliest time; the ETM turns to be a conventional one when the DoS attack is in sleeping period. Meanwhile, the valid attack period is proposed to address the problem of the DoS attack ending within a sampling period, which is a challenging problem in modeling DoS attacks. Takagi–Sugeno (T–S) fuzzy model is used to characterize the uncertainties of sprung and unsprung mass of SVSSs. By converting the cloud-aided active SVSS into a fuzzy-based switched time-delay system, and using the method of piecewise Lyapunov function, sufficient conditions are derived to ensure the performances of active SVSSs subject to DoS attacks. Finally, the effectiveness of the proposed method is validated by a numerical example of active SVSSs subject to DoS attacks.

This article is concerned with attack-resilient event-triggered$H_{\infty }$filtering for a class of networked nonlinear systems described by an interval type-2 (IT2) fuzzy model. Suppose that data transmission from the plant to the filter is completed through a wireless sensor network subject to denial-of-service attacks (DoS). In order to save the limited network bandwidth and resist the effects of DoS attacks, a resilient event-triggered communication scheme is devised. Then, an attack-resilient IT2 filter model is introduced to estimate system states of the nonlinear plant. Based on a piecewise Lyapunov–Krasovskii functional, sufficient conditions are obtained to ensure that the filtering error system is exponentially stable and satisfies a certain$H_{\infty }$performance level. Moreover, explicit expressions for the attack-resilient filter gain parameters and event-triggering parameters can be derived if a set of linear matrix inequalities are feasible. Finally, a practical example is provided to demonstrate the effectiveness of the proposed theoretical results.

This article proposes improved stability and stabilization criteria for Takagi–Sugeno (T–S) fuzzy systems with time-varying delays. First, a novel augmented fuzzy Lyapunov–Krasovskii functional (LKF) including the quadratic fuzzy Lyapunov matrix is constructed, which can provide much information of T–S fuzzy systems and help to achieve the lager allowable delay upper bounds. Then, improved delay-dependent stability and stabilization criteria are derived for the studied systems. Compared with the traditional methods, since the third-order Bessel–Legendre inequality and the extended reciprocally convex matrix inequality are well employed in the derivative of the constructed LKF to give tighter bounds of the single integral terms, the conservatism of derived criteria is further reduced. In addition, the quadratic fuzzy Lyapunov matrix introduced in LKF, which contains the quadratic membership functions, is also an important reason for obtaining less conservative results. Finally, numerical examples demonstrate that the proposed method is less conservative than some existing ones and the studied system can be well controlled by the designed controller.

A novel multi-instant gain-scheduling scheme is proposed in order to further improve the state estimation performance of discrete-time Takagi–Sugeno fuzzy systems in this article. Different from those existing methods, the enabled working pattern at each sampling instant can be determined in cycle according to utilization of the updated information of adjacent normalized fuzzy weighting functions in depth, and then the featured time-varying free matrices are introduced for each working pattern, which can remove those existing constraints on traditional free matrices. Consequently, the conservatism can be reduced significantly and it does broaden the range of application for observer-based fuzzy state estimation. Despite the fact that the quantity of the free matrices becomes much bigger than before, it needs to be pointed out that the actual computational complexity only increases by a small amount through depressing the number of cycles. Given that the developed designing process belongs to an offline computation, it is an acceptable tradeoff between the increasement of computational burdens and the reduction of conservatism. In the end, the effectiveness of the developed method is illustrated through the detailed analysis of numerical simulations.

This article focuses on developing a static output feedback (SOF) control scheme for Takagi–Sugeno fuzzy systems. The proposed SOF controller does not share the same premise membership functions with the model, which permits enhancing the flexibility in controller design and implementation. By contrast with the state feedback case, the SOF control generally results in nonconvex design conditions. To circumvent this problem, we develop a successive convex optimization algorithm, which is based on solving a sequence of more tractable convex optimization problems obtained by approximating the nonconvex constraints with some convex ones. As a heuristic algorithm, the validity of the developed successive convex optimization algorithm is highly affected by initial conditions, and, recognizing this, we put forward an iterative procedure for determining the feasible initial condition. Finally, two illustrative examples are presented to validate the efficiency of the proposed algorithms.

This article is devoted to the development of multi-instant gain-scheduling stabilization of discrete-time Takagi–Sugeno fuzzy systems by developing a time-variant balanced matrix approach. Many of the reported advances have provided more and more relaxed results via choosing higher order dependent gain matrices, which will be a trouble in the case of real-time implementation. Therefore, a multi-instant gain-scheduling fuzzy state-feedback controller with different working modes is given to stabilize the closed-loop systems by updating the enabled pair of lower order gain matrices in cycle. For each possible working mode, the real-time situation information of the normalized fuzzy weighting functions can be fully considered by using a set of time-variant balanced matrices in accordance to certain rules and, thus, much freedom is introduced for proposing less conservative results. More importantly, our relaxed result is obtained without requiring higher order dependent gain matrices than the existing ones, i.e., its conservatism is reduced in a more meaningful way and thus it is more conducive to real-time implementation. Finally, both the effectiveness and the superiority of the proposed results are discussed and validated in the numerical section.

In this paper, relaxed observer-based state estimation of discrete-time Takagi–Sugeno fuzzy systems is proposed via developing a new augmented matrix approach. In contrast with the recent method reported in the literature, a more advanced introduction mode of additional matrices is developed without any redundant constraint under the framework of homogeneous polynomials. Then, the proposed augmented matrices can be built in order to depict the characteristic information of each possible working mode in a superior way, and thus our obtained result is less conservative than the recent one. Moreover, it is worth noting that that the recent method belongs to the special case of ours. Finally, two numerical simulations are given to test and validate the superiority and generality of the developed method.

Resilient fuzzy stabilization is capable of providing much less conservative results than conventional fuzzy stabilization while the alert threshold condition should be always satisfied at each sampling instant. In order to make the alert threshold condition more easily to be guaranteed, the short paper employs the switching-type gain-scheduling control law so that the real-time information, which is specific to the current sampling instant, can be integrated into resilient fuzzy stabilization. More importantly, a new kind of time-variant balanced matrix is introduced for the first time for adjusting positive/negative terms of different monomials in a more flexible way. As a result, the conservatism of resilient fuzzy stabilization can be further reduced even if the alert threshold condition becomes more difficult to be violated. Finally, the advantage of the developed method is tested and validated via related comparisons on a benchmark example.

This study is concerned with proposing much more effective Luenberger-like fuzzy observers than relevant multiinstant observers reported in recent literature, in other words, less conservative results can be given while less computing resource is consumed as an important premise. For the first time, the variation bound of two adjacent time-variant Lyapunov matrices encountered in the synthesis of fuzzy observer is characterized by a contraction factor, and thus the key replacement of the lagged term is developed in order to construct an effective synchronization framework of fuzzy observer synthesis. Since there only exist the current-time normalized fuzzy weighting functions in the obtained synchronization framework, the conservatism caused by the mismatch of different sampling instants can be avoided. Based on this, a lightweight gain-scheduling law is designed in which a large number of redundancy gains in recent multiinstant observers can be condensed in order to save computing resource to the greatest extent. Finally, two benchmark examples are borrowed for validating the superiority of our proposed results.

This article studies the weighted memory-event-triggered$H_{\infty}$static output control issue of Takagi–Sugeno fuzzy wind turbine systems with uncertainty. To decrease the frequency of data communication, a novel adaptive memory-event-triggered mechanism is presented to choose the “necessary” control signals, which has the following two benefits. First, a weighted average signal over a historic period is utilized as the input of event-triggered scheme, instead of the current system information in the conventional one. This could reduce the control signal updating rate and avoid the false triggering events incurred by stochastic environment noises and disturbances. Second, a dynamic triggering threshold is adopted to adaptively regulate the control signal updating frequency along with the average signal. By applying the distributed delay system method to describe the weighted historic signal, a new uncertain T–S fuzzy wind turbine system with distributed delay is established. With the aid of the measured outputs and the integral inequality based on the weighting function of the average signal, the memory-event-triggered static output controller design conditions are obtained to ensure the system exponential stability and the$H_{\infty}$performance. Lastly, an experiment platform integrating Zigbee modules as the wireless network is set up to illustrate the advantages of the proposed strategy.

In this article, an event-triggered practical fixed-time containment control issue for stochastic nonlinear multiagent systems is addressed. The event-triggering mechanism is designed for the controller update which is reduced update frequency. In combination with the backstepping technique and fuzzy logic systems, an adaptive fuzzy containment control strategy is developed for stochastic uncertain multiagent systems. By adopting the protocol, an adaptive containment controller is devised, which can ensure that the containment errors gather to a small range in fixed time. Finally, simulation results for the practical example demonstrate the correctness of the proposed scheme.

This article focuses on the design of fuzzy secure control for a class of coupled systems, which are modeled by a nonlinear$N$-dimensional ($N$-D) parabolic partial differential equation (PDE) subsystem and an ordinary differential equation (ODE) subsystem. Under stochastic deception attacks, a fuzzy secure control scheme is designed, which is effective to tolerate the attacks and ensure the desired performance for the considered systems. A new fuzzy-dependent Poincare–Wirtinger’s inequality (PWI) is proposed. Compared with the traditional Poincare’s inequality, the fuzzy-dependent PWI is more flexible and less conservative. Meanwhile, an augmented Lyapunov–Krasovskii functional (LKF) is newly constructed, which strengthens the correlations of the PDE subsystem and ODE subsystem. Then, on the ground of the fuzzy-dependent PWI and the augmented LKF, new exponential stabilization criteria are set up for the PDE-ODE coupled systems. Finally, a hypersonic rocket car is presented to verify the effectiveness and less conservatism of the obtained results.

This article is concerned with the fuzzy functional observer-based finite-time adaptive sliding-mode control for nonlinear systems with the partly unmeasurable states and some matched uncertainties. First, considering that the upper bound of the uncertain function exists but unknown, a fuzzy functional observer (FFO) with an adaptive compensator is constructed. Second, an FFO-based fuzzy integral sliding mode controller (ISMCr) is designed such that the closed-loop fuzzy systems are finite-time bounded with$H_{\infty }$performance over the reaching phase, the sliding phase, and the whole finite-time interval, respectively. To reduce the conservatism and increase the solution space of linear matrix inequality conditions, the fuzzy Lyapunov functional approach and equivalent fuzzy relaxed matrices technique are developed by introducing some relaxed matrices in the derivative of the fuzzy normalized membership function. Compared with the common Luenberger-type observer-based approach, the gain matrices of ISMCr depend on the FFO designed, which also enhances the flexibility of controller design. Finally, a simulation example with some comparison is given to show the effectiveness of the proposed method.

In this article, we investigate the periodic event-triggered synchronization of discrete-time complex dynamical networks (CDNs). First, a discrete-time version of periodic event-triggered mechanism (ETM) is proposed, under which the sensors sample the signals in a periodic manner. But whether the sampling signals are transmitted to controllers or not is determined by a predefined periodic ETM. Compared with the common ETMs in the field of discrete-time systems, the proposed method avoids monitoring the measurements point-to-point and enlarges the lower bound of the inter-event intervals. As a result, it is beneficial to save both the energy and communication resources. Second, the "discontinuous" Lyapunov functionals are constructed to deal with the sawtooth constraint of sampling signals. The functionals can be viewed as the discrete-time extension for those discontinuous ones in continuous-time fields. Third, sufficient conditions for the ultimately bounded synchronization are derived for the discrete-time CDNs with or without considering communication delays, respectively. A calculation method for simultaneously designing the triggering parameter and control gains is developed such that the estimation of error level is accurate as much as possible. Finally, the simulation examples are presented to show the effectiveness and improvements of the proposed method.

This brief considers the security control problem for nonlinear cyber-physical systems (CPSs) against jamming attacks. First, a novel event-based model-free adaptive control (MFAC) framework is established. Second, a multistep predictive compensation algorithm (PCA) is developed to make compensation for the lost data caused by jamming attacks, even consecutive attacks. Then, an event-triggering mechanism with the dead-zone operator is introduced in the adaptive controller, which can effectively save communication resources and reduce the calculation burden of the controller without affecting the control performance of systems. Moreover, the boundedness of the tracking error is ensured in the mean-square sense, and only the input/output (I/O) data are used in the whole design process. Finally, simulation comparisons are provided to show the effectiveness of our method.

This article investigates the problem of event-triggered switched fault-detection filters for networked stochastic systems under Denial-of-Service (DoS) jamming attacks. The considered DoS attacks are imposed by a power-constrained pulse-width modulated (PWM) jammers. A new resilient event-triggered communication strategy is designed to save network resources while counteracting the periodic PWM DoS jamming attacks. A new event-based switched residual model for fault detection is established, which characterizes the effects of the event-triggering scheme and DoS attacks simultaneously. By employing a piecewise stochastic Lyapunov functional method, sufficient conditions for achieving the exponentially mean-square stability and the prescribed performance of the residual system under the DoS attacks are formulated in terms of linear matrix inequalities. Consequently, co-design of the desired fault-detection filter parameters and the triggering parameters is achieved if the previous presented conditions are feasible. At last, an F-18 aircraft model is provided to show the validity of the proposed theoretical results.

In this article, we investigate a novel reinforcement-learning (RL)-based scheme to address the optimal leader–follower consensus issue for constrained-input continuous-time multiagent systems. First, as for input-constrained problems, the fundamental smooth assumption is not satisfied for the value function. To deal with this problem, we employ the method of vanishing viscosity solutions to relax this smooth assumption to a continuity assumption for the value function, which broadens the scope of RL applications. Second, the control cost functions take a more general form which guarantees the continuity of the optimal control policy instead of the specific integrand form used in previous input-constrained RL-based schemes. Based on these results, we introduce a novel identifier–critic–actor structure to extend the conventional critic–actor RL framework into a distributed model-free one, where the learning of the identifier, critic, and actor is online and simultaneous. We provide the simulation examples to validate the effectiveness of the proposed scheme.

This article studies the robust adaptive asymptotic tracking control problem for uncertain nonlinear systems with event-triggered inputs. Contrary to the existing results, a novel nonaffine nonlinear control input separated design scheme is developed based on the Taylor decoupling technique instead of the previous approximation ways. Correspondingly, the augmented dimension parameter updated laws and the unknown bound estimation of the compounded disturbance with a positive continuous integrable function are skillfully introduced. Also, by introducing a suitable decreasing function of tracking error variables, an improved adaptive event-triggered mechanism is constructed to achieve the asymptotic tracking and the communication load can be effectively alleviated. Moreover, it is shown that all the signals in the closed-loop system are uniformly bounded and the tracking errors converge to zero in a preset compact set. Finally, the validity of the proposed method is illustrated by simulation on an inverted pendulum model.

Relaxed fault estimation (FE) criteria of a class of discrete-time nonlinear plants are proposed based on a new multi-instant real-time scheduling fuzzy FE observer. Compared with the existing methods given in the recent literature, the newly developed fuzzy observer is capable of providing much freedom for reducing the conservatism of designing feasible FE criteria. At each sampling point, the information of adjacent groups of normalized fuzzy weighting functions can be updated and utilized for deciding the activated mode of our developed fuzzy FE observer. Based on this, an exclusive pair of gain matrices can be given by introducing a set of well-designed free matrices into the designed FE criteria for every activated mode. Moreover, it can be found that the proposed result will include the previous one as a special case if all of those free matrices are removed. Finally, the well-known nonlinear truck–trailer plant with actuator fault is utilized to validate the superiority of our approach over the existing ones reported in the literature.

The problem of enhanced stabilization of discrete-time Takagi–Sugeno fuzzy system is investigated in depth via proposing a new way to employ much more information implied in various time-varying differences of multi-instant normalized fuzzy weighting functions. Benefit from the given comprehensive real-time scheduling model, these time-varying differences on time vertical dimension and two different transverse dimensions are for the first time integrated into fuzzy stabilization and two key alterable weights are also introduced. Consequently, much considerable freedom can be produced and, thus, it brings much less conservative results than the reported ones in recent literature. More importantly, a very simple workable way has been provided to online recognize the specific enabled mode at each sampling instant so that those existing time-consuming online operations in referred literature can be avoided to ease online implementation costs. Indeed, this feature is very beneficial to the practical application of our theoretical results. Finally, the superiority of our developed method over previous ones is validated adequately via two benchmark simulations.

This article is concerned with the problem of observer-based dynamic event-triggered control for a networked control system (NCS) under a class of power-constrained denial-of-service (DoS) attacks that aim at impeding the network communication from time to time. First, by carefully modeling such DoS attacks as aperiodic pulse-width-modulated (PWM) jamming signals, a switching observer, adapting to the DoS attacks, is delicately constructed to deal with the unavailability of full-state information. Second, to economize the limited bandwidth resources, a dynamic event-triggered communication scheme is designed under the aperiodic DoS jamming attacks, whose duration and frequency are assumed to be restricted. Third, a switching system model with artificial state delay is formulated, which characterizes the effects of the aperiodic DoS attacks and event-triggered communication scheme in a unified framework. Then, the asymptotic stability analysis and controller/observer synthesis conditions of the resulting switching system are obtained by using a piecewise Lyapunov-Krasovskii functional approach. Furthermore, a co-design method of the dynamic triggering parameters, controller, and observer gains is presented. Finally, an example is employed to verify the effectiveness of the obtained results.

The problem of secure adaptive-event-triggered filter design with input constraint and hybrid cyber attack is investigated in this article. First, a new model of hybrid cyber attack, which considers a deception attack, a replay attack, and a denial-of-service (DoS) attack, is established for filter design. Second, an adaptive event-triggered scheme is applied to the filter design to save the limited communication resource. In addition, a novel adaptive-event-triggered filtering error model is established with the consideration of hybrid cyber attack and input constraint. Moreover, based on the Lyapunov stability theory and linear matrix inequality technique, sufficient conditions are obtained to guarantee the augmented system stability, and the parameters of the designed filter are presented with explicit forms. Finally, the proposed method is validated by simulation examples.

This article considers an adaptive fuzzy control problem for nonstrict-feedback nonlinear stochastic systems, which contain input delay, output constraints, and unknown control coefficients, simultaneously. First, an original stochastic nonlinear mapping and the Pade approximation transformation techniques are developed to solve the symmetric output constraints and input delay. Then, an adaptive fuzzy controller is designed for the unknown nonlinear systems, in which the Nussbaum function is employed to deal with the unknown time-varying control coefficients. Tracking errors are ensured to converge to a small neighborhood around the origin, and the system output does not violate the predefined constrained conditions. All the signals of the closed-loop systems have proven to remain bounded in probability. Moreover, the asymmetric output-constrained control is also studied. Two simulation examples are provided to show the effectiveness of the developed method.

In this article, an adaptive fuzzy tracking control scheme is developed for a class of uncertain switched nonlinear systems with input saturations and full-state constraints. First to surmount the design difficulty with respect to a saturation nonlinearity controller, a nonlinear smooth function approximating the nondifferential saturation function is introduced to establish a standard switched adaptive tracking control strategy based on the mean-value theorem and the input compensation technique. Then, invoking fuzzy-logic systems (FLSs), a novel analysis method of average dwell time for switched nonlinear systems with full-state constraints is proposed by using an artful logarithmic inequality. Furthermore, the designed adaptive controller can ensure that all the states of uncertain switched nonlinear systems are not to violate the set constraint bounds by employing barrier Lyapunov functions (BLFs), and that the system output tracking error can converge to a desired neighborhood of the origin within a suitable compact set. Finally, the simulation results are given to demonstrate the validity of the presented approach.

Due to uncertainty and dynamic characteristics from intermittent energy and load demand response (DR), the optimal operation of the hybrid energy system is a great challenge. This article proposes an event-triggered multiagent coordinated optimization strategy with two-layered architecture. First, the price-bidding-based DR model is proposed with different stakeholders, and it also deduces the optimal bidding price with the Nash equilibrium theory. Then, four agents are designed to control different kinds of energy resources: agent 1 mainly analyzes the uncertainty or randomness caused by intermittent power, agent 2 takes charge of the dynamic economic dispatch (DED) within thermal units, agent 3 manages the optimal scheduling of energy storage, and agent 4 mainly undertakes the load-shifting strategy from consumers. In the upper-layer level, all agents coordinate together to ensure the stability of the hybrid energy system with an event-triggered mechanism, and the intelligent control approach mainly depends on switching ON/OFF power generators or curtailing system load, and the consensus algorithm is utilized to optimize the subsystem problem in the lower-layer level. Furthermore, the simulation results can further verify the efficiency of the proposed method, and it also reveals that the event-triggered multiagent optimization strategy can be a promising way to solve the hybrid energy system problem.

This article focuses on the exponential synchronization problem of T-S fuzzy reaction-diffusion neural networks (RDNNs) with additive time-varying delays (ATVDs). Two control strategies, namely, fuzzy time sampled-data control and fuzzy time-space sampled-data control are newly proposed. Compared with some existing control schemes, the two fuzzy sampled-data control schemes cannot only tolerate some uncertainties but also save the limited communication resources for the considered systems. A new fuzzy-dependent adjustable matrix inequality technique is proposed. According to different fuzzy plant and controller rules, different adjustable matrices are introduced. In comparison with some traditional estimation techniques with a determined constant matrix, the fuzzy-dependent adjustable matrix approach is more flexible. Then, by constructing a suitable Lyapunov-Krasovskii functional (LKF) and using the fuzzy-dependent adjustable matrix approach, new exponential synchronization criteria are derived for T-S fuzzy RDNNs with ATVDs. Meanwhile, the desired fuzzy time and time-space sampled-data control gains are obtained by solving a set of linear matrix inequalities (LMIs). In the end, some simulations are presented to verify the effectiveness and superiority of the obtained theoretical results.

This article investigates the problem of resilient control for the Takagi–Sugeno (T–S) fuzzy systems against bounded cyberattack. A novel memory-based event triggering mechanism (ETM) is developed, by which the past information of the physical process through the window function is utilized. Using such an ETM cannot only lead to a lower data-releasing rate but also reduce the occurrence of wrong triggering event. Furthermore, the frequency of event generation is relatively smoother than existing ETMs. From the current releasing instant to the next, two periods are designed. The ETM works only when the first period ends, thereby avoiding the Zeno behavior that commonly exists in continuous ETM designs. The control system is then formulated as a switched fuzzy control system with two modes in each releasing period. Based on an assumption of secure control, and the proposed ETM, sufficient conditions are obtained to guarantee the exponential stability of networked T–S fuzzy systems in the presence of deception attacks in secure sense. Finally, a single-link rigid robot is taken as an example to illustrate the advantages of theoretical results.

Due to the complicated model characteristics, only a few results focusing on stability analysis have appeared on singularly perturbed descriptor systems (SPDSs). This article instead proposes an integral sliding-mode control strategy for a kind of Takagi-Sugeno fuzzy approximation-based nonlinear SPDSs under time-varying nonlinear perturbation. An appropriate fuzzy integral switching manifold that fully accommodates the system features is designed to completely reject the matched perturbation without amplifying the unmatched one. To facilitate the synthesis of the high-level controller (HLC), the sliding-mode dynamics (SMD) is transformed into an augmented form. Thanks to the adoptions of a novel singular perturbation Lyapunov function, Finsler's lemma, as well as the fixed-point principle, the existence and uniqueness of the solution and the exponential admissibility for the augmented SMD are analyzed. A solution for the designed HLC is further provided. To guarantee the sliding motion, a fuzzy integral sliding-mode controller (FISMC) is synthesized by analyzing the sliding motion reachability. An adaptive FISMC is also given to deal with the unknown upper bounds of the matched perturbation. Finally, the applicability of the developed FISMC strategy is testified by a practical example.

This article is concerned with the fuzzy adaptive tracking control problem for a class of uncertain nonaffine nonlinear systems with full state constraints and event-triggered inputs. First, based on the mean-value theorem and the input compensation method, the control input signal of nonaffine nonlinear term is successfully decoupled, and the remained compound nonlinear function can be approximated by fuzzy logic systems. Then, an improved event-triggered control strategy including the fixed threshold, the event-trigger control input, and the decreasing function of tracking errors, is given to update the actual control input. Correspondingly, the computation burden of the communication procedure is effectively alleviated. In addition, the developed control scheme guarantees that all the states of the closed-loop systems are not to violate the predefined compact sets by constructing barrier Lyapunov functions. Also, the system output tracking error can converge to a desired neighborhood of the origin. Finally, the validity of the proposed approach is demonstrated by the simulation results.

This article proposes an enhanced switching stabilization of Takagi-Sugeno fuzzy systems by developing a new fuzzy switching controller. A distinctive feature of the proposed approach is the enhanced ability to utilize the updated information of the normalized fuzzy weighting functions at each sampling point. Compared with those recent results in the literature, two key performance indexes, i.e., reducing the conservatism and alleviating the online computational burden, can be improved together while the off-line computational burden increases as a tradeoff but is still affordable from the point of algorithmic complexity. As a result, the efficiency of fuzzy stabilization is enhanced and thus its scope of application can be enlarged much more than before. Finally, the superiority of the proposed approach is illustrated by some simulation comparisons.

This article is concerned with a neural adaptive tracking control scheme for a class of multiinput and multioutput (MIMO) nonaffine nonlinear systems with event-triggered mechanisms, which include the fixed thresholds, triggering control inputs, and decreasing functions of tracking errors. Unlike the existing results of nonaffine nonlinear controller decoupling, a novel nonlinear multiple control inputs separated design method is proposed based on the mean-value theorem and the Taylor expansion technique. By this way, a weaker condition of nonlinear decoupling is provided to instead of the previous ones. Then, introducing a prescribed performance barrier Lyapunov function (PPBLF) and using neural networks (NNs), the presented event-triggered controller can maintain better tracking performance and effectively alleviate the computation burden of the communication procedure. Furthermore, it is proved that all the closed-loop signals are bounded and the system output tracking errors are confined within the prescribed bounds. Finally, the simulation results are given to demonstrate the validity of the developed control scheme.

This article focuses on the design of an adaptive event-triggered sampled-data control (ETSDC) mechanism for synchronization of reaction-diffusion neural networks (RDNNs) with random time-varying delays. Different from the existing ETSDC schemes with predetermined constant thresholds, an adaptive ETSDC mechanism is proposed for RDNNs. The adaptive ETSDC mechanism can be promptly adaptively adjusted since the threshold function is based on the current sampled and latest transmitted signals. Thus, the adaptive ETSDC mechanism can effectively save communication resources for RDNNs. By taking the influence of uncertain factors, the random time-varying delays are considered, which belongs to two intervals in a probabilistic way. Then, by constructing an appropriate Lyapunov-Krasovskii functional (LKF), new synchronization criteria are derived for RDNNs. By solving a set of linear matrix inequalities (LMIs), the desired adaptive ETSDC gain is obtained. Finally, the merits of the adaptive ETSDC mechanism and the effectiveness of the proposed results are verified by one numerical example.

This article investigates the consensus tracking of exponentially unstable multiagent systems with time-varying input delay. The truncated predictor feedback approach is utilized for designing delay-dependent state and output feedback protocols. And the explicit conditions that can realize consensus tracking are established in terms of parametric Lyapunov equations and scalar inequalities. Besides, the protocol design algorithms under the maximum allowable delay and the maximum convergence rate are, respectively, provided. Compared with the existing results, the salient characteristic of the current results is to reveal the quantitative relationship among the time delay, unstable plant, network topologies, and the convergence rate. Specifically, for achieving the consensus tracking, the synchronization force from network connectivity needs to dominate the anti-synchronization force from unstable open-loop poles and input delays; the maximum allowable input delay is inversely proportional to the sum of the unstable open-loop poles; the convergence rate becomes smaller as the input delay bounds or/and the sum of the unstable poles in plant increase. Numerical simulations confirm the effectiveness of the proposed theoretical design.

This article studies the security of networked interconnected systems (NISs) subject to cyber-attacks based on a new event-triggered mechanism (ETM). NISs with spatially distributed subsystems are vulnerable to cyber-attacks. With a new concept of security control, attention is focused on designing a novel ETM together with a decentralized output feedback control (DOFC) scheme such that the NIS subject to cyber-attacks is stable in secure sense. Under the proposed ETM, the average data-releasing rate over the whole operating period can be extremely decreased, thereby reducing the burden of network bandwidth, computation, and battery-supply. Moreover, during the system with external disturbance or attack on the communication network, more transmission-events can be generated than other periods. As a result, the desired control performance can be achieved. By using stochastic analysis techniques and Lyapunov stability theory, sufficient conditions are derived to obtain both the controller gains and the parameters of the ETM. Numerical simulation of chemical reactor systems is given to illustrate the advantages and effectiveness of the proposed theories and design techniques.

This paper focuses on the resilient H∞filter design for event-triggered networked systems subject to nonperiodic denial-of-service (DoS) jamming attacks. In this paper, a new resilient event-triggered transmission strategy is first proposed to improve the efficiency of network resource utilization while counteracting the nonperiodic DoS jamming attacks. Then, by using a time-delay approach, the filtering error system is modeled as a switched system, which characterizes the effects of the event-triggering scheme and nonperiodic DoS jamming attacks simultaneously. Based on the established model, by using the piecewise Lyapunov-Krasovskii functional method, linear matrix inequality (LMI)-based sufficient conditions are formulated to achieve the globally exponential stability as well as the weighted H∞performance of the resulting switched system under the DoS jamming attacks. Consequently, the co-design method for the desired filter parameters and event-triggering parameters can be formulated provided that the above LMIs are feasible. Finally, the effectiveness of the proposed method is demonstrated by a practical example.

This paper investigates the situation awareness issue of power system with massive measured data. To address this issue, first, a graph-theory-based network partitioning algorithm is proposed to realize decentralized detection in a faster response speed, while using power flow characteristics highlights the independency of different groups. Further, a hierarchical event detection method is proposed to judge voltage change and locate event position according to spectral distribution change of established multidimensional matrix. With the proposed method, the system situation can be assessed and the knowledge of the system model is not required. In addition, the accurate result of weak event happened in system could also be obtained. The simulation results are presented to illustrate the effectiveness of the proposed detection method.

An observer-based containment control issue is addressed for a class of uncertain nonlinear multiagent systems with a directed topology via the active disturbance rejection control and backstepping techniques. A kind of nonlinear extended state observers (ESOs) based on fractional power functions is developed, and the estimations of extended states are utilized to compensate uncertain dynamics in real time. Compared with linear ESOs, the advantages of the ESOs in this paper lie in peaking reduction and better tolerance of measurement noise for the closed-loop system. Moreover, tracking differentiators are employed to avoid the explosion of complexity caused by repeated differentiations of nonlinear functions. It is proven that the containment errors of the followers converge to small neighborhoods of the origin and they are adjustable by suitable choice of parameters. Finally, two simulation examples, both practical and numerical ones, are shown to demonstrate the effectiveness of the proposed control approach.

This paper is concerned with the observer-based event-triggered control for a continuous networked linear system subject to denial-of-service (DoS) attacks, where the attacks are launched periodically to block the data transmission in control channels. First, a new observer state-based resilient event-triggering scheme is developed in the presence of DoS attacks. Second, a novel event-based switched system model is established by considering the effect of the event-triggering scheme and DoS attacks simultaneously. By virtue of this new model combined with a piecewise Lyapunov-Krasovskii functional method, the sufficient conditions are derived to guarantee exponential stability of the resulting switched system. It is shown that the proposed results can establish a quantitative relationship among the launching/sleeping periods of the attacks, the event-triggering parameters, the sampling period, and the exponential decay rate. Third, criteria for designing a desired observer-based event-triggered controller are provided and expressed in terms of a set of linear matrix inequalities. Finally, an offshore structure model is presented to illustrate the efficiency of the developed control method.

This paper proposes an improvement on observer design of discrete-time fuzzy systems based on an alterable weights method. Different from the recent result, a more effective ranking-based switching mechanism is developed by introducing a bank of alterable weights for the sake of making use of the size difference information of the normalized fuzzy weighting functions more freely than before. Therefore, a positive result can be provided in this paper, that is, less conservative conditions of designing feasible fuzzy observers can be obtained than those existing results, while the computational cost of designing feasible fuzzy observers is even less than the up-to-date one. Finally, two numerical examples are given to show the progressiveness of the proposed method.

The problem of observer-based state estimation of discrete-time fuzzy systems is investigated by constructing a joint switching mechanism for adjacent instants. Thanks to the usage of both the proposed spatial partitioning method and a set of new free matrix-valued variables, abundant information about size differences of all the normalized fuzzy weighting functions for adjacent instants can be interactively integrated into the fuzzy observer design for the first time. Compared with the recent result from three important aspects (conservatism level, online computational burden, and offline computational burden), three positive results can be obtained: 1) it provides a chance for reducing the conservatism by a large margin; 2) the required online computational burden remains unchanged as referred ones; and 3) as a tradeoff, the required offline computational burden increases to some extent but is still affordable from the view of complexity analysis. Finally, two numerical simulations have been given to validate the effectiveness of our developed theoretical results.

This paper investigates the output feedback stabilization problem for networked control systems under a stochastic scheduling protocol. First, an independent and identically distributed (i.i.d) scheduling protocol is introduced to orchestrate the signal transmission via a communication network. Taking into account the i.i.d protocol, network-induced delay, and packet dropout, a stochastic impulsive delayed model is presented for the studied system. Second, by use of the Lyapunov-Krasovskii functional approach, sufficient conditions for guaranteeing the stability of the studied system in the mean-square sense are obtained in the form of matrix inequalities. Moreover, an optimization algorithm is investigated to obtain the suitable dynamic output feedback controller and optimal i.i.d protocol parameters simultaneously. Finally, two numerical examples are presented to show the validity of the proposed method.

This paper investigates finite-horizon optimal consensus control problem for unknown multiagent systems with state delays. It is well known that optimal consensus control is the solutions to the coupled Hamilton-Jacobi-Bellman (HJB) equations. An off-policy reinforcement learning (RL) algorithm is developed to learn the two-stage optimal consensus solutions to the coupled time-varying HJB equations using the measurable state data instead of the knowledge of the state-delayed system dynamics. Subsequently, for each agent, a single critic neural network (NN) is utilized to approximate the time-varying cost function and help to calculate optimal consensus control policy. Based on the method of weighted residuals, adaptive weight update laws for the critic NNs are proposed. Finally, the simulation results are provided to illustrate the effectiveness of the proposed off-policy RL method.

Due to the uncertainty of intermittent energy and system load, it is a big challenge to optimally operate an isolated power system. This article proposes a two-stage optimal operation strategy with a Takagi–Sugeno–Kang (TSK) fuzzy system to address the supply security under uncertainty circumstance. For proper analysis of the uncertainty characteristics, adjustable uncertainty parameters of intermittent energy resource and system load are taken as fuzzy sets; with the consideration of the robustness of these uncertainty parameters on isolated power system, it creates a supply-security identification model with the TSK fuzzy approach under radial basis function (RBF) neural network, and deduces optimal weight values with a recursive least square method. For properly avoiding potential risks, security index is classified into several degrees, each degree of risk can switch a different operation model, which can ensure the supply security of an isolated power system. For properly solving the optimization model, gradient descent-based multiobjective cultural differential evolution is employed to minimize economic cost and emission rate simultaneously. With simulations on isolated regional network, the obtained results reveal that the proposed method can be a viable alternative for optimal operation in isolated power systems.

This paper addresses the problem of reducing the conservatism for stabilization of discrete-time Takagi-Sugeno fuzzy systems via a new extended representation approach. Different from previous slack variable methods, an advanced slack variable method without limitations is proposed for further making good use of available fuzzy weighting functions. Owing to the introduction of extended representations for homogenous polynomials, those strong limitations in recent literature are relaxed and thus the primary and secondary sequences of all normalized fuzzy weighting functions can be mapped to one augmented multi-indexed matrix for each homogeneous polynomial. Therefore, less conservative stabilization conditions can be provided as a result of these effective measures and thus a part of the online computational cost is transferred to the offline implementation. Finally, the benefits of the proposed method are illustrated by means of numerical experiments.

This article proposed a novel event-triggered integral sliding-mode control (ISMC) strategy for nonlinear system with disturbances via robust adaptive dynamic programming (ADP) considering control constrains. A mixed event-triggered ISMC scheme with two different trigger parts is developed and the optimal performance of sliding-mode dynamics with input constrains is ensured. By guaranteeing that the system trajectory converges to the sliding-mode surface with removing the input disturbances, a discontinuous part triggering rule is presented together with the existence analysis of a lower trigger interval time bound. Then, the optimal event-triggered control of sliding-mode dynamics is converted into a discounted factor-based H∞constrained control problem under continuous part triggering condition. To solve the event-triggered HJI equation, a critic-only neural network (NN)-based ADP scheme is developed by applying a concurrent learning. The NN weight is updated by analyzing the uniformly ultimately bounded (UUB) stability of sliding-mode dynamics considering the event-triggered condition via the Lyapunov technique. Finally, the validity of our control strategy is verified by simulation.

In this paper, the event-based controller synthesis problem for networked control systems under the resilient event-triggering communication scheme (RETCS) and periodic denial-of-service (DoS) jamming attacks is studied. First, a new periodic RETCS is designed under the assumption that the DoS attacks imposed by power-constrained pulsewidth-modulated jammers are partially identified, that is, the period of the jammer and a uniform lower bound on the jammer's sleeping periods are known. Second, a new state error-dependent switched system model is constructed, including the impacts of the RETCS and DoS attacks. According to this new model, the exponential stability criteria are derived by using the piecewise Lyapunov functional. In these criteria, the relationship among DoS parameters, the triggering parameters, the sampling period, and the decay rate is quantitatively characterized. Then, a criterion is also proposed to obtain the explicit expressions of the triggering parameter and event-based state feedback controller gain simultaneously. Finally, the obtained theoretical results are verified by a satellite yaw-angles control system.

This paper studies the adaptive event-triggered fuzzy control issue for active vehicle suspension systems with uncertainties. Takagi-Sugeno fuzzy model is applied for considered systems. In the process of designing controller, a crucial problem, actuator failure, is taken into account. An adaptive event-triggered mechanism is adopted to economize limited communication resource. Compared with the traditional event-triggered scheme with a constant threshold, the adaptive event-triggered mechanism can save more resource effectively. Based on Lyapunov stability theory, an adaptive event-triggered fuzzy control approach is proposed to guarantee the desired performance. Meanwhile, suspension constrained requirements are also ensured. Finally, simulation examples are presented to testify the feasibility of the approach proposed in this paper.

This paper is concerned with data-driven distributed optimal consensus control for unknown multiagent systems (MASs) with input delays. The input-delayed MAS model is first converted into a delay-free form using a model reduction method. By establishing an equivalent relationship on the predesigned performance indices of the two MASs, optimal consensus control of input-delayed MAS can be fully transformed to that of delay-free MAS. Based on the coupled Hamilton-Jacobi equations and Bellman's optimality principle, optimal consensus control policies are derived for the transformed delay-free MAS. Then a policy iteration algorithm based on distributed asynchronous update mechanism is proposed to learn the coupled Hamilton-Jacobi-Bellman equations online. To perform the proposed data-driven adaptive dynamic programming algorithm, we adopt the measured data-based critic-actor neural networks to approximate the value functions and the control policies, respectively. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.

This paper is concerned with the dissipativity-preserving model reduction problem for Takagi–Sugeno (T–S) fuzzy systems. The principal goal is to approximate the high-order T–S model with a dissipative reduced-order T–S model. The number of fuzzy rules and the membership functions of the reduced-order T–S model are chosen freely to enhance design flexibility. To this end, an$H_{\infty }$performance index is used to describe the approximation error. Meanwhile, dissipativity of the reduced-order model is guaranteed by satisfying a dissipation inequality. With the aid of fuzzy-basis-dependent Lyapunov functions and slack variable techniques, less conservative design conditions for reduced-order models are derived. An algorithm is proposed to calculate a desired reduced-order model. A rail traction control system is given to illustrate the effectiveness of the proposed method and the advantages over the existing methods.

This paper focuses on the hybrid-driven-based H∞control for networked cascade control systems (NCCSs) with actuator saturations and stochastic cyber attacks. In order to relieve the network bandwidth load effectively, a hybrid triggered scheme is introduced, which contains a switch between time-triggered scheme and event-triggered scheme. A newly hybrid-driven-based NCCS model is established by considering the effects of both actuator saturations and stochastic cyber attack, which is an important threat to network security. By using the Lyapunov stability theory, sufficient conditions are obtained to ensure the system stability. Furthermore, both primary controller gain and secondary controller gain are achieved explicitly in terms of linear matrix inequality techniques. Finally, a power plant gas-turbine system is presented to illustrate the usefulness of the designed state feedback controllers.

This paper examines quantized stabilization for Takagi-Sugeno (T-S) fuzzy systems with a hybrid-triggered mechanism and stochastic cyber-attacks. A hybrid-triggered scheme, which is described by a Bernoulli variable, is adopted to mitigate the burden of the network. By taking the effect of the hybrid-triggered scheme and stochastic cyber-attacks into consideration, a mathematical model for a closed-loop control system with quantization is constructed. Theorems for main results are developed to guarantee the asymptotical stability of networked control systems by using Lyapunov stability theory and linear matrix inequality techniques. Based on the derived sufficient conditions in theorems, the controller gains are presented in an explicit form. Finally, two practical examples demonstrate the feasibility of designed algorithm.

This paper investigates the event-triggered predictive control problem for networked nonlinear systems with imperfect premise matching. First, a model of networked nonlinear system is well constructed, which has integrated the event-triggered communication scheme (ETCS) and the predictive control together, in which, an ETCS is introduced to alleviate the communication burden by reducing the number of transmitted packets; and a fuzzy predictive controller is designed to predict future states and control signals between two successfully transmitted instants. Therefore, the data dropout induced by the networks can be actively compensated. Second, by using a common Lyapunov theory, a stability criterion and two stabilization criteria are deduced to ensure the asymptotical stability of the studied system and find the controller gains, respectively. Different from the traditional parallel distributed compensation method, the synchronous premise variables between the T-S fuzzy system and the fuzzy event-triggered predictive controller (FETPC) are no longer needed again. Since the imperfect premise matching condition is well considered in the derivation of the main results, the design flexibility and low cost of the FETPC implementation can be expected. Finally, the validity of the method proposed in this paper is demonstrated by a nonlinear mass-spring example.

The problem of relaxed real-time scheduling stabilization of nonlinear systems in the Takagi-Sugeno fuzzy model form is studied by proposing a new alterable-weights-based ranking switching mechanism. Thanks to the proposed alterable-weights-based ranking switching mechanism, a new fuzzy switching controller is developed with a set of activated modes that are adjusted by the real-time joint distribution of normalized fuzzy weighting functions. It is worth noting that those existing real-time scheduling stabilization results can be improved without introducing additional offline computational burden while solving control gain matrices. More importantly, less conservative stabilization conditions lead to a smaller degree of the fuzzy homogenous polynomially parameter-dependent switching controller, and thus, less online computational burden is required in the actual application. The effectiveness and superiority of the proposed method are verified by two simulation examples in the numerical section.

This paper deals with more relaxed designs of discrete-time Takagi-Sugeno fuzzy-model-based observers via two effective technical measures. Different from previous methods of this field, two effective technical measures are developed for obtaining more relaxed results, i.e., 1) A novel ranking-based switching mechanism is proposed by introducing a set of weighted variables so as to make use of the size differences information among normalized fuzzy weighting functions more freely. 2) A new slack variable method is proposed via the introduction of some extended representations for homogenous polynomials, and those major and minor relationships among all normalized fuzzy weighting functions are mapped to sole augmented multiindexed matrix for each homogeneous polynomial. Therefore, two positive results are provided in this paper, i.e., less conservative fuzzy observers can be given as a result of the above effective measures whilst a part of the online computational cost can be transferred to the offline implementation. Finally, two numerical examples are applied to illustrate the effectiveness of our approach.

This paper focuses on a problem of event-triggered stabilization for a class of nonuniformly sampled neural-network-based control systems (NNBCSs). First, a new event-triggered data transmission mechanism is designed based on the nonperiodic sampled data. Different from the previous works, the proposed triggering scheme enables the NNBCSs design to enjoy the advantages of both nonuniform and event-triggered sampling schemes. Second, under the nonperiodic event-triggered data transmission scheme, the nonperiodic sampled-data three-layer fully connected feedforward neural-network (TLFCFFNN)-based event-triggered controller is constructed, and the resulting closed-loop TLFCFFNN-based event-triggered control system is modeled as a state delay system based on time-delay system modeling approach. Then, the stability criteria for the closed-loop system is formulated using Lyapunov-Krasovskii functional approach. Third, the sufficient conditions for the codesign of the TLFCFFNN-based controller and triggering parameters are given in terms of solvability of matrix inequalities to guarantee the asymptotical stability of the closed-loop system and an upper bound on the given cost function while reducing the updates of the controller. Finally, three numerical examples are provided to illustrate the effectiveness and benefits of the proposed results.

This paper is focused on the issue of scheduling stabilization of Takagi-Sugeno fuzzy control systems by the aid of digging down much deeper of implicit information in the underlying systems. An event-triggered real-time scheduler that decides which control mode should be executed at any given instant is constructed by periodically evaluating the joint-distribution-type of multi-instant normalized fuzzy weighting functions at every sampled instant. Profiting from the proposed event-triggered scheduling policy, the proper control mode for the current instant is updated in order to adapt time-varying situations once if the underlying joint-distribution-type changes, and thus previous implementations of control tasks with an unchanged control mode can be further relaxed in this paper. The effectiveness of our approach is verified by several simulation examples in the end.

This paper addresses the problem of an event-triggered non-parallel distribution compensation (PDC) control for networked Takagi-Sugeno (T-S) fuzzy systems, under consideration of the limited data transmission bandwidth and the imperfect premise matching membership functions. First, a unified event-triggered T-S fuzzy model is provided, in which: 1) a fuzzy observer with the imperfect premise matching is constructed to estimate the unmeasurable states of the studied system; 2) a fuzzy controller is designed following the same premise as the observer; and 3) an output-based event-triggering transmission scheme is designed to economize the restricted network resources. Different from the traditional PDC method, the synchronous premise between the fuzzy observer and the T-S fuzzy system are no longer needed in this paper. Second, by use of Lyapunov theory, a stability criterion and a stabilization condition are obtained for ensuring asymptotically stable of the studied system. On account of the imperfect premise matching conditions are well considered in the derivation of the above criteria, less conservation can be expected to enhance the design flexibility. Compared with some existing emulation-based methods, the controller gains are no longer required to be known a priori. Finally, the availability of proposed non-PDC design scheme is illustrated by the backing-up control of a truck-trailer system.

The augmented multi-indexed matrix approach acts as a powerful tool in reducing the conservatism of control synthesis of discrete-time Takagi-Sugeno fuzzy systems. However, its computational burden is sometimes too heavy as a tradeoff. Nowadays, reducing the conservatism whilst alleviating the computational burden becomes an ideal but very challenging problem. This paper is toward finding an efficient way to achieve one of satisfactory answers. Different from the augmented multi-indexed matrix approach in the literature, we aim to design a more efficient slack variable approach under a general framework of homogenous matrix polynomials. Thanks to the introduction of a new extended representation for homogeneous matrix polynomials, related matrices with the same coefficient are collected together into one sole set and thus those redundant terms of the augmented multi-indexed matrix approach can be removed, i.e., the computational burden can be alleviated in this paper. More importantly, due to the fact that more useful information is involved into control design, the conservatism of the proposed approach as well is less than the counterpart of the augmented multi-indexed matrix approach. Finally, numerical experiments are given to show the effectiveness of the proposed approach.

This paper investigates the problem of robust fault estimation (FE) observer design for discrete-time Takagi-Sugeno fuzzy systems via homogenous polynomially parameter-dependent Lyapunov functions. First, a novel framework of the fuzzy FE observer is established with the help of a maximum-minimum-priority-based switching mechanism. Then, for every activated switching case, a targeted result is achieved by the aid of exploring an important property of improved homogenous polynomials. Since the helpful information of the underlying system can be duly updated and effectively utilized at every sampled point, the conservatism of previous results is availably reduced. Furthermore, the proposed result is further improved by eliminating those redundant terms of the introduced matrix-valued variables. Simulation results based on a discrete-time nonlinear truck-trailer model are provided to show the advantages of the theoretic result that is developed in this paper.

This paper generalizes recent results on multi-instant observer design for discrete-time Takagi-Sugeno fuzzy systems through a valid ranking-based switching approach. The approach hereby develops a concentrated subdivision of spanning space composed of normalized fuzzy weighting functions and then substantially produces a new ranking-based switching mechanism. By taking advantage of this ranking-based switching mechanism, a class of new fuzzy multi-instant observers are achieved and more relaxed design conditions with respect to the recent work can be obtained for ensuring the asymptotically stability of the developed state estimation error system. Two illustrative examples are provided to validate the effectiveness of the result given in this study.

Robust fault estimation (FE) observer designs for discrete-time nonlinear system are deeply discussed via a joint real-time scheduling law. Different from previous results involved in the field, a fresh FE observer is produced by means of intermittently launching a joint real-time scheduling law in the light of updated multi-instant information. Thanks to the overall vision of system information across several adjacent sampled points, less conservative result is favorably acquired. Second, the given result is ulteriorly ameliorated by effectively developing an improved introduction technique of free matrix variables. Finally, one nonlinear truck-trailer example is employed for validating the superiority of theoretic fruits that is given in this paper.

This paper focuses on a problem of event-based stabilization for a class of sampled-data neural-network-based control systems. By using a new discrete event-triggering mechanism, an event-based sampled-data three-layer fully connected feedforward neural-network-based controller is constructed. Compared with the conventional periodic sampled-data neural-network-based control in previous works, the main advantage of this paper is that the proposed event-based sampling and transmission scheme not only reduces the updating frequency of the controller, but also guarantees the asymptotical stability of the closed-loop system without dramatically degrading the overall system performance. Based on a discontinuous Lyapunov Krasovskii functional, a convex combination technique and the Wirtinger-based integral inequality, some new criteria are derived to guarantee the asymptotical stability and certain performance of closed-loop system in terms of linear matrix inequalities (LMIs). Based on the proposed criteria, a co-design method is presented to obtain the triggering parameter and the connection weights of the neural network simultaneously while ensuring a certain system performance. Finally, simulation results are provided to show the effectiveness and advantage of the proposed theoretical results.

This paper deals with the problem of control synthesis of discrete-time Takagi-Sugeno fuzzy systems by employing a novel multiinstant homogenous polynomial approach. A new multiinstant fuzzy control scheme and a new class of fuzzy Lyapunov functions, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions, are proposed for implementing the object of relaxed control synthesis. Then, relaxed stabilization conditions are derived with less conservatism than existing ones. Furthermore, the relaxation quality of obtained stabilization conditions is further ameliorated by developing an efficient slack variable approach, which presents a multipolynomial dependence on the normalized fuzzy weighting functions at the current and past instants of time. Two simulation examples are given to demonstrate the effectiveness and benefits of the results developed in this paper.

This paper considers the model-reduction problem for continuous-time Takagi–Sugeno (T–S) fuzzy systems. Different from existing full-frequency methods, a finite-frequency model-reduction method is proposed in this paper. The proposed method can get a better approximation performance when input signals belong to a finite-frequency domain. To this end, a finite-frequency$H_\infty$performance index is first defined. Then, a sufficient finite-frequency performance analysis condition is derived by the aid of Parseval's theorem and quadratic functions. Based on this condition and projection lemma, three model-reduction algorithms for T–S fuzzy systems with input signals in low-frequency, middle-frequency, and high-frequency domain are obtained, respectively. Finally, an example is given to illustrate the effectiveness of the proposed method.

This paper investigates the sampled-data fuzzy stabilization problem for a class of nonlinear systems that is exactly modeled in Takagi-Sugeno fuzzy form at least locally. A new method for designing parallel distribution compensation fuzzy controller is proposed, which just requires that the nonlinear function is locally Lipschitz. By considering the sample-and-hold behavior of the system and using Jensen's integral inequality, an inequality constrain condition is derived from the locally Lipschitz property. Further, by defining a time-dependent Lyapunov-Krasovskii functional term, a new technique instead of the use of S-procedure is developed, and stabilization conditions for state feedback and observer-based output feedback under nonuniform sampling are obtained. Compared with the existing ones, the new design method not only avoids the difficulty of finding exact upper bounds of asynchronous errors of mismatch membership functions, but contains less conservatism and less numerical complexity as well. Finally, some illustrative examples are given to show the effectiveness of the proposed design method and the significant improvement over the existing results.

This paper is concerned with further studies on control synthesis of discrete-time Takagi-Sugeno (T-S) fuzzy systems. To do this, a novel slack variable technique, which is homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions with arbitrary degrees, is presented by developing an efficient augmented multi-indexed matrix approach. Under the framework of homogenous matrix polynomials, the algebraic properties of both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions are collected into sets of augmented multi-indexed matrices. Thus, more information about the underlying normalized fuzzy weighting functions is involved into control synthesis. Consequently, the relaxation quality of control synthesis of discrete-time T-S fuzzy systems is improved significantly. Finally, a numerical example is provided to illustrate the effectiveness of the proposed method.

This paper is concerned with the design of observer for discrete-time nonlinear systems in the Takagi-Sugeno (T-S) fuzzy form. Under the framework of multi-instant homogenous matrix polynomials, a novel fuzzy observer and a new Lyapunov function, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the m-steps past-time normalized fuzzy weighting functions, are proposed for conceiving less conservative observer design conditions. Since the algebraic properties of both the current-time normalized fuzzy weighting functions and the m-steps past-time normalized fuzzy weighting functions are fully considered, the relaxation quality of the fuzzy observer design of discrete-time T-S fuzzy systems is significantly improved. In particular, some existing fuzzy Lyapunov functions and fuzzy observers are special cases of the Lyapunov function and the fuzzy observer given in this paper, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed approach.

This paper is concerned with further studies on the control synthesis of discrete-time nonlinear systems in the Takagi-Sugeno (T-S) fuzzy form. To do this, a novel slack variable technique is presented by developing some useful matrix equalities, which are homogenous polynomially parameter-dependent on both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions. Under the framework of homogenous matrix polynomials, the algebraic properties of both the current-time normalized fuzzy weighting functions and the past-time normalized fuzzy weighting functions are collected for the first time into sets of united collection matrices. Consequently, the relaxation quality of control synthesis of discrete-time T-S fuzzy systems is improved, i.e., the convergence of asymptotically necessary and sufficient stabilization conditions is further sped up. Finally, a numerical example is provided to illustrate the effectiveness of the proposed result.

This paper proposes relaxed stabilization conditions of discrete-time nonlinear systems in the Takagi–Sugeno (T–S) fuzzy form. By using the algebraic property of fuzzy membership functions, a novel nonparallel distributed compensation (non-PDC) control scheme is proposed based on a new class of fuzzy Lyapunov functions. Thus, relaxed stabilization conditions for the underlying closed-loop fuzzy system are developed by applying a new slack variable technique. In particular, some existing fuzzy Lyapunov functions and non-PDC control schemes are special cases of the new Lyapunov function and fuzzy control scheme, respectively. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed method.

This paper is concerned with the problem of developing an advanced strategy to reduce the conservatism in stability analysis and control synthesis of continuous-time Takagi-Sugeno (T-S) fuzzy systems. A novel augmented multi-indexed matrix approach is proposed to implement new right-hand-side slack variables technique for the homogenous polynomial setting. Combining with the Finsler lemma with homogenous-matrix Lagrange multipliers, convergent linear-matrix-inequality (LMI) relaxations for stability analysis are proposed by using the generalization of the Polya theorem for the case of positive polynomials with matrix-valued coefficients. A new type of state-feedback controller, namely, the homogeneous polynomially nonquadratic control law (HPNQCL), is developed to conceive less-conservative stabilization conditions. The obtained stability and stabilization conditions are further relaxed by using the proposed right-hand-side slack variables technique. Moreover, the advantages over the existing control schemes are certificated in theory. Three numerical examples are also provided to illustrate the effectiveness of the proposed methods.

This paper proposes a novel H(∞) filtering technique for a class of discrete-time fuzzy systems. First, a novel kind of fuzzy H(∞) filter, which is homogenous polynomially parameter dependent on membership functions with an arbitrary degree, is developed to guarantee the asymptotic stability and a prescribed H(∞) performance of the filtering error system. Second, relaxed conditions for H(∞) performance analysis are proposed by using a new fuzzy Lyapunov function and the Finsler lemma with homogenous polynomial matrix Lagrange multipliers. Then, based on a new kind of slack variable technique, relaxed linear matrix inequality-based H(∞) filtering conditions are proposed. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approach.

In this paper, the problems of quadratic stabilization conditions for stochastic Takagi-Sugeno fuzzy systems have been studied. A new quadratic stability condition, which takes into account the knowledge of the membership function's shape by considering bounds on their cross products, has been proposed. And then a new sufficient condition in terms of linear matrix inequalities is developed to synthesize the state feedback controller that stabilizes the stochastic fuzzy systems. An numerical example is provided to illustrate the effectiveness of the proposed results.