With the rise of gamification in virtual corporate social responsibility (CSR) campaigns, its impact on user engagement has drawn increasing attention. However, the definition and impact of gamification affordances remain unclear, especially in virtual CSR co-creation. This study examines how gamification affordances affect users’ continued intention to participate, using the “Affordances-Psychological Outcomes-Behavioral Outcomes” framework. Based on a survey of 581 Ant Forest users, structural equation modeling (SEM) shows that both human-computer (autonomy support, achievement, telepresence) and human-human (competition, interactivity) affordances positively influence flow experience and continued intention to participate. Moreover, flow experience fosters self-expansion, mediating the relationship between gamification affordances and continued intention to participate. The Fuzzy-set qualitative comparative analysis (FsQCA) results provided insights into the multiple causal solutions and configurations of continued intention to participate. This study advances gamification research, refines affordance classifications, and provides practical insights for designing CSR initiatives that promote user engagement and co-creation.

This paper investigates the adaptive group fault-tolerant time-varying formation tracking (GFTFT) problem for linear multiagent systems (MASs) subject to actuator faults and switching communication networks. To fulfill complex tasks, a novel multi-layer framework is proposed, organizing agents into leaders, informed followers, and uninformed followers across multiple subgroups. To this end, firstly, a fault-tolerant GFTFT protocol is proposed to relax the restrictions on the severity of actuator faults, thereby enhancing tolerance to unknown faults. Secondly, novel multiple asynchronous event-triggered mechanisms (MAETMs) are designed, which enhance coordination and transparency by implementing a layered triggering strategy with distinct functions for inter-layer and inter-group communication. Third, the connectivity condition is relaxed, requiring only joint connectivity of the graphs over time, which accommodates intermittently disconnected topologies. Finally, the simulation experiment is conducted to validate the theoretical results.

This article investigates the mode cluster-based event-triggered control (MCETC) of stochastic Markovian jump systems (SMJSs) under denial-of-service (DoS) attack. First, a novel MCETC framework is designed by considering the interplay among subsystems, DoS attacks, and the event-triggered mechanism (ETM). In this framework, the controller mode is reconstructed, and the number of controller modes is reduced by reclustering the system modes. It significantly reduces the conservatism of the system compared to existing mode-dependent/-independent controllers. Second, a switching ETM is designed for scenarios with and without DoS attack activation, which can effectively save network bandwidth resources and reduce computational load. Third, a multi-Lyapunov function based on DoS attacks is proposed to ensure the stability of the closed-loop SMJSs. Then, the controller gains and event-triggered parameters are jointly solved via the linear matrix inequality (LMI) technique. Moreover, the maximum allowable sampling interval (MASI) is given such that the controller can restore the control signals as soon as a DoS attack ends, which enables faster stabilization of the closed-loop system. Finally, a numerical example is used to verify the effectiveness and superiority of the proposed method.

This article explores an adaptive security formation control issue for nonlinear multiagent systems (MASs) against unknown deception attacks. The stable operation of multiagent formation is highly dependent on effective communication transmission between agents. To realize the formation control task, first, a state observer is developed to estimate the states under FDI attacks. Then, the nonlinear state-dependent function is introduced to cope with the asymmetric constraints to ensure a safe and stable operation environment of the agent formation. Furthermore, with the help of coordinate transformation and fuzzy logic systems (FLSs), a fuzzy adaptive formation control scheme with an attack compensation mechanism is developed so that various desired formation patterns are achieved with free collision. Under the proposed scheme, the resulting formation tracking error is uniformly ultimately bounded, and the state constraint of the multiagent system is always maintained, even if the agents are subjected to malicious unknown deception attacks. The effectiveness of the control method is validated through simulation examples.

This paper proposes an innovative Energy-Efficiency-Aware Fixed-Time (EEAFT) control strategy for distributed permanent-magnet synchronous motor systems. The primary contribution is achieving rapid, precise speed consensus while effectively balancing energy consumption against consensus error, a challenge often overlooked in fixed-time (FxT) control designs. A key novelty lies in the introduction of a real-time reward mechanism, uniquely derived from low-pass filtering both the system's consensus error and the control input signals. This adaptive reward function dynamically adjusts the upper bound on convergence time. When the convergence time becomes excessively stringent, a substantial increase in control effort is required. This can lead to energy spikes and hardware overload. To mitigate these risks, the bound on convergence time is then relaxed. Conversely, when large consensus errors necessitate an accelerated response, the bound on convergence time is tightened to expedite error correction. To enhance robustness against unmodeled friction, winding losses, and external disturbances, a fuzzy logic system is employed to approximate unknown nonlinear dynamics, while a disturbance observer compensates for residual errors. Rigorous theoretical analysis confirms the boundedness of all system signals and guarantees FxT convergence under the proposed EEAFT framework. Extensive experimental results demonstrate the effectiveness and superiority of the EEAFT-based controller, showcasing high-precision speed synchronization across multiple motors and achieving an improved trade-off between rapid transient response and overall energy efficiency.

Aiming at the path-tracking problem of autonomous ground vehicle systems (AGVSs) under randomly activated network attacks, this article proposes a real-time dynamic integrated scheduling (RT-DIS) mechanism. First, the uncertain vehicle–road dynamics model is described by the Takagi–Sugeno fuzzy model through the time-varying speed of the vehicle. Second, a class of switching gain-scheduling controller is designed based on the difference of the normalized fuzzy membership functions in the vertical dimension of time and two different horizontal dimensions, which is fully adapted to all potential system dynamics behaviors of AGVSs. At the same time, by designing the homogeneous polynomially parameter-dependent Lyapunov function, the mean-square exponential stability satisfying the premise of${H_\infty }$performance is derived in a unified analysis framework. Finally, the simulation results demonstrate that the proposed RT-DIS mechanism can effectively enhance the vehicle lane-keeping performance.

This article presents a novel secondary voltage consensus control framework for microgrids equipped with multiple distributed generators. The framework ensures that these units consistently achieve specified performance levels while demonstrating resilience to abnormal voltage signals. First, an innovative overload-avoiding performance transformation method is proposed. This approach confines the synchronization errors of all generators within prescribed performance boundaries without imposing restrictions on their initial voltage conditions. In addition, a mean-filtering-based memory event-triggered mechanism is developed to bolster the robustness of the secondary voltage control process against non-real-time signals, while also mitigating undesirable voltage fluctuations that may occur in microgrids by utilizing stored stable data. It is shown that the generators' output voltages accurately track the desired reference voltage, with the tracking performance strictly adhering to the prescribed performance criteria. Simulation results further validate the efficacy of the proposed method.

This article presents a constraint-based finite-time tracking control scheme for multivehicle systems (MVSs) with communication and operation restrictions, including network attacks and actuator faults. The stable operation of MVSs significantly depends on the effective communication transmission of state information (position and velocity) between vehicles and the ideal operation of the vehicle’s own actuators. However, the actual transmission signals may be tampered with due to malicious attacks, and different faults may occur during the operation of transportation. Therefore, first, a novel coordinate transformation is developed to cope with the difficulty of distorted position and velocity information, which will lead to follower vehicles making incorrect decisions. Then, an adaptive controller is designed with the help of the fuzzy approximation method to solve the problems of actuator fault compensation and unknown nonlinearity of vehicle’s dynamic. Besides, the nonlinear velocity constraint function is designed to avoid collisions and congestion between vehicles so as to ensure a safe and comfortable transportation environment. Not only a safe distance between vehicles is achieved in a finite time, but also the velocity constraint of vehicles is maintained based on the proposed finite-time control scheme. Finally, the simulation example elaborates the effectiveness of the presented method in this article.

Accurate self-localization is increasingly required for Intelligent Vehicles (IVs) in underground parking lots. Among various self-localization methods, the vision-based approach is considered an effective scheme due to its low cost and capability to provide rich information. In this paper, a novel method is proposed to enhance the localization performance. A fusion method, named Dynamic K-KNN, is developed to improve scene recognition by fusing handcrafted features, convolutional features, and semantic topology. For localization computation, a Maximum Likelihood Estimation based on semantic topology constraints is proposed to improve localization accuracy. The proposed method has been tested in two scenarios. Experimental results demonstrate that the proposed method achieves improved localization accuracy, reaching sub-meter level performance.

This article proposes a hierarchical neural learning (HNL) algorithm for optimal tracking control (OTC) of nonlinear strict-feedback systems (SFSs) with unmatched disturbances (uMDs) and unknown dynamics. Leveraging the recursive structure of SFSs, we introduce the virtual target (VT) construction scheme in which each VT is a nonlinear mapping of the current state and desired output, thereby eliminating the noncausal that typically plagues discrete-time SFS control. The VTs serve as auxiliary inputs for low-order subsystems, while a time-varying affine Hamilton-Jacobi-Isaacs (HJI) formulation establishes an explicit relationship between the auxiliary control and the disturbance. The controller is synthesized directly from input-output data, removing the need for an accurate plant model. Within an adaptive dynamic programming (ADP) framework, we further enhance the neural architecture by replacing the conventional action network with a tracking network (T-network) whose energy function merges gradient information with future tracking errors, ensuring that each policy update simultaneously reduces control effort and improves tracking accuracy. Simulations confirm that the proposed HNL scheme achieves outstanding performance in both (optimal) tracking modes, exhibiting strong robustness to uMDs and significant model uncertainties.

This article investigates the fully distributed adaptive fault-tolerant cluster consensus tracking problem of multiagent systems (MASs) under prescribed performance conditions. First, a novel multihop neighborhood partition approach is proposed, enabling fully distributed control without relying on global Laplacian information. Then, an improved prescribed performance method is developed, which integrates the spatial information of agents into the performance function through function mapping. Unlike traditional prescribed performance methods, the proposed performance function accounts for the relative position information of agents during operation, ensuring that the tracking error between the leader and followers remains consistently negative. Furthermore, the demands of transient and steady-state performance of the system increase the consumption of communication resources. Therefore, a dynamic preset boundary event-triggered mechanism (DPETM) is proposed, which dynamically adjusts the triggering conditions based on the tracking error and predefined performance boundaries. Additionally, an adaptive command filter error compensation system is constructed to eliminate the differential explosion caused by higher-order derivatives of virtual control signals. Finally, a simulation case is presented to demonstrate the validity of the proposed control approach.

This manuscript presents an adaptive funnel controller applying to the active magnetic bearing for position constraint control with prescriptive tracking performance. To better depict the actual active magnetic bearing dynamics, a nonlinear active magnetic bearing model with switched parameters instead of the existing fixed parameters is constructed considering the inherent properties of uncertainties and nonstationarities of active magnetic bearings. Then, by designing the funnel control scheme and adaptive laws based on Lyapunov stability theory and backstepping technique, the rotor displacement is constrained to not exceed the prescribed funnel boundary in view of safety concerns. Moreover, the funnel boundary integrated into the proposed controller is in line with the rotor displacement characteristics of active magnetic bearing systems under different speeds during real operation process. The boundness of the position tracking error is confirmed via Lyapunov synthesis. Eventually, the effectiveness of the proposed controller is verified by simulated and experimental examples.Note to Practitioners—The motivation of this manuscript is to investigate a control strategy with potential application for the displacement control of active magnetic bearings. In most of the existing displacement control schemes for active magnetic bearings, the constraint and limitation of displacement is not taken into account. However, considering the high-speed rotation and active controllability of active magnetic bearings, it is necessary to preset the performance indicators of rotor displacement including convergence speed, overshoot, and constraint limit, which can not only avoid serious safety accidents, but also give full play to the active control advantages of active magnetic bearings in different actual situations. Therefore, this manuscript suggests an adaptive funnel control strategy for prescriptive performance. Moreover, this manuscript solves the modeling and control problems for active magnetic bearings subject to nonlinearity, uncertainty, and external disturbances, which are difficult to be tackled in practical applications. The stability and convergence of the proposed controller are analyzed mathematically, and the practical experimental results reveal that the proposed controller has the potential and possibility to be applied in practice.

This paper proposes an all agents connectivity-preserving method and a data-filter memory-based event-triggered (ET) strategy to design cooperative learning control algorithm. Firstly, a type of error functions are proposed to achieve that all agents are within the communication boundary, which do not limit the initial values of agents. The designed method can dynamically adjust the boundary function based on the initial position of agents and gradually converge to the preset communication boundary, without abandoning any agents. Secondly, a data-filter memory-based ET strategy is proposed, which includes the designed error-based data filtering rules. The filtering rules avoid the problem that the ET mechanism stores abnormal historical data when the system has faults. Moreover, the presented error-based cooperative learning adaptive protocol does not need to presuppose that neighbor weights are bounded, reducing the conservatism. Finally, based on the above works, the constructed ET control method can achieve control objectives, and the effectiveness is demonstrated through theoretical analysis and simulation results. Note to Practitioners—In practice, multiagent systems (MASs) communicate through wireless communication mostly, which inevitably leads to an upper limit on the communication distance between agents. Exceeding the limitation of communication module will cause the problem that MASs cannot achieve signal transmission. Therefore, it is crucial to design appropriate constraint methods for different initial positions of agents to ensure that all agents can enter the predetermined communication boundary. In addition, the memory ET strategy can calculate the threshold of conditions based on the historical data. But in practice, it cannot guarantee the continuous normal operation of the system. If there are abnormal values in the stored signal data, this will lead to unreasonable calculation of the threshold. In response to this issue, this paper considers additional data filtering rules to avoid storing data when systems exist faults. Meanwhile, the cooperative learning algorithm proposed in this paper can adjust the learning information weights based on the control performance of neighbor agents, and remove the assumption of bounded neighbor learning laws.

This paper investigate the input constraint and signal encryption for distributed control. Firstly, for the algorithm operation session, an additional information protection mechanism is designed, and the designed encryption algorithm can ensure that both the encrypted signal and the key signal have chaotic randomness. The mask signal is composed of multiple chaotic states, which has higher randomness. The key signal is also encrypted, effectively improving the security of the encryption algorithm. Even when the channel of key is not secure, information security can still be guaranteed. Moreover, information decryption only requires an integral algorithm and does not require an embedded decryption module that satisfies chaotic synchronization conditions, effectively reducing the complexity of decryption. Secondly, the proposed output constraint function can dynamically adjust the constraint boundaries based on control performance, which avoids the problem that the boundary is too strict to affect the control performance. At the same time, the boundary initial value is related to the output initial value, which effectively improves the convenience of algorithm migration and avoids the need to consider designing different parameters in different application environments. Based on the above two main works, the designed control algorithm can meet the considered control objectives using Lyapunov theory, and the simulation results also verify the effectiveness of proposed methods.

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.

This article is concerned with the memory-based event-triggered leader-following dissipative fault-tolerant consensus (LFDFTC) problem for the nonlinear multi-agent systems (NMASs) with semi-Markov switching topologies subject to the generally uncertain semi-Markov (GUSM) jumping process. Unlike the existing event-triggered (ET) consensus results, the dynamic memory event-triggered mechanism (DMETM) and memory-based distributed fault-tolerant (FT) controllers are designed to reduce the ET times. By constructing a general mode-dependent Lyapunov-Krasovskii functional (LKF) and strictly$(\bf {\mathcal {R,Q,T}})-\boldsymbol {\gamma }$dissipative analysis, the dissipative FT consensus conditions of NMASs are derived in this paper. Finally, three actual physical systems are utilized to verify the validity of the proposed method. Note to Practitioners—Owing to the complexity of engineering environment, the consensus control issue of NMASs has attracted widespread attention. Nowadays, the consensus control of NMASs is generally utilized in diverse fields, such as multi-vehicle coordination, smart grids, and unmanned aerial vehicle formation. However, for the electronic device in practical applications, the channel bandwidth is limited due to power and energy constraints, and it is difficult for the fixed communication topologies and traditional periodic sampled-data control method to cope with these unexpected situations. Therefore, the LFDFTC issue for the NMASs with GUSM switching topologies is investigated by adopting DMETM and memory-based distributed FT controllers in this paper. In addition, the proposed FT consensus control methods with prescribed dissipative performance are applied to multiple vehicles time-invariant formation, Chua’s circuits synchronization, and multiple manipulators consensus.

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.

A multi-bus voltage regulation strategy based on distributed fault-tolerant control is proposed in a microgird (MG). The strategy addresses the challenges posed by the presence of actuator partial loss of effectiveness (PLOE) and deviation faults in multiple distributed generators (DGs) communicating through a directed network. The concept of containment control is introduced in the multi-bus voltage regulation strategy. In this paper, the bus voltages are limited to a reasonable range while still allowing voltage differences between buses for efficient power flow. In addition, a hierarchical mechanism is proposed to divide the voltage fault-tolerant containment control problem into a cooperative control problem for virtual systems and a decentralized control problem for real systems. Notably, the mechanism avoids relying on global information about the directed communication network and specific quantitative details about the magnitude, frequency, and type of actuator failures. In addition, we devise a consensus-based control strategy to regulate the frequency and efficiently share active power among DGs. The strategy is thoroughly evaluated through comprehensive simulation experiments, demonstrating its effectiveness and performance in voltage regulation and fault management scenarios.Note to Practitioners—This paper aims to propose a fault-tolerant secondary control strategy for bus voltages and frequency. First, considering that the power flow between buses is based on voltage differences, the problem of regulating the bus voltages is transformed into a containment control problem for linear multi-agent system (MAS) containing unknown nonlinear dynamics. Next, we design a fault-tolerant secondary control strategy with hierarchical control. At the network layer, a fault-free virtual system with adjacency information is created and approximated with a neural network for nonlinear dynamics. In the physical layer, a decentralized adaptive tracking controller is designed to synchronize the virtual system with the existing system. This layering process decouples time-varying PLOE fault parameters and adaptive control gains under an asymmetric network, thus enabling fault-tolerant control of actuator PLOE faults and deviation faults in a fully distributed framework. In addition, the boundaries of the fault parameters can be unknown. A feasible strategy is provided for industrial applications.

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 proposes some novel algorithms for photovoltaic (PV) energy DC circuit conversion systems to extract maximum power under the constraint of information security. First, a discrete-degree-judging-based composite chaotic mask function generation (DCCG) algorithm is constructed. This algorithm utilizes all the states in the chaotic system to construct a more volatile chaotic signal, effectively increasing the complexity of the mask signal and enhancing the encryption of the photovoltaic energy system. Secondly, for the superposition process of the encrypted signal and the mask signal, a Gaussian-high-dimensional mapping-based adaptive weight calculation (GMAWC) method is designed to adaptively adjust the superposition weights. This adaptive adjustment helps avoid issues of insufficient encryption and excessive noise interference caused by the large value domain variation between the mask signal and the system states. Moreover, an upper bound on the decryption bias tolerated by the PV energy conversion system is explored, ensuring that the algorithmic framework has greater decryption bias tolerance while achieving maximum power extraction. Finally, both theoretical analysis and data results show that the proposed encryption-decryption-control framework has better security, applicability and decryption bias tolerance.

In this paper, the problem of adaptive fault-tolerant optimal control is investigated for nonstrict-feedback nonlinear systems with deferred output and performance constraints (DOPCs). By skillfully constructing the shifting transformation and finite-time constraining function, a novel error-dependent barrier function is innovated to achieve the preassigned time tracking performance without the conservative initial limitations, helping the property of DOPCs be preserved. Neural networks (NNs)-based reinforcement learning (RL) is exploited, which takes advantage of approximation means to solve the Hamiltonian equation under the backstepping framework, optimally reconciling the tracking performance and control behavior. By utilizing NNs to online estimate the unaware faults and uncertainty, an adaptive fault-tolerant optimal controller is designed. Finally, the efficiency of the proposed method is confirmed by simulations.

This article addresses a new type of adaptive time-varying group formation tracking (TVGFT) problem for linear multiagent systems (MASs) with nonautonomous leaders. To fulfill complicated formation tasks, a TVGFT protocol is proposed, where the agents are decomposed into multiple subgroups and each subgroup can successfully track the corresponding leader. Additionally, novel multiple asynchronous dynamic edge-event-triggered mechanisms (DEETMs) are designed to further conserve communication resources and optimize network utilization by enabling the leader to send information intermittently and allowing each follower to transmit information asynchronously when the trigger mechanisms are satisfied. The DEETMs consider both interlayer and intergroup information interactions to improve communication efficiency. Different from the existing results, the proposed DEETMs are used for intergroup information exchange to enhance both the coordination of formation and information transparency. At last, the simulation experiment is offered to validate the designed protocol.

In this article, a model-free reinforcement learning (RL) approach is proposed for solving the optimal consensus control issue of nonlinear discrete-time multiagent systems with input constraint. To address the challenge of solving the coupled discrete Hamilton-Jacobi-Bellman (HJB) equation, a RL approach based on actor-critic framework is proposed for optimal consensus control. A well-defined cost function is designed, and the actor and critic networks are updated through online learning to obtain the optimal controllers. Furthermore, the actuator's performance is often limited due to physical constraints. To address such actuator constraints, a gradual transition control (GTC) method is proposed, and update-free and update-weak policies are introduced to further optimize network performance. Additionally, in real-world distributed systems, the actor-critic networks deployed in each agent rely on data from neighboring agents, which necessitates addressing the issue of distributed synchronization. To address this challenge, the synchronization blocking method is designed, which designs additional control signals for each agent to handle these issues. Finally, two simulations under different scenarios are presented to verify the effectiveness of the proposed approach.

In this article, the tracking control problem for nonlinear systems is investigated. For the first time, a fixed-time dynamic signal is constructed to handle unmodeled dynamics. A novel error-based function is first designed and applied to prescribed performance control, significantly enhancing the transient performance of the system. To mitigate the issue of extensive differential calculations, a modified fixed-time dynamic surface technique is incorporated into the backstepping design process. Combining the backstepping technique with fixed-time stability theory, a fast practical fixed-time controller is proposed to effectively address the control problem. Finally, the proposed scheme is validated for its effectiveness through the practical simulation example.

In this article, the investigation is centered on the problem of fixed-time control within nonlinear systems. A quantized fixed-time prescribed performance control is proposed for the first time, which does not rely on preset thresholds within the performance function. Leveraging the properties of the designed continuous quantizers, the constraint boundaries are dynamically adjusted to ensure that the behavior of the controlled entity remains within a desired narrow range. The challenge of intensive differential computations is bypassed through the adoption of a dynamic surface approach in the backstepping design phase. By seamlessly integrating the principles of backstepping with fuzzy logic systems, an innovative practical fixed-time tracking controller is suggested to address the identified issue. Through a series of simulation examples, the practicality and efficiency of the proposed approach are validated.

In this article, a finite-time learning-based optimal tracking problem for nonlinear systems with preassigned performance constraint is investigated. By designing a state predictor, a fuzzy approximator driven by prediction errors rather than tracking errors is formulated to precisely compensate the effect of the unknown uncertainties. The design realizes a decoupling of control and estimation loops, effectively ensuring transient approximation performance and avoiding chattering induced by nonzero initial tracking errors. Then, based on the estimated components, a robust steady-state control scheme embedded with a prescribed performance mechanism is tailored to guarantee that the output state can converge to a predefined range within a preassigned time. This endows the designed controller with a specified time tracking capability independence on control parameters. To make a tradeoff between tracking precision and energy cost, a finite-time learning-based optimal control policy is exploited by utilizing adaptive dynamic programming technique to serve as an adaptive supplementary controller, where single critic neural network is trained for acquiring the solution of the Hamilton–Jacobi–Bellman equation. Compared with the traditional gradient descent method, the established learning law is updated by introducing an auxiliary variable, which enhances learning performance and guarantees finite-time convergence of adaptive weights. Simulation examples examine the effectiveness and superiority of the suggested scheme.

This paper presents a distributed saturation-tolerant fuzzy control scheme for stochastic multiagent systems (MASs) with unknown measurement sensitivity, where the states, consensus errors, and control inputs all are constrained. A concise nonlinear mapping is tactfully devised to impose appropriate constraints on full states without reliance on feasibility conditions. Besides, a novel resilient quantitative prescribed performance control (RQPPC) is developed, which incorporates finite-time performance boundaries with input-relevant dynamic boundaries generated by an auxiliary system, being expected to flexibly adapt to input saturation without violating performance constraints. Building upon the RQPPC, the transient and steady-state behaviors of consensus errors can be quantitatively predesigned free from repeated parameter tuning processes. Uncertain nonlinear terms in the converted system are successfully addressed by fuzzy approximation. The superiority and effectiveness of theproposed algorithms are confirmed by simulations with comparisons.

This article investigates adaptive dynamic programming (ADP)-based optimal control issue of nonlinear stochastic systems with asymmetric input constraints. The solution starts with developing generalized fuzzy hyperbolic model (GFHM) in the stochastic system, which aims to approximate unknown nonlinear terms. By establishing a nonquadratic cost function, the constrained$H_{\infty }$control problem is converted into zero-sum game and Hamilton–Jacobi–Isaacs equation (HJIE) is derived. To solve the HJIE, the ADP algorithm is developed by constructing a single-network adaptive critic framework. Assisted by GFHM, the updating process obviates the necessity for the dynamics of unknown nonlinear terms. Under the designed controller, the stability of the stochastic system is guaranteed by the Lyapunov method. Two illustrative examples validate the presented method.

We propose an encrypted controller framework for linear time-invariant systems with actuator non-linearity based on fully homomorphic encryption (FHE). While some existing works explore the use of partially homomorphic encryption (PHE) in implementing linear controller systems, the impacts of the non-linear behaviors of the actuators on the systems are often left unconcerned. In particular, when the inputs to the controller become too small or too large, actuators may burn out due to unstable system state oscillations. To solve this dilemma, we design and implement FHECAP, an FHEbased controller framework that can homomorphically apply non-linear functions to the actuators to rectify the system inputs. In FHECAP, we first design a novel data encoding scheme tailored for efficient gain matrix evaluation. Then, we propose a high-precision homomorphic algorithm to apply non-arithmetic piecewise function to realize the actuator normalization. In the experiments, compared with the existing state-of-the-art encrypted controllers, FHECAP achieves 4×–1000× reduction in computational latency. We evaluate the effectiveness of FHECAP in the real-world application of encrypted control for spacecraft rendezvous. The simulation results show that the FHECAP achieves real-time spacecraft rendezvous with negligible accuracy loss.

This article introduces a hierarchical learning (HL) framework for discrete-time (DT) systems with strict feedback structures to enable tracking control. Unlike the backstepping approach, our method creates dynamically adjustable virtual targets (VTs) for state variables at each layer, forming a cascading optimization structure. This innovative framework enables each layer to learn by approximating the solution to the DT Hamilton-Jacobi-Bellman (HJB) equation, thereby facilitating inter-layer self-optimization and directing the modification of adjacent VTs. To tackle the noncausal problem, we implement an iterative predictive learning framework that maps the current measurable state and known reference trajectories to VTs. This process allows the VTs to gradually align with the optimal trajectory during policy evaluation and update, achieving indirect tracking of state variables toward the desired targets. Additionally, the action network is transformed into a tracking network, incorporating future tracking errors to optimize its weights. This approach reduces tracking costs in the subsequent policy update while improving tracking performance. Rigorous convergence analysis and numerical simulations confirm the effectiveness of our method, highlighting its considerable potential in adaptive control.

This article proposes a resilient performance-based funnel control approach for transmission control protocol (TCP)/active window management (AWM) networks subject to sudden external disturbances, enabling effective congestion control within a prescribed time. The proposed scheme utilizes an error transformation mechanism with a fixed-time convergence performance function, which not only enhances the flexibility in handling initial conditions but also ensures tight performance guarantees. Additionally, a novel self-adjustable funnel boundary is constructed to mitigate the reliability degradation of control schemes caused by bursty factors such as strong disturbances and highly fluctuating reference signals. These techniques are then integrated into a command-filtered backstepping framework to ensure predefined tracking performance and the boundedness of all closed-loop signals. Finally, simulations demonstrate the feasibility and superiority of the proposed theoretical approach.

In this article, an adaptive dynamic programming (ADP)-based optimal control strategy for a series of fractional-order nonlinear systems (FONS) with unknown control directions is investigated. To eliminate the challenges posed by unknown control directions, fractional-order Nussbaum-type functions are introduced for FONS, expanding the range of possible applications. Additionally, since system performance is compromised by disturbances, a fractional-order disturbance observer is designed to counteract the effects of external disturbances and enhance system robustness. Furthermore, differential geometric methods are employed to investigate FONS, constructing appropriate diffeomorphism that provide equivalent systems for decoupled linearization. Then, an optimal control method is studied for a class of strictly feedback FONS, in which Nussbaum-type functions are combined with ADP theory during the backstepping design process. Finally, based on fractional Lyapunov stability theory and backstepping method, it is guaranteed that all signals of the closed-loop FONS are uniformly ultimately bounded (UUB). Numerical simulation and a PMSM model are utilized to verify the effectiveness of the presented method.

This article studies a prescribed finite-time consensus problem for uncertain nonlinear multiagent systems (MASs) with event-triggered updates. First, the novel finite-time performance boundaries are proposed to ensure that consensus deviations converge to the predefined steady-state zones within a preassigned time, and by using asymmetrically parallel boundaries to constrain consensus errors to narrow feasible regions, small overshoots of consensus errors are assured. Second, by utilizing the inherent approximation property of fuzzy logic systems (FLSs), a fuzzy state observer is devised to recover the unmeasurable states. Based on the observation outcomes, an improved event-triggered output-feedback controller is synthesized so that the number of control input updates is reduced without incurring an evidently deteriorated control performance. The salient merits of the proposed approach are that all consensus errors are free from great overshoots, while settling time can be explicitly assigned in advance. Finally, two examples are given to verify the validity of theoretical results.

To address the finite-horizon coupled two-player mixedH2/H∞control challenge within a continuous-time affine nonlinear system, this research introduces a distinctiveQ-function and presents an innovative adaptive dynamic programming (ADP) method that operates autonomously of system-specific information. Initially, we formulate the time-varying Hamilton–Jacobi–Isaacs (HJI) equations, which pose a significant challenge for resolution due to their time-dependent and nonlinear nature. Subsequently, a novel offline policy iteration (PI) algorithm is introduced, highlighting its convergence and reinforcing the substantive proof of the existence of Nash equilibrium points. Moreover, a novel action-dependentQ-function is established to facilitate entirely model-free learning, representing the initial foray into the mixedH2/H∞control problem involving coupled players. The Lyapunov direct approach is employed to ensure the stability of the closed-loop uncertain affine nonlinear system under the ADP-based control scheme, guaranteeing uniform ultimate boundedness (UUB). Finally, a numerical simulation is conducted to validate the effectiveness of the aforementioned ADP-based control approach.

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.

In this paper, to tackle the optimal control problem, we propose a$\mathcal{Q}$-Learning approach for continuous-time nonlinear systems without any dynamic information. Primarily, the Hamiltonian and optimum cost functions are utilized to articulate the$\mathcal{Q}$-function of continuous-time affine systems. To reduce the dependence of algorithms on system information, a novel$\mathcal{Q}$-Learning approach is derived to obtain optimal solutions of nonlinear continuous-time systems without requiring knowledge of either the drift information$p(x)$or input gain$q(x)$. To implement this approach, critic and actor neural networks can be iterated alternately using an integral reinforcement learning method to estimate the$\mathcal{Q}$-function. Furthermore, all signals in closed-loop system are demonstrated to be ultimate uniform bounded (UUB). It is worth noting that there exist rare literatures focused on the optimal control problem of continuous-time nonlinear uncertain systems via the$\mathcal{Q}$-Learning for actor/critic networks iteration. Finally, two simulations are used to confirm the effectiveness of the proposed algorithm.Note to Practitioners—Nonlinear continuous-time systems, being ubiquitous in engineering practice, are widely employed due to their versatility and effectiveness. Aiming at such systems, a$\mathcal{Q}$-learning approach with optimal feature is proposed to strengthen control efficiency while reduce costs. However, it is well known that accurately capturing all the dynamic information of the system is a formidable task in practical operation. This defect inevitably weakens the feasibility of model-based control algorithms. Since the$\mathcal{Q}$-learning algorithm presented in this paper does not require any dynamic knowledge of systems, it is promising enabler in enhancing the effectiveness and flexibility of engineering activities.

This article investigates the cooperative control problem for stochastic multiagent systems (MASs) with dynamic constraints. A new universal barrier function is proposed, which is applicable to many systems with different types of constraint functions, even unconstrained systems. Several mapping functions are constructed to constrain the state variables directly without feasibility conditions, and the tracking control is achieved for stochastic MASs with deferred full-state constraints under the backstepping framework. In order to regulate the tracking error more precisely, the funnel error transformation is improved and the deferred funnel controller is developed by introducing a preassigned finite-time function. Based on the deferred funnel controller, the tracking error can be maintained within the predetermined funnel in the preassigned time. The convergence time can be defined according to the actual requirements, and it is independent of the design controller parameters and initial conditions. Finally, some simulation results are given to demonstrate the effectiveness of the proposed control algorithm.

In this article, the optimal control strategy for organism is investigated by using the adaptive dynamic programming (ADP) method under the architecture of nonzero-sum games (NZSGs). First, a tumor model is established to formulate the interaction relationships among normal cells, tumor cells, endothelial cells, and the concentrations of drugs. Then, the ADP-based method of single-critic network architecture is proposed to approximate the coupled Hamilton-Jacobi equations (HJEs) under the medicine dosage regulation mechanism (MDRM). According to the game theory, the approximate MDRM-based optimal strategy can be derived, which is of great practical significance. Owing to the proposed mechanism, the dosages of the chemotherapy and anti-angiogenic drugs can be regulated timely and necessarily. Furthermore, the stability of the closed-loop system with the obtained strategy is analyzed via the Lyapunov theory. Finally, a simulation experiment is conducted to verify the effectiveness of the proposed method.

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.

This article investigates the tracking control problem for nonlinear systems. An adaptive model is proposed to represent the dead-zone phenomenon and solve its control challenge with a Nussbaum function in conjunction. Drawing inspiration from the existing prescribed performance control schemes, a novel dynamic threshold scheme is developed that fuses a proposed continuous function with a finite-time performance function. A dynamic event-triggered strategy is applied to reduce the redundant transmission. The proposed time-varying threshold control strategy has fewer updates than the traditional fixed threshold and improves the efficiency of resource utilization. A command filter backstepping approach is employed to prevent the complexity explosion faced by the computation. The suggested control strategy ensures that all system signals are bounded. The validity of the simulation results has been verified.

This article investigates the finite-time containment control problem for fractional-order nonlinear multiagent systems (FOMASs) with event-triggered inputs. First, a new Lyapunov stability lemma is developed, which provides a basic approach for the completely unknown nonlinear fractional-order system to realize finite-time convergence. Considering the containment control for FOMASs, the restricted assumption that the derivatives of leaders' trajectories are known to the followers is removed, and only the boundedness of derivatives is required in this article, whose upper bound need not be known. To reduce the burden of communication, an event-triggered condition consisting of the control input and a decreasing function related to the containment errors is devised, which can provide more design freedom to balance the system performance and communication resources. According to the proposed fractional-order finite-time convergence lemma, a distributed adaptive containment control scheme is developed, such that each follower can be steered to the convex hull spanned by the leaders in finite time. Simulation examples further demonstrate the effectiveness of our proposed method.

This article studies the containment control problem of nonlinear multiagent systems (MASs) subjected to communication link faults and dead-zone inputs. In case of an unknown fault in the communication link, there is no constant Laplacian matrix anymore and each follower agent cannot be informed of the global information simultaneously. To deal with this problem, an adaptive compensating estimator is constructed to estimate the signal spanned by the leaders. Instead of using the linear filter, a nonlinear filter is employed, which both solves the classical complexity explosion in the traditional backstepping method and flushes out the usefulness of the boundary layer error. Considering the dead zone input, we propose two event-triggered schemes, that is, the update-triggered scheme and the transmit-triggered scheme. In the former, the threshold function involves the tracking errors and additional dynamic variable, which can provide the desirable tradeoff between the containment control performance of the considered MASs and saving communication resources. In the latter, the triggered condition is designed according to the characteristic of dead zone, which makes the communication burden be reduced further. Following the backstepping design framework, an adaptive containment control is constructed, it is shown that the containment error can converge to an adjustable residual set even if MASs are subjected to the unknown and bounded communication link faults and dead-zone inputs. Finally, an example is given to show the effectiveness of the proposed results.

In this article, the constrained adaptive control strategy based on virotherapy is investigated for organism using the medicine dosage regulation mechanism (MDRM). First, the tumor-virus-immune interaction dynamics is established to model the relations among the tumor cells (TCs), virus particles, and the immune response. The adaptive dynamic programming (ADP) method is extended to approximately obtain the optimal strategy for the interaction system to reduce the populations of TCs. Due to the consideration of asymmetric control constraints, the nonquadratic functions are proposed to formulate the value function such that the corresponding Hamilton-Jacobi-Bellman equation (HJBE) is derived which can be deemed as the cornerstone of ADP algorithms. Then, the ADP method of a single-critic network architecture which integrates MDRM is proposed to obtain the approximate solutions of HJBE and eventually derive the optimal strategy. The design of MDRM makes it possible for the dosage of the agentia containing oncolytic virus particles to be regulated timely and necessarily. Furthermore, the uniform ultimate boundedness of the system states and critic weight estimation errors is validated by Lyapunov stability analysis. Finally, simulation results are given to show the effectiveness of the derived therapeutic strategy.

An extend-policy iterative algorithm is proposed for solving the ecological evolving-lung cancer cells growth inhibition optimal drug delivery scheme. With the analysis of the cell proliferation-apoptosis process of lung cancer cells with primitive immune system and external drug interventions, such as chemotherapeutic drugs and immunological agents, a model of ecological containment of lung cancer cells mimicking injection labeling is constructed. The HJB equation for biological tissue damage has also been established by considering the concentration of lung cancer cells in the blood and the amount of drug administered. The final simulation experiment proved the effectiveness of the drug delivery scheme.

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.

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 is considered on underactuated fractional-order stochastic systems (FOSSs) with actuator saturation and incrementally conic nonlinear terms, whose fractional-order α ∈ (0,1) . First, to bring FO dynamic signals, solving the unmodeled dynamics, in the meantime, the saturated nonlinear term of the control input is taken into account. At the time, to cope with the stability issue of FOSS under such situation, the fault tolerant resilient controller based on underactuated condition is designed. Then, according to the method of the Lyapunov and It∧ o differential formulation to design proper multiple Lyapunov-Krasovskii (L-K) functions, such that, a novel sufficient condition of the robustly asymptotically stability of fuzzy FOSS under underactuated conditions is rigorously proved in terms of linear matrix inequality (LMI). Furthermore, in order to research the mean square stability of the above-mentioned system, so the solution of FOSS is obtained to achieve this purpose. By applying the above method, which is proposed in this work that the controlled system can be obtained with faster response and higher control accuracy. At last, to display the superiority of the above-mentioned scheme is effective, tethered satellite system and numerical results are presented.

This article investigates an optimized containment control problem for multiagent systems (MASs), where all followers are subject to deferred full-state constraints. A universal nonlinear transformation is proposed for simultaneously handling the cases with and without constraints. Particularly, for the constrained case, initial values of states are flexibly managed to the midpoint between upper and lower boundaries by utilizing a state-shifting function, thus eliminating the initial restriction conditions. By deferred constraints, the state is forced to fall back into the restrictive boundaries within a preassigned time. A neural network (NN)-based reinforcement learning (RL) algorithm is executed under the identifier-critic-actor architecture, where the Hamilton-Jacobi-Bellman (HJB) equation is built in every subsystem to optimize control performance. For actor and critic NNs, updating laws are simplified, since the gradient descent method is performed based on a simple positive function rather than square of Bellman residual error. In view of the Lyapunov stability theorem and graph theory, it is proved that all signals are bounded and the outputs of followers can eventually enter into the convex hull constituted by leaders. Finally, simulations confirm the validity of the proposed approach.

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.

This article analyzes and validates an approach of integration of adaptive dynamic programming (ADP) and adaptive fault-tolerant control (FTC) technique to address the consensus control problem for semi-Markovian jump multiagent systems having actuator bias faults. A semi-Markovian process, a more versatile stochastic process, is employed to characterize the parameter variations that arise from the intricacies of the environment. The reliance on accurate knowledge of system dynamics is overcome through the utilization of an actor-critic neural network structure within the ADP algorithm. A data-driven FTC scheme is introduced, which enables online adjustment and automatic compensation of actuator bias faults. It has been demonstrated that the signals generated by the controlled system exhibit uniform boundedness. Additionally, the followers' states can achieve and maintain consensus with that of the leader. Ultimately, the simulation results are given to demonstrate the efficacy of the designed theoretical findings.

In this paper, a self-triggered fuzzy adaptive switched control strategy is proposed to address the synchronous tracking issue in switched stochastic multiagent systems (MASs) based on mode-dependent average dwell-time (MDADT) method. Firstly, a synchronous slow switching mechanism is considered in switched stochastic MASs and realized through a class of designed switching signals under MDADT property. By utilizing the information of both specific agents under switching dynamics and observers with switching features, the synchronous switching signals are designed, which reduces the design complexity. Then, a switched state observer via a switching-related output mask is proposed. The information of agents and their preserved neighbors is utilized to construct the observer and the observation performance of states is improved. Moreover, a modified self-triggered mechanism is designed to improve control performance via proposing auxiliary function. Finally, by analysing the relationship between the synchronous switching problem and the different switching features of the followers, the synchronous slow switching mechanism based on MDADT is obtained. Meanwhile, the designed self-triggered controller can guarantee that all signals of the closed-loop system are ultimately bounded under the switching signals. The effectiveness of the designed control method can be verified by some simulation 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.

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, fractional-order nonautonomous system (FONAS) with the input delay and nonlinear terms are considered and investigated using adaptive fuzzy control method based on Q-learning. With the novel estimation model, the defined predictions for the error system determines the weights of the fuzzy logic system (FLS). On this basis, an error derivative-based cost function is introduced, which not only deals with the classic problem that quadratic term cost function is unbounded in infinite time, but also resolves the challenge that the exponential discount factor cost function fails to stabilize asymptotically. For the unmeasurable part of the state, the designed fuzzy observer eliminates the restriction on the gain parameters. Furthermore, based on the measured information and the actor–critic architecture of the online training FLSs, the improved adaptive fault-tolerant control (FTC) input approximate the optimal control. Utilizing a fractional-order Lyapunov method, the stability of FONAS with actuator faults is discussed, and a sufficient criterion for stability is obtained, which is easier to perform with convex optimization tools. Finally, numerical simulations are shown to display the effectiveness of the optimal adaptive fuzzy FTC strategy.

This article investigates a class of optimal joint therapeutic regimens based on adaptive dynamic programming (ADP) and generalized fuzzy hyperbolic model (GFHM) for multiple tumor populations subject to immune effects as well as multiple drugs. Obtaining a model of the abnormal proliferation process of single tumor cells with multiple interventions is then the first step to conducting the treatment. In this article, the trajectories of healthy and unhealthy systems are obtained by constructing a virtual affine proliferation model. A strong connected trace of multiple agents is further developed by constructing a Hamiltonian function of the drug delivery cost of the unhealthy system. ADP and GFHM are gathered as consensus–fuzzy policy iterative algorithms, in which convergence and stability are ensured and the optimal dosing scheme achieves tumor cell inhibition.

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 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 investigates a finite-time fuzzy quantized control problem for a class of nonlinear systems considering deferred constraints. Instead of the tracking errors themselves, the auxiliary error variables constructed via the shifting function are employed into nonlogarithm barrier Lyapunov function to perform error constraints, not only making the restrictive conditions in initial phase be removed but also ensuring tracking errors to evolve within the preassigned regions after a given time. Then, to allow for a reduced computational cost concerning fuzzy/neural approximators, a single parameter updating based fuzzy wavelet neural network is devised to approximate the unknown nonlinearity acting on every subsystem. Furthermore, by using hysteresis quantizer to convert continuous control inputs into discrete scalars, a robust fuzzy quantized controller is synthesized with the aid of a novel quantization decomposition scheme, where the problem of constrained data bandwidth is successfully handled without involving chattering in control signals. Finally, simulations confirm the benefits and efficiency of the proposed method.

In this article, the event-triggered saturation-tolerant control problem of nonlinear multiagent systems (MASs) is investigated based on the finite-time fuzzy composite learning approach. Specifically, a novel concept, named as deferred saturation-tolerant prescribed performance control, is proposed, which guarantees the flexible prescribed performance in the face of input saturation, while there are no needs of initial restrictions on distributed errors. Moreover, by extracting weight errors from filtering operations and auxiliary variables, a finite-time fuzzy composite learning rule driven by weight and distributed errors is developed for improving the learning performance and ensuring that unknown nonlinearities are precisely estimated. Then, resorting to event-triggered communication mechanism, signal transmissions among connected agents only occur when triggering conditions are satisfied, contributing to a reduced communication burden. Finally, simulations with comparative studies are provided to confirm the effectiveness and superiority of the proposed method.

This article proposes a distributed containment-based critical bus voltage coregulation strategy of submicrogrids (SMGs) with positive minimum interevent times (MIETs) in a multimicrogrid system (MMGS). First, the feedback linearization technique allows us to deal with nonlinear distributed generator (DG) dynamics. The critical bus voltage regulation problem of an ac microgrid (MG) is transformed into an output feedback tracking problem of a linear multiagent system (MAS) containing nonlinear dynamics. In addition, an event-triggered strategy based on containment control is proposed. The strategy limits each critical bus voltage within a reasonable range while having a voltage difference between SMGs to allow power flow. Furthermore, an innovative trigger mechanism has been designed based on multiple measurement errors. Based on this mechanism, the controllers are updated in an acyclic manner at the moment of event sampling, saving computational resources and transmission load. In addition, the proposed event-triggering mechanism guarantees the absence of Zeno behavior and a strictly positive MIET between each DG event. It is also more practical than the traditional event triggering because the hardware constraint always imposes a positive minimum time constraint between two consecutive event times. The protocol proposed in this article is fully distributed and scalable and does not depend on global information about the network graph. Finally, simulation results verify the effectiveness of the strategy.

This article studies a preassigned time adaptive tracking control problem for stochastic multiagent systems (MASs) with deferred full state constraints and deferred prescribed performance. A modified nonlinear mapping is designed, which incorporates a class of shift functions, to eliminate the constraints on the initial value conditions. By virtue of this nonlinear mapping, the feasibility conditions of the full state constraints for stochastic MASs can also be circumvented. In addition, the Lyapunov function codesigned by the shift function and the fixed-time prescribed performance function is constructed. The unknown nonlinear terms of the converted systems are handled based on the approximation property of the neural networks. Furthermore, a preassigned time adaptive tracking controller is established, which can achieve deferred prescribed performance for stochastic MASs that provide only local information. Finally, a numerical example is given to demonstrate the effectiveness of the proposed scheme.

This article mainly proposes an evolutionary algorithm and its first application to develop therapeutic strategies for ecological evolutionary dynamics systems (EEDS), obtaining the balance between tumor cells and immune cells by rationally arranging chemotherapeutic drugs and immune drugs. First, an EEDS nonlinear kinetic model is constructed to describe the relationship between tumor cells, immune cells, dose, and drug concentration. Second, the N-level hierarchy optimization (NLHO) algorithm is designed and compared with five algorithms on 20 benchmark functions, which proves the feasibility and effectiveness of NLHO. Finally, we apply NLHO into EEDS to give a dynamic adaptive optimal control policy and develop therapeutic strategies to reduce tumor cells, while minimizing the harm of chemotherapy drugs and immune drugs to the human body. The experimental results prove the validity of the research method.

The article is devoted to evolutionary dynamics optimal control-oriented tumor immune differential game system. First, the mathematical model covering immune cells and tumor cells considering the effects of chemotherapy drugs and immune agents. Second, the bounded optimal control problem covering is transformed into solving Hamilton-Jacobi-Bellman (HJB) equation considering the actual constraints and infinite-horizon performance index based on minimizing the amount of medication administered. Finally, approximate optimal control strategy is acquired through iterative-dual heuristic dynamic programming (I-DHP) algorithm avoiding dimensional disaster effectively and providing optimal treatment scheme for clinical applications.

This article researches the sliding mode control (SMC) for fuzzy fractional-order multiagent system (FOMAS) subject to time-varying delays over directed networks based on reinforcement learning (RL),$\alpha\in(0,1).$First, since there is information communication between an agent and another agent, a new distributed control policy$\xi_{i}(t)$is introduced so that the sharing of signals is implemented through RL, whose propose is to minimize the error variables with learning. Then, different from the existed papers studying normal fuzzy MASs, a new stability basis of fuzzy FOMASs with time-varying delay terms is presented to guarantee that the states of each agent eventually converge to the smallest possible domain of$0$using Lyapunov–Krasovskii functionals, free weight matrix, and linear matrix inequality (LMI). Furthermore, in order to provide appropriate parameters for SMC, the RL algorithm is combined with SMC strategy, and the constraints on the initial conditions of the control input$u_i(t)$are eliminated, so that the sliding motion satisfy the reachable condition within a finite time. Finally, to illustrate that the proposed protocol is valid, the results of the simulation and numerical examples are presented.

This article focuses on solving the synchronization problem of neural networks (NNs) in the presence of denial-of-service (DoS) attacks and communication delays. Specifically, an attack detection algorithm constructed based upon the acknowledgment (ACK) signal is provided to detect the sleeping and active intervals of DoS attacks. To reduce information transmission during the synchronization-seeking process, a new kind of Lyapunov function-based resilient event-triggered mechanism (ETM) is designed to modulate the information transmission between the master and slave systems. Then, an event-based impulsive controller is designed to achieve synchronization in the master–slave systems with event-triggered communication and communication delay between the event generator and the controller, where the impulsive control instants are produced by the resilient ETM rather than prescribed. Furthermore, a resilient sampled-data-based ETM and an event-based controller consisting of hybrid state feedback and impulsive controllers are developed. Under the proposed ETMs and controllers, some sufficient yet efficient criteria are derived to guarantee the master–slave synchronization of NNs. The influence of the attack parameters and triggering parameters on the synchronization performance is also discussed. Finally, two numerical examples and an application in image encryption and decryption based on the master–slave chaotic systems are given to demonstrate the effectiveness of the theoretical results.

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.

In order to solve the two-player Stackelberg differential game (SDG) for the continuous-time nonlinear Markov jump system (MJS), this article defines a unique$Q$-function and suggests a novel adaptive dynamic programming (ADP) method which is completely independent of system information. First, the optimal policies for the leader and follower are determined from down to the top, and it is further demonstrated that these policies are what make up the Stackelberg–Nash equilibrium point. Then, a novel action-dependent$Q$-function is established in order to attain completely model-free learning, which is the first attempt for SDG-based nonlinear MJS. Furthermore, the Lyapunov direct approach is employed to guarantee the stability of the closed-loop uncertain nonlinear MJS under the control scheme based on ADP, ensuring uniform ultimate boundedness (UUB). Ultimately, a numerical simulation is presented to validate the efficacy of the aforementioned ADP-based control approach.

In this article, the critical value problem of a class of model-free nonlinear surfaces with strong constraints is studied, and a$\boldsymbol {\gamma }$-iterative dual heuristic dynamic programming algorithm is proposed. Considering the high coupling of nonlinear surface and the algorithm structure of traditional dual heuristic dynamic programming, this article directly uses neural network to reconstruct the gradient relationship between adjacent strips of the Janbu segmentation method, so as to reduce the superdimensional calculation of partial derivatives still needed by first fitting the model. The critical value of the strongly constrained nonlinear surface is transformed into the optimal control law for solving the input-constrained nonquadratic HJB equation with discount factor$\boldsymbol {\gamma }$and the cofunction is defined to avoid the need to calculate the integral term in the repeated iterative process. Finally, the simulation results show that the$\boldsymbol {\gamma }$-iterative dual heuristic dynamic programming algorithm is effective in solving the critical sliding surface of a kind of rock and soil mass.

This article investigates the optimal control problem for the discrete-time (DT) nonlinear semi-Markovian jump systems (s-MJSs) that possess unknown dynamics. The study uses the semi-Markovian kernel approach to address the problem of mode-switching in these systems. This approach employs the transition probability and the sojourn-time distribution function to jointly determine the transitions between different modes. Then, with a neural network (NN) identifier, the demand for accurate information on the system dynamics is eliminated, and an optimal control method for the nonlinear s-MJSs is utilized to solve the Hamilton-Jacobi–Bellman equation (HJBE) built upon adaptive dynamic programming methodology. Additionally, a detailed analysis of the convergence of a value iteration-based algorithm, which solves the optimal control issue for the DT s-MJSs, is thoroughly discussed. Furthermore, an actor-critic NN is trained to attain an estimated solution to the relevant HJBE. Finally, to validate the designed approach, two simulations are performed to prove its effectiveness.

This article investigates optimal regulation scheme between tumor and immune cells based on the adaptive dynamic programming (ADP) approach. The therapeutic goal is to inhibit the growth of tumor cells to allowable injury degree and maximize the number of immune cells in the meantime. The reliable controller is derived through the ADP approach to make the number of cells achieve the specific ideal states. First, the main objective is to weaken the negative effect caused by chemotherapy and immunotherapy, which means that the minimal dose of chemotherapeutic and immunotherapeutic drugs can be operational in the treatment process. Second, according to the nonlinear dynamical mathematical model of tumor cells, chemotherapy and immunotherapeutic drugs can act as powerful regulatory measures, which is a closed-loop control behavior. Finally, states of the system and critic weight errors are proved to be ultimately uniformly bounded with the appropriate optimization control strategy and the simulation results are shown to demonstrate the effectiveness of the cybernetics methodology.

This article presents an online off-policy policy iteration (PI) algorithm using reinforcement learning (RL) to optimize the distributed synchronization problem for nonlinear multiagent systems (MASs). First, considering that not every follower can directly obtain the leader's information, a novel adaptive model-free observer based on neural networks (NNs) is designed. Moreover the feasibility of the observer is strictly proved. Subsequently, combined with the observer and follower dynamics, an augmented system and a distributed cooperative performance index with discount factors are established. On this basis, the optimal distributed cooperative synchronization problem changes into solving the numerical solution of the Hamilton-Jacobian-Bellman (HJB) equation. Finally, an online off-policy algorithm is proposed, which can be used to optimize the distributed synchronization problem of the MASs in real time based on measured data. In order to prove the stability and convergence of the online off-policy algorithm more conveniently, an offline on-policy algorithm whose stability and convergence are proved is given before the online off-policy algorithm is proposed. We give a novel mathematical analysis method for establishing the stability of the algorithm. The effectiveness of the theory is verified by simulation results.

This article investigates the event-driven fault-tolerance (ETFT) consensus problem for general linear multiagent systems (MASs) with partial loss of effectiveness (PLOE) and bias faults of actuators in leader-follower networks. Each agent's controller is only updated relatively infrequently at its event moments. A desirable feature of this article is that the proposed event-driven algorithm is fully distributed also independent of global information and additive fault boundaries. Based on this, a consensus error prediction model is used to avoid the limitation that each agent needs to monitor its neighbors' state under event-driven conditions continuously. We further excluded the Zeno behavior by proving that any adjacent event interval for each agent is greater than zero. The simulations verify our results.

This article investigates the optimal control strategy problem for nonzero-sum games of the immune system based on adaptive dynamic programming (ADP). First, the main objective is approximating a Nash equilibrium between the tumor cells and the immune cell population, which is governed through chemotherapy drugs and immunoagents guided by the mathematical growth model of the tumor cells. Second, a novel intelligent nonzero-sum games-based ADP is put forward to solve the optimization control problem by reducing the growth rate of tumor cells and minimizing chemotherapy drugs and immunotherapy drugs. Meanwhile, the convergence analysis and iterative ADP algorithm are specified to prove feasibility. Finally, simulation examples are listed to account for availability and effectiveness of the research methodology.

The cooperative output regulation (COR) problem of heterogeneous linear multiagent systems under digraphs has been considered under the assumption that continuous communication between neighbors and continuous update of controllers. To get rid of this assumption, that is, to realize event-triggered communication between neighbors and discrete update of controllers, this article proposes the fully distributed event-triggered observers to estimate the matrix and the state for the exosystem, and the event-triggered controllers to solve the COR problem. Moreover, the Zeno behavior is excluded by proving that the interevent times of each agent are strictly greater than zero under the design triggering conditions. Finally, two examples are given to verify the effectiveness and advantages of the proposed methods.

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 article investigates the distributed fuzzy adaptive containment control problem of stochastic nonlinear multiagent systems under a directed communication topology suffering denial-of-service (DoS) attacks. First, considering unknown stochastic disturbance and nonlinear characteristics for the followers, the mathematical models are modeled as It$\hat{o}$stochastic nonlinearity terms approximated through fuzzy logic systems. Second, the proposed dynamically adjusted event-triggered condition can effectively avoid inefficient transmission behavior. Moreover, an adaptive compensation protocol for input saturation is constructed to eliminate the effects of nonlinearities caused by input saturation. Finally, instead of the previous uniformly ultimately bounded containment control results, stability and asymptotic performance are guaranteed through valid reasonable adaptive control laws acquired through the backstepping control approach despite suffering DoS cyberattacks. Moreover, a simulation is given to verify the feasibility of the proposed method.

In this article, the leaderless adaptive fuzzy consensus control problem is studied for a class of stochastic nonlinear multiagent systems with unknown measurement sensitivity under false data injection attacks. Unknown measurement sensitivity and false data injection attacks can prevent sensors from obtaining right state information and make it difficult to design controllers and adaptive laws. The existing works considered only one of these cases for deterministic systems. In this article, the coexistence of both cases is considered with the help of Nussbaum functions and fuzzy logic systems, and the corresponding controllers and auxiliary variables are not only codesigned to solve the problem, but also extended to stochastic multiagent systems. Then, an improved switching threshold event-triggered mechanism is proposed to reduce the communication burden of the control channel. Furthermore, the leaderless asymptotic consensus control scheme for stochastic multiagent systems is proposed. The boundedness of all signals and leaderless asymptotic consensus control performance are guaranteed via the Lyapunov stability theorem. Finally, two simulation examples are given to verify the effectiveness of the proposed control scheme.

Deep learning methods have demonstrated promising performance in magnetic flux leakage (MFL) defect detection under adequate amounts of labeled samples. However, in industrial occasions, obtaining adequate amounts of labeled samples is time-consuming and expensive, and applying only limited labeled samples can lead to unsatisfactory defect detection accuracy. To address the above issues, a defect detection method named semisupervised circular teacher network (SSCT-Net) is proposed in this article. First, a parallel feature extraction network with hybrid attention is proposed in SSCT-Net so that the useful features of multiview MFL signals can be extracted simultaneously. Second, semisupervised circular learning is proposed for the first time. In semisupervised circular learning, a distinguishable feature embedding space is constructed, and two structurally identical deep networks cosupervise and collaborate through the proposed consistent circular strategy so that the decision bias of unlabeled samples can be reduced. Finally, the trained model is applied for defect detection in practice. The proposed method can establish a potential connection between multiview MFL signals and fully utilize labeled and unlabeled MFL signals. The experiments in simulations and real-world applications demonstrate that SSCT-Net can reach 92% detection accuracy with only 20% labeled samples, which is more effective than the state-of-the-art methods and leads to a promising practical utility of the proposed method.

This article considers the bipartite time-varying output formation-containment tracking control issue for general linear heterogeneous multiagent systems with multiple nonautonomous leaders, where the full states of agents are not available. Both cooperative interaction and antagonistic interaction between neighboring agents are taken into account. First, an observer is constructed using the output information to observe the state information. Then, based on the information between neighboring agents, an independent asynchronous fully distributed event-triggered bipartite compensator is put forward to estimate the convex hull spanned by the states of multiple leaders. Note that the compensator does not require to use of any global information. Subsequently, a formation-containment tracking control strategy based on the observer and compensator and an algorithm to determine its control parameters are given. The Zeno behavior is further proved to be excluded in any finite time. In addition, a novel self-triggered control strategy based only on the sampled information at triggering instants is also formulated, which avoids continuous communication among agents. Finally, a numerical example is given to validate the effectiveness and performance of the proposed control strategies.

This article considers the consensus problem of unknown linear multiagent systems (MASs) through adaptive event-driven control in leader-follower and leaderless networks. The proposed event-driven algorithms do not involve any global information related to the network communication structure and rely only on local information exchange to achieve consensus on MASs and are therefore fully distributed. Furthermore, the constraint of continuous communication among the agents is eliminated in terms of control law updates and triggering state monitoring. Another desirable aspect of this article is that the design process of the control algorithms is independent of the parameters of each agent's dynamics and thus does not require precise information about the dynamics of MASs. We further exclude the Zeno behavior of each agent by proving the existence of a strict positive lower bound between any two adjacent events. Finally, the effectiveness of the proposed adaptive event-driven algorithms is verified by a simulation example.

The article investigates full information control problem for switched neural networks subject to fault and disturbance. First, the main objective is realizing interval stability and zero tracking error under condition that neither of the neuron states’ vectors including the plant and reference models is available. Second, the desired full information controller and neural networks’ observer are designed to ensure observer-based dynamic error system mean-square exponentially stable with sufficient condition of strict weight$\mathcal {H}_{\infty } /\mathcal {H}_{-}$performance levels. Finally, we concentrate on stability analyses and fault tolerance for switched neural networks with fault accompanied by disturbance through linear matrix inequalities (LMIs), Lyapunov function, and average dwell time, discussing it according to different values of fault. Finally, simulation examples are listed to account for the availability and effectiveness of the research methodology.

Considering that cooperative interactions and antagonistic interactions between neighboring agents may exist simultaneously in practice, this article studies the bipartite time-varying output formation tracking (BTVOFT) problems for homogeneous/heterogeneous multiagent systems with multiple nonautonomous leaders under switching communication networks. First, a full-dimensional observer-based nonsmooth distributed dynamic event-triggered (DDET) output feedback control scheme is proposed to ensure that BTVOFT is achieved, and the Zeno behavior is excluded. Note that the nonsmooth distributed control scheme requires global communication network information and may cause unexpected chattering effect, and the design cost of full-dimensional observer is relatively high. Thus, a reduced-dimensional observer-based continuous fully DDET scheme is proposed. Compared with the existing event-triggered schemes, the dynamic event-triggered scheme can ensure larger interevent times by introducing an additional internal dynamic variable. Finally, the effectiveness and performance of the theoretical results are validated by numerical simulations.

In this article, the fixed-time fuzzy adaptive tracking control problem is studied for a class of one-link manipulator systems with stochastic disturbances and multiple constraints. First, a modified dynamic surface control technique is proposed for the stochastic system, which provides a useful filtering solution to the fixed-time control of the stochastic nonlinear systems. Then, an extended stochastic fixed-time stability criterion is introduced to simplify the complex discussion process of stability analysis instead of existing fixed-time stability criteria. By using the unified barrier function, the constrained nonlinear system can be transformed into the nonconstrained nonlinear system. Moreover, a fuzzy adaptive controller is constructed with the funnel error transformation function, which improves the transient response of the system. The control objective of this article is that the steady-state error can be driven to the prespecified funnel in a fixed time based on the Lyapunov stability theorem and the extended stochastic fixed-time stability criterion. Finally, a simulation example is given to demonstrate the effectiveness of the proposed method.

For nonlinear systems, a novel adaptive dynamic programming (ADP) algorithm of self-triggered control (STC) strategy is proposed. This is a novel attempt to introduce self-triggering into the ADP algorithm. First, an identifier based on a generalized fuzzy hyperbolic model (GFHM) is established, which only uses input–output data to reconstruct the unknown system, thus reducing the requirements for system dynamics. Then, the critic neural network (NN) adjusts continuously, while actor NN updates the control strategy only at triggering instants. The event-triggered control (ETC) reduces the use of control resources and improves the anti-interference capability. However, it requires dedicated hardware to monitor whether triggering rules are violated, which is not feasible on most general-purpose devices. Hence, we propose a novel technique, which uses the current state of the device to determine the state measurement at the next moment, calculate the control law, and then abandon persistently monitoring of the plant. This technique is called STC. Finally, the closed-loop system is guaranteed to be ultimate uniform boundedness (UUBs). Furthermore, a simulation example is given.

Though voltage-regulation and current-sharing of distributed generations (DGs) in dc-microgrids have been widely studied, additional communication links or independent modulation circuit should be added to achieve information transmission. To accomplish precise current-sharing/voltage-regulation without additional communication devices, this article proposes a communication-free intelligent edge control regarding voltage and current for dc-microgrids. First, the power-information dual modulation (PIDM) is designed to achieve information exchange among DGs and eliminate additional communication devices. Second, the cooperative control problem with two coupled targets, i.e., accurate voltage-regulation and current-sharing, is converted into a matter of optimal control. Therefore, the voltage-regulation and current-sharing could be solved concurrently. In addition, the control objective function of each DG is switched to provide the optimal controller and minimize the voltage/current control deviation, which is further switched to solve the Hamilton–Jacobi–Bellman (HJB) function. In order to solve this HJB function, which is difficult to obtain analytical solution, an intelligent edge control strategy with PIDM is proposed to solve the HJB function. Therefore, the precise voltage-regulation and current-sharing can be accomplished. Finally, the proposed control approach is verified through simulation results.

This article devotes to solve the fault-tolerant control problem based on interval type-2 (IT2) Takagi-Sugeno (T-S) fuzzy stochastic switched uncertain time-delayed systems with signal quantization. Stochastic switched systems can model a dynamic structure susceptible to abrupt faults, making it more practically significant in power systems or economic systems. The core design is an observer-based fault-tolerant control scheme that can estimate incomplete measurable variables and eliminate the influence of fault dynamically well and enhancing the robust stability of the systems subject to quantization effects. A novel method in seeking the upper bound solution of time-varying delay efficiently decreases conservativeness, especially for the proposed time-delayed system. The simulated analysis is specified to verify the availability and validity of the obtained design method.

This article investigates the fault-tolerant control problem for stochastic switched interval type-2 (IT2) fuzzy time-delayed uncertain systems based on unknown input observer synthesis, which can avoid uneasy measurement on the time derivative of output, and estimate unavailable or partially measurable states, including sensor and actuator faults accurately. First, a desired fuzzy observer is designed to ensure the observer-based dynamic error system mean-square exponentially stable with sufficient condition of a strict$(\ell,\hbar,\wp)$-$\mho $-dissipative performance, which is a unified framework of passivity, and$\mathcal {H}_{\infty }$provides results with less conservativeness. Then, we concentrate on stability analyses on dissipativity-based switched IT2 fuzzy systems with stochastic perturbation through linear matrix inequalities, Lyapunov function, free-weighting matrices, and average dwell time, discussing it according to different values of disturbance. Finally, simulation examples are listed to account for availability and effectiveness of the research methodology.

Considering that there are many systems with limited network bandwidth in practice, this article studies the leader-following consensus problem for a class of nonlinear multiagent systems (MASs). The purpose of this article is to reduce unnecessary information transmission between any pair of adjacent agents including the leader in the MASs through intermittent communication. The novel event-triggered and asynchronous edge-event triggered mechanisms are designed for the leader and all edges, respectively. The static and dynamic consensus protocols under these mechanisms are proposed to address the leader-following consensus problem for MASs with Lipschitz dynamics, and the systems will not exhibit Zeno behavior under these two control schemes. Note that the dynamic consensus protocol does not rely on any global values of MASs, it is a fully distributed way. Finally, a practice simulation example is introduced to illustrate the theoretical results obtained.

The cooperative bipartite containment control problem of linear multiagent systems is investigated based on the adaptive distributed observer in this article. The graph among the agents is structurally balanced. A novel distributed error term is designed to guarantee that some outputs of the followers converge to the convex hull spanned by the leaders, and the other followers' outputs converge to the symmetric convex hull. The matrices of the exosystems are not available for each follower. A general method is presented to verify the validity of a novel distributed adaptive observer rather than the previous approach. In other words, the definition of the M -matrix is not necessary in our result. Based on the distributed adaptive observer, an output-feedback control protocol is designed to solve the bipartite containment control problem. Finally, a numerical simulation is given to illustrate the effectiveness of the theoretical results.

In this article, the finite-time containment control problem of the nonlinear multiagent systems (MAS) is investigated, in which the follower agents are subjected to full state constraints. The fuzzy logic system is employed to approximate the uncertain dynamic of the nonlinear MAS. A new nonlinear transformation function (NTF) is proposed, which serves as a unified tool for coping with the systems subjected to state constraints and no constraint. By combing the variable transformation with the proposed NTF, the original systems with state constraints are converted into the equivalent free-constrained systems. Moreover, as long as the boundedness of the states in transformed systems is guaranteed, the states of the original MAS do not transgress the preassigned boundaries. Based on the finite-time stability theory, the adaptive fuzzy control scheme is constructed for the transformed systems. It is proved that the outputs of all the followers are driven to converge to the convex hull spanned by the leaders in a finite time, and all the signals in the closed-loop systems are bounded in sense of mean square. The full state constraints for the followers are not violated all the time. Especially, the control structure does not need to change even there is no constraint imposes on the state. Finally, simulation examples are given to verify the effectiveness of the proposed finite-time control scheme.

This article investigates multiple delay-dependent robust$H_\infty$finite-time filtering for uncertain Itô stochastic Takagi–Sugeno (T–S) fuzzy semi-Markovian jump systems with state constraints. Few studies exist for Itô stochastic T–S fuzzy semi-Markovian jump systems with state constraints. First, a T–S fuzzy semi-Markovian jump filter is explored and a controller is designed. In terms of linear matrix inequalities, delay-dependent sufficient conditions as well as bounded real lemma are gathered by utilizing stochastic Lyapunov function. Robust finite-time boundedness and input–output finite-time mean square stabilization are achieved and gain matrices of the filter and controller are obtained at the same time. A numerical example is presented to validate the feasibility of the proposed results in this article. And the admissible maximal delay bounds are calculated.

Aiming at the efficient online solution of the time-variant linear matrix inequality (LMI) under nonideal conditions (e.g., noise pollution), a predefined-time convergent and integral-enhanced zeroing neural network (PCIE-ZNN) model is built for the first time in this article. Compared with existing zeroing neural network (ZNN) models for settling the time-variant LMI, the PCIE-ZNN model proposed in this article is proved to have better convergence and stronger robustness even in the presence of noise interference through strict mathematical analysis and detailed numerical simulations. Specifically, the stability, predefined-time convergence, and robustness of the PCIE-ZNN model are guaranteed in theory. Then, numerical simulation cases fully compare the results of the proposed PCIE-ZNN model and the existing ZNN models for the time-variant LMI, which demonstrates the correctness of theoretical proof and the superiority of the PCIE-ZNN model in settling the time-variant LMI under various noise pollution. In addition, through comparative experiments of three sets of design parameters, the convergence speed of the PCIE-ZNN model can be further accelerated by selecting proper parameters.

In this work, we study simultaneous reconstructions of sensor fault and actuator fault, as well as fault-tolerant control (FTC) for nonlinear systems approximated by the T–S fuzzy model. By making the sensor fault as part of the state, a rectangular singular system is firstly given, based on which, a proportional-integral observer (PIO) is synthesized to realize the reconstructions of sensor and actuator faults simultaneously. With the support of these estimation information, an FTC scheme is well provided to maintain the stability of the closed-loop system even in the occurrence of faults. Furthermore, by resorting to linear matrix inequalities (LMIs), the stability criteria are formulated via the fuzzy Lyapunov function method. Finally, the performance of the theoretical result is verified through two real dynamics.

In this article, by use of sliding-mode control, a descriptor stochastic fuzzy system with time-varying delay is considered. First, a new sliding-mode surface is proposed. By use of it, the fuzzy system with different input matrices could be studied. At the same time, the controlled system still has strong robustness to external disturbance. Second, since time delay is variable, there is not the time-delay term in the function of the new sliding-mode surface. It makes the controller construct hard. Third, the process of constructing the controller is different from the traditional method. The process of designing the controller does not use the border of external disturbance. Using a new self-adaptive method, the considered system reaches and is kept on the surface. Unlike the earlier sliding-mode controller, the virtue of this controller is that the fluctuation of the controller is small. Finally, two simulations are given to illustrate the effect of this method.