This paper investigates the security path-tracking control problem for the connected vehicle swarm with uncertain dynamics, specifically emphasizing its resilience against dual-channel deception attacks. To ensure the security and reliability of data transmission against such cyber threats, a novel attack compensation mechanism is proposed to eliminate the impact of deception attacks by securing data transmission against signal tampering in both sensor-controller and controller-actuator channels. We design a fuzzy state estimator to reconstruct uncompromised signals from tampered data, thereby constructing a security control strategy resilient to deception attacks. Considering practical network bandwidth constraints, a fuzzy adaptive dynamic event-triggered path-tracking control strategy is developed, which integrates the proposed attack compensation mechanism and state estimator to mitigate the impact of cyber attacks. Sufficient conditions are established to guarantee the security path-tracking performance. With the Lyapunov stability theory, it is proved that error systems are uniformly ultimately bounded, and the Zeno phenomenon can be effectively prevented. Simulation results validate the effectiveness of the theoretical approach.

This work considers the security formation control for the autonomous mobile robot swarm with uncertain nonlinearity under dual-terminal false data injection attacks on both actuators and sensors. A feasible attack compensation mechanism is developed to eliminate the influence of tampering on the transmitted signals of actuators and sensors. Reconstruction of uncompromised signals is achieved through an adaptive neural network state estimator. Considering the limited network bandwidth, an event-triggered adaptive neural network security formation control strategy is proposed by integrating the compensation mechanism and the state estimator. Sufficient conditions are derived to ensure the uniformly ultimate boundedness of the formation error system. It is rigorously proven that the proposed method can avoid the Zeno phenomenon. Finally, simulation verification demonstrates the validity of theoretical results.

This paper addresses the adaptive finite-time fault-tolerant tracking control problem for nonlinear output feedback systems with actuator faults under multiplicative deception attacks. First, a composite observer is developed by integrating a fault compensation mechanism with the compromised output signal. Unlike conventional state observers, the proposed observer can simultaneously estimate unmeasured system states, actuator faults, and external disturbances. Second, a sig function, novel coordinate transformations, and an attack compensator are introduced to develop a nonsingular finite-time adaptive tracking controller under deception attacks. The proposed controller effectively eliminates the singularity problems inherent in traditional finite-time controllers and ensures the desired tracking performance. In addition, an improved finite-time adaptive filter is introduced to enhance control accuracy and relax constraints on design parameter selection, compared to existing filtering methods. To reduce communication burden, a dynamic event-triggered mechanism (DETM) is incorporated. The proposed control strategy guarantees practical finite-time stability of the closed-loop system while successfully avoiding the Zeno phenomenon. Simulation results further verify the effectiveness of proposed strategy.

In this paper, an adaptive time-varying formation optimal tracking control strategy is presented for nonlinear heterogeneous multi-agent systems (MASs) with performance constraints and unknown dynamics. A prescribed-time performance function is designed to quantify the tracking error constraints, while an error transformation function is introduced to eliminate initial value constraints and address singularity issues. Notably, the settling time and initial conditions of the performance function are independent of both the initial tracking error and system parameters. To facilitate reinforcement learning (RL)-based optimal formation control, a performance index function is formulated that incorporates the transformed tracking error, control input, and an exponentially discounted term. This design effectively avoids infinite integral values and ensures minimization of the index function. Moreover, stability analysis demonstrates that the time-varying formation tracking errors converge to the desired accuracy within a prescribed time, regulated by a sliding-mode control mechanism. Finally, numerical simulations on two practical examples validate the feasibility and effectiveness of the proposed control strategy.

This paper investigates a novel learning-based sliding mode control (SMC) strategy for a class of nonhomogeneous semi-Markov switching systems with incomplete sojourn-time information. In contrast to existing studies, the sojourn-time probability density functions of semi-Markov kernel are considered to be incompletely known, relaxing the assumption of completely known sojourn-time distributions. The main novelty lies in constructing a novel learning-based SMC scheme to realize the attainment of the quasi-sliding mode, overcoming the difficulty caused by incomplete sojourn-time information. By utilizing the upper bounds of sojourn time for each subsystem mode and constructing the multiple-Lyapunov function, sufficient conditions for mean-square stability are derived for the resulting closed-loop system. Moreover, a recursive sliding mode learning controller is developed to ensure finite-time reachability of the sliding motion and to effectively suppress both parametric uncertainties and switching-induced chattering. The effectiveness and practical applicability of the proposed method are validated through the DC-DC buck converter application.

For interconnected nonlinear systems, the global continuous-time/event-triggered decentralized output feedback prescribed-time (PT) stabilization problem is discussed in this paper. A strategy employing dual time-varying gains with distinct properties is introduced to facilitate the design of the observer and controller. Using these gains within a nonrecursive design approach, a continuous-time decentralized output feedback PT controller is developed to achieve PT stabilization. Further, an event-triggered decentralized output feedback PT controller is constructed to reduce communication resources while fulfilling the control objective. A numerical example and a hardware-in-the- loop simulation of a 2-degree-of-freedom (DOF) helicopter system are employed to illustrate the availability of the decentralized output feedback PT controller.

This work addresses the nonfragile fault-tolerant control for power cyber-physical systems (CPSs) under denial-of-service (DoS) attacks, in which the cyber attacks are considered to be strongly concealed. In the fact of power CPSs frequently subject to various attacks during the operation, the innovation is to construct a double-layer stochastic process composed of a semi-Markov chain and a sequence of observed mode to analyze the DoS attacks from the viewpoint of hidden semi-Markov chain. To address potential actuator failures and controller gain perturbations, an observed-mode-dependent nonfragile control scheme is developed. By constructing a mode-dependent Lyapunov function that incorporates both attack modes and observed modes, sufficient conditions are derived to ensure mean-square stability of the closed-loop system through the semi-Markov kernel (SMK) approach, which systematically handles the stochastic characteristics of dwell time (DT) distributions under incomplete attack mode information. Finally, a simulation example demonstrates the validity of the proposed approach.

This study focuses on the model reference adaptive tracking control problem for uncertain switched systems using a dynamic event-triggered approach. Compared with the existing studies, the switching adaptive laws and switching adaptive tracking controller are dynamically event-triggered simultaneously for data transmission, leading to several challenges in achieving the tracking task and Zeno-free behavior. A multiple Lyapunov function method is established to design a switching event-triggered adaptive law and switching dynamic event-triggered adaptive tracking controller. The proposed dynamic event-triggered mechanism guarantees that the interexecution time between two consecutive triggered points has a positive lower bound. The state-dependent switching signal and switching dynamic event-triggered adaptive tracking controller are designed such that all the signals of the error dynamic system are bounded, and the system state asymptotically tracks the desired reference model state. Finally, an example of an electro-hydraulic system illustrates the availability of the established strategy.

Multi-UAV collaborative interception decision-making is a critical task in uncrewed aerial vehicle (UAV) applications. The core challenge lies in achieving real-time decision-making and precise coordination among multiple agents in highly dynamic and uncertain complex environments to successfully intercept highly maneuverable targets. However, existing methods still fall short in terms of rapid adaptability for interception decision-making, and the generalization performance of traditional reinforcement learning (RL) on new tasks needs improvement. To address these limitations, this article presents a novel meta-RL-based approach for multi-UAV interception decision-making. First, a task allocation method based on greedy strategy is proposed to achieve the rapid assignment of interception targets. Then, we design a task inference model that employs a probabilistic encoder to extract the shared structure across tasks from contextual information, thereby generating a latent variable to represent the task and enhance the training of the algorithm's network. Meanwhile, the proposed method is integrated with RL to improve its generalization capability in new tasks, enabling fast decision-making for the interception task. Finally, the comparative results against baseline algorithms validated the superiority of our method.

This article investigates iterative learning control of robot arms with initial errors and actuator faults. Resorting to backstepping technique, an actual controller that removes the iterative convergemt sequence is constructed to simplify the design. New updating laws with equilibrium factor are developed to treat the nonstrictnegative difference of composite energy function. A contraction mapping-based composite energy function method is executed to provide the convergence of errors. Finally, the validity of the proposed method is verified through a robot arm example.

This article addresses the security-based practical fixed-time adaptive stabilization problem for nonlinear cyber-physical systems (CPSs) with higher powers under deception attacks. First, a novel practical fixed-time stability criterion is proposed based on Nussbaum functions. The criterion introduces a relaxed convergence condition, facilitating the analysis of practical fixed-time stability for high-power nonlinear systems. Second, to compensate for the compromised states, a dual coordinate transformation structure consisting of a virtual coordinate transformation and an available coordinate transformation is proposed. This structure is applicable to both low- and high-power systems. Moreover, a security-based fixed-time control strategy is developed by combining adaptive methods with Nussbaum functions to mitigate the influence of unknown attack gains. The proposed strategy also effectively overcomes the singularity problem. Finally, the effectiveness of the designed control strategy is validated through simulations.

In this work, a new tracking control algorithm based on integral reinforcement learning (IRL) is proposed for nonlinear Markov jump systems (MJSs) represented by interval type-2 fuzzy (IT2F) model. The adoption of IT2F approach to describe nonlinear objects can overcome the uncertainty problem of traditional Takagi–Sugeno (T-S) fuzzy model. The control input and external disturbance are considered as two opposing competitors, and the optimal control problem is transformed into a zero-sum game problem. Furthermore, a mode-free IRL algorithm is designed to solve the fuzzy-coupled algebraic Riccati equations without the system dynamics information. The stability and the convergence of new scheme are demonstrated through Lyapunov theory, and the desired tracking goal is achieved. Finally, the designed model-free IRL algorithm is applied to a typical mass-spring-damper mechanical system and the implementation results demonstrate the practicality and effectiveness of the proposed method.

This article addresses the real-time security reachable set (RS) control problem for nonlinear semi-Markov jump cyber–physical systems (s-MJCPSs) subject to multiple time-varying delays and actuator attacks. Then, based on the neural network (NN) approximation approach and employing a sliding mode control (SMC) strategy, an adaptive NN SMC scheme is proposed to tackle challenges arising from nonlinear attack functions and mode jumps. The proposed strategy ensures s-MJCPSs stability and mean-square boundedness of system states within a predefined RS. Sufficient conditions for real-time security RS control are derived. Finally, an example is presented to demonstrate the effectiveness of the proposed strategy in realizing adaptive real-time RS control.

This paper studies the problem of dynamic periodic event-triggered control (DPETC) for networked control systems subject to external disturbances, quantization errors and time-varying delays. The developed DPETC scheme has potential in making full use of scarce network resources. Moreover, to cope with the quantization effect, an improved dynamic quantization scheme is innovated, considering both the encoder and decoder processes to ensure that a finite number of bits are transmitted at each transmission instant. With the help of a novel constructed Lyapunov function, sufficient conditions are derived and an appropriate dynamic periodic event-triggering mechanism is designed to guarantee the input-to-state stability in the neighborhood of the origin. Furthermore, the number of zoom actions of quantizer parameter, the upper bounds on the maximally allowable delay and the maximally allowable transmission interval are also provided. Finally, effectiveness of the theoretical results is illustrated by a numerical example.

This paper focuses on the adaptive neural network output feedback control problem for heterogeneous vehicle platoon system (HVPS) under the condition of sensor deception attack. Firstly, an event-triggered mechanism by double-channel transmissions is constructed, which considers both controller triggering and output triggering, effectively reducing the waste of communication resources and unnecessary data transmission. Secondly, in order to estimate the unmeasured states in the system, a neural network state observer is designed. It takes the output signals caused by output triggering and sensor failures as input to generate usable state estimates and ensure the smooth operation of the backstepping method. In addition, barrier Lyapunov functions (BLFs) are used to impose constraints on vehicle spacing errors to ensure that the errors will not expand infinitely. Combined with dynamic surface control (DSC) technology, an adaptive event-triggered output feedback control scheme based on backstepping is proposed in this paper. It guarantees both individual vehicle stability and weak string stability of HVPS. Through Lyapunov stability analysis, it is proved that all signals remain bounded. Finally, a simulation example verifies the effectiveness of the proposed method.

In this paper, an observer-assisted model free adaptive predictive control algorithm is designed for nonlinear heterogeneous multi-agent systems under denial-of-service (DoS) attacks. To begin with, consensus error of the system is transformed into an equivalent linear data model at the operating point by means of a dynamic linearisation technique. Thereafter, in order to conserve network communication resources, a dynamic event-triggering mechanism is devised for the consensus error and an observer is incorporated to facilitate the acquisition of a time-varying parameter called "pseudo partial derivative" in the linear data model. Subsequently, to mitigate impact of random DoS attacks, we introduce an attack compensation strategy that allows each agent’s output to swiftly revert to the neighbourhood of leaderless consensus objective in DoS-free intervals. Finally, the pseudo partial derivative parameter estimates, observation errors, and consensus errors are rigorously proved to be bounded in mean using the contraction mapping principle. Simulation results on heterogeneous nonlinear multi-agent systems demonstrate that, compared with conventional event-triggered model free control, the proposed approach improves the convergence rate by 33.82%, reduces steady-state consensus error by 93.80%, and decreases pre-convergence fluctuations by 21.91%. Furthermore, it achieves a 64.00% faster recovery speed and a 95.98% higher recovery accuracy after DoS attacks. Meanwhile, the average communication load is reduced by 59.79%.

This paper investigates neural network-based dynamic adaptive event-triggered security compensation feedback control for implicit power systems (IPSs) subjected to false data injection (FDI) attacks. By introducing a time-varying positive exponential term, a new dynamic adaptive event-triggered mechanism (DAETM), which can avert Zeno phenomenon and address the issue that the controller fails to cancel the internal impulses of singular systems when using period-sampling based event-triggered mechanisms, is proposed to achieve the goal of enhancing communication efficiency while relieving channel load. Via adopting radial basis function (RBF) neural network (NN) approximation method to estimate the unknown FDI attack signals, the event-based security compensation feedback (SCF) controller with adaptive corrective term is designed, which can compensate the FDI attack signals and minimize the effect of FDI attacks. Considering the designed DAETM as well as the adopted RBF NN approximation method, a novel Lyapunov-Krasovskii (L-K) functional is constructed, which captures the dynamic adaptive event-triggered information and facilitates to obtain the ideal adaptive law of NN weight matrix, thereby contributing to the realization of regularity, impulse-freeness and ultimate boundedness of IPSs and promoting the collaborative design of DAETM and SCF controller. The final simulation results for IPSs validate the effectiveness of the studied methodology.

This paper is concerned with the co-design problem of the adaptive neural sliding mode compensation controller and multidomain DoS-attack-aware scheduling protocol (MDSP) for the direct current microgrids (DC-MGs). It is considered that the process of transmitting the system data over wireless networks is vulnerable to intrusion by cyber-attacks, in which the aggressors might send denial-of-service (DoS) attacks to the output data and inject fake messages into the control signal. Due to the fact that not all data in DC-MGs can be acquired from direct measurements, an attack-parameter-dependent observer is introduced to estimate the unknown states under DoS attacks. Then, with the objective of enhancing the system responsiveness and bandwidth utilization, a novel MDSP is presented by introducing a multidomain structure, which enables to maintain the communication function of DC-MGs when some channels fail or are blocked. In the meantime, the neural network technique is employed to approximate unknown attack information based on the observer states, thus recovering normal data attacked by potential false data injection (FDI) attacks. Additionally, by introducing the partitioning strategy, the corresponding resilient finite-time boundedness for both the reaching phase and sliding motion phase is acquired, respectively. An adaptive sliding mode compensation controller is devised by introducing the additional compensation terms, which can improve the control accuracy and the adaptability to cyber-attacks, thus ensuring that the states of DC-MGs are rapidly entered and maintained on the sliding surface during a finite-time interval. Finally, the availability and validity of the presented approach is verified through a DC-MG with three constant power loads.

In this paper, the stabilization problem is addressed for a class of globally Lipschitz nonlinear dynamical systems. An event-triggered impulsive control (ETIC) method is introduced to establish asymptotic stability and exponential stability criteria for the resulting closed-loop systems without and with time delay, respectively. Compared with the extant results, a new type of switching and event-triggered impulsive systems are considered, and some general asymptotic stability and exponential stability conditions are provided. It is proved that Zeno behaviors can be excluded and the control frequency can be appropriately regulated through the appropriate selection of event parameters. Finally, an application example of the Chua’s circuit is given to verify the efficiency of the approach and theoretical analyses. Note to Practitioners—Since impulsive control provides an easier and cheaper strategy than continuous control, it has been widely applied to many practical situations, such as control of satellite rendezvous, synchronization of permanent magnet synchronous motors, consensus of multi-agent systems and so on. Different from the time-triggered impulsive control methods, the proposed ETIC method can flexibly regulate the control frequency, which meets the increasing requirement for reducing unnecessary waste of communication resources in modern industries. Compared with the extant results, an ETIC method is established with time-varying threshold parameters and event interval parameters in this paper. Moreover, the effects of event parameters and time delay on convergence rate are analyzed, which can provide reference for improving system performance in practical applications.

This paper investigates the event-triggered secure control problem for fuzzy Markov jump systems (MJSs) with time-varying delays. In order for higher resource efficiency, a multi-level probabilistic event-triggered mechanism (MLPETM) is newly established, which reduces the data transmission frequency by investigating possible variations of triggering thresholds. Given the network-induced phenomena, the MLPETM’s output may undergo cyber-attacks, and the controller may not switch synchronously along with the system. Asynchronous secure controllers are thus developed to perform secure control of fuzzy MJSs. Sufficient conditions dependent on fuzzy basis functions, state delays and jumping modes are established to guarantee the dissipative finite-time boundedness of the resultant closed-loop system. Afterward, an easy-to-check fuzzy secure control algorithm is developed to compute the controller gains. Finally, the one-link robotic arm system and the truck-trailer system are borrowed to validate the proposed results. Note to Practitioners—Networked control systems (NCSs) play a key role in real applications like automobile industry, power systems, and autonomous mobile robots. As a key part, the communication network such as Controller Area Network is embedded into the NCSs to perform the communication tasks between different control units. In spite of great benefits from the communication network, both the security and the efficiency issues of the data transmission are challenging for the engineering designer. Besides, the target physical system is usually nonlinear, and is very likely to undergo abrupt changes in the networked environment. In terms of these challenges, this paper studies the asynchronous security control of networked Markov jump systems with time-varying delays and randomly occurring cyber-attacks. A multi-level probabilistic event-triggered mechanism (MLPETM) is newly established, which studies the effect of the stochastic variation regarding the triggering threshold on the triggering performance. Potential cyber-attacks are modelled in a randomly occurring fashion and then absorbed into to the control law which allows operation modes asynchronous to the system modes. Finally, the one-link robotic arm system and the truck-trailer system are borrowed to check the proposed findings. Note that both the transmission security and communication traffic regulation are well concerned, which renders the developed method applicable to practical systems.

This paper studies the dynamic event-triggered output feedback control problem for networked switched systems (NSSs) under communications consisting of network congestion and data collisions. A dynamic event-triggered mechanism (ETM) is constructed in the sensor-controller network channel, which reduces unnecessary communications and saves network resources. To prevent data collisions in the controller-actuator network channel, the Round-Robin protocol (RRP) is used for communication scheduling, where a periodic function is used to select nodes gaining access to the network. Under the dynamic ETM and RRP, a dynamic output feedback controller is designed, and sufficient conditions are derived to ensure the mean square exponential stability (MSES) of the underlying NSSs using the mode-dependent average dwell time (MDADT) approach and multiple Lyapunov function techniques. Switching-mode-dependent controllers are further derived to achieve the desired stability. Finally, an application oriented example of F-18 aircraft model is provided to verify the usefulness of the proposed theoretical results.

This paper deals with the event-triggeredH∞asynchronous secure control problem for piecewise homogeneous Markov jump systems (PHMJSs) with denial-of-service (DoS) attacks and mode-dependent deception attacks. With the aid of acknowledgement character technique and probabilistic threshold division method, a mode-dependent switching-like probabilistic event-triggered mechanism is established to save communication resources while remedying the adverse effects of both DoS attack-induced packet losses and stochastic fluctuation of the triggering threshold on PHMJSs. Sufficient criteria are developed to ensure the stochastic stability andH∞performance of PHMJSs with hybrid cyber-attacks. It analytically builds the relationship between the maximum number of consecutive packet losses induced by DoS attacks and the triggering parameter. A co-design scheme is provided to calculate the event-triggering weight matrices and controller gains. Ultimately, an application-oriented example of the F-404 aircraft engine system is offered to demonstrate the validity of the proposed approach.

In this work, the asynchronous dynamic output feedback control is investigated for discrete nonlinear networked semi-Markov jump models with cyber attacks, in which asynchronous phenomenon refers to the mode mismatch between the controller and the system. For the potential uncertainty of system parameters, the interval type-2 fuzzy method is adopted to characterize nonlinear semi-Markov jump models. In light of actual state information unavailable in complex environment, the dynamic output feedback technique is proposed. The main novelty is to construct an appropriate dynamic output feedback control scheme, fully consider the asynchronous phenomenon of the controller mode, and introduce auxiliary variables to solve the matrix dimensional problem, so that the IT2 fuzzy network semi-Markov jump models under the influence of cyber attacks have better dynamic performance. According to stochastic theory, semi-Markov kernel, interval type-2 fuzzy method, and dwell-time-dependent Lyapunov function, sufficient criteria are established to ensure that the networked system is$\vartheta $-error mean-square stable under random denial-of-service attacks. Furthermore, numerically checkable conditions are formulated to solve the asynchronous dynamic output feedback controller gain. Finally, a two-degree-freedom quarter-car suspension model is given to explain the superiorities of the proposed design approach. Note to Practitioners—As one of the research hotspots, networked control systems show outstanding advantages of low maintenance cost, easy installation, and high flexibility. However, cyber attacks often occur in networked control systems, posing a great threat to signal transmission. With the development of modern science and technology, semi-Markov jump models, owing to their excellent engineering background in modeling complex system, have a wide range of application prospects in solar receiver control, power electronics, chemical processes, and network communication. Note that some factors in the practical dynamical systems, such as parameter uncertainty and dwell information, cannot be completely obtained, and actual controller mode has switching delay with the system mode. In this paper, the asynchronous output feedback control is studied for discrete nonlinear networked semi-Markov jump models with cyber attacks. On the basis of interval type-2 fuzzy and dwell-time-dependent Lyapunov function, the$\vartheta $-error mean-square stability is realized under random denial-of-service attacks. This research provides a new approach to study output feedback control strategies for discrete networked systems.

In this paper, the sliding mode control (SMC) problem is investigated for continuous stirred tank reactor (CSTR) via dynamic self-triggered protocol subject to external disturbance. By introducing the switched stochastic system with semi-Markov parameter, the fluctuations in product concentration and the variations in reaction temperature within the CSTR are modeled. Without the sojourn-time constraint, novel strategy about asymptotic mean-square stability is adopted to design the SMC scheme based on the Lyapunov function and the stationary distribution of embedded Markov chain. Furthermore, to enhance the transmission efficiency and the dynamic performance, novel self-triggered protocol is developed in combination with SMC technology, predicting the subsequent triggered moment under the current sampling data and providing the lower bound of internal execution time. Under the dynamic self-triggered protocol, an appropriate SMC law is proposed to ensure the finite-time reachability of the specified sliding surface. Sufficient conditions are established for asymptotic mean-square stability of the associated switched stochastic systems. Finally, the proposed method is verified the simulation. Note to Practitioners—The continuous stirred tank reactor (CSTR) system is widely used in the industrial processes, in which the performance and control are critical to efficiency and quality. Under the key parameters of temperature and concentration, it is necessary to strictly control the temperature and monitor the concentration in real-time. Modern manufacturing and industrial processes have become increasingly complex, and single system can no longer accurately describe the dynamic characteristics. As a special hybrid system with continuous evolution, instantaneous change, and stochastic effect, switched stochastic semi-Markov system can describe the concentration fluctuations and reaction temperature changes in the CSTR, showing significant potential for applications. In recent years, networked control system has attracted attention due to their advantages in remote task execution. The self-triggered protocols conserve bandwidth and reduce dependence on external devices by predicting the next triggered time. In this work, switched stochastic system with semi-Markov parameter is adopted to investigate the self-triggered sliding mode control (SMC) problem for the CSTR. This research provides a novel perspective of SMC strategy based on switched stochastic semi-Markov system and self-triggered algorithm in the CSTR.

The paper addresses the fault-tolerant optimized control of switched complex networks with unknown state and actuator fault. A proportional-integral intermediate observer is constructed to estimate unknown elements by relaxing known boundary requirement. An optimized controller is proposed to achieve fault-tolerant synchronization via adaptive dynamic programming scheme. A critic neural network is employed to solve the value of the Hamilton–Jacobi–Bellman equation. Sufficient conditions are established to ensure the uniformly ultimately bounded synchronization performance. Finally, an example is simulated to deliver the effectiveness of the proposed approach.

This paper mainly focuses on fixed time control for interlayer synchronism problem under voltage-flux–time (VFT) delay deplux memristive neural networks (DDMNNs). Distinct from most previously reported achievements, continuous memristive VFT neural networks (MMNs) field with$2^{2{n^{2}} + n}$variables are considered, where the memristor is considered as a continuous time-varying uncertain parameter, and n is the number of states in DDMNNs. This memristor is a type of continuous system built on the HP memristor. To synchronize VFT DDMNNs, a fixed time control policy is proposed for interlayer synchronism of flux and voltage values under the VFT DDMNNs. According to the second method of Lyapunov, selecting appropriate Lyapunov functionals and using inequality techniques, the structure and parameters of a kind of fixed time controller are designed, and interlayer synchronism criteria for DDMNNs are obtained. Finally, a secure communication scheme based on interlayer synchronism is designed. It is found that the fixed settling time is relative to the constructive of DDMNNs and the parameters of the fixed time controller. Note to Practitioners—This work solves the fixed time interlayer synchronism control problem of VFT DDMNNs, which can be applied to some practical scenarios, such as information security communication and image encryption. When transmitting signals in computer networks, for security, encryption mechanisms are usually added to network communication protocols to achieve secure communication. In some encryption applications, there are special requirements for speed of encryption and decryption, which requires reducing encryption and decryption time and improving efficiency of encryption. This work provides a fixed time control strategy which can achieve synchrony for VFT DDMNNs under controllable time, thereby achieving encryption under controllable time. Meanwhile, improve encryption efficiency in secure communication.

The article studies an adaptive practical fixed-time tracking control problem of nonlinear system using the funnel control method and the dynamic event-triggered control mechanism. First, an adaptive practical fixed-time controller is built using radial basis function neural networks and an improved funnel function. On the one hand, it eliminates the impact of unknown nonlinear functions on system performance and forces the tracking error to evolve within the funnel boundary. On the other hand, the transient performance of the system is enhanced by the preassigned funnel boundary. Second, a nonlinear command filter with high-order nonlinear term is constructed to solve the problem of “explosion of complexity” in the backstepping approach. Further, the filter error compensating input is designed to counteract the detrimental impacts of the filter error on the tracking performance. In addition, to achieve the dynamic modification of threshold parameters and minimize communication resources, a dynamic event-triggered mechanism is devised based on auxiliary dynamic variables and dynamic threshold parameters. It is rigorously proved theoretically that the closed-loop system is practical fixed-time stable and Zeno behavior is ruled out. Ultimately, the single-link robotic arm system validates the efficiency of the acquired control approach. Note to Practitioners—The application of traditional control algorithms is severely limited in real industrial systems due to typical constraints on input, output, and communication resources, particularly in autonomous surface vehicles and robot fields. Nevertheless, the existing methods only take into account asymptotic tracking control problems based on the time-triggered mechanism, which is impracticable for a large number of systems in reality. Therefore, the paper studies the problem of funnel control and communication resource of the nonlinear system, and an adaptive practical tracking control scheme is proposed through the dynamic event-triggered mechanism and funnel function, which not only ensures that the nonlinear system is practical fixed-time stable but also improves the transient and steady-state performances of the nonlinear system.

This article focuses on a dynamic event-triggered adaptive neural networks backstepping control for a class of uncertain strict-feedback systems with communication constraints. The uncertain terms including external disturbances and unknown nonlinear functions are approximated by radial basis function neural networks, in which the weight update laws are obtained via the gradient descent algorithm, ensuring the local boundedness of the approximation error of neural networks. Then, to enhance the transmission efficiency of control signals, a dynamic event-triggered mechanism is introduced, which enables the dynamic adjustment of threshold parameters in response to the actual tracking performance. It is strictly proved via the Lyapunov stability criterion that the tracking error can converge to a desired small neighborhood of the origin, and all signals in the closed-loop system are bounded. Finally, the validity of the control strategy is demonstrated through a simulation example.Note to Practitioners— In practical network control systems, control signals are typically transmitted continuously or periodically to devices through the communication network in the form of data packets. As communication networks are usually shared by various system nodes, and resources such as communication channel bandwidth and computational capabilities are limited, improving the transmission efficiency of control signals becomes a crucial design problem for controllers in network control systems. Therefore, This study introduces a control method via event-triggered sampling, aiming to enhance sampling efficiency while ensuring the stability and reliability of the system. The proposed control method is suitable for a broad category of strict-feedback nonlinear systems with communication constraints, offering notable advantages such as low-complexity design and straightforward implementation.

The asymptotic tracking control problem is investigated for nonstrict-feedback switched nonlinear systems by developing a dynamic event-triggered adaptive control technology. A key contribution is to design a hysteresis-type switching rule and an event-triggering-based switching controller to realize the asymptotically convergent target. First, by utilizing the Nussbaum-type function technique, the obstacle caused by unknown nonsmooth saturation nonlinearity is circumvented. Second, a novel gain-dependent switching signal is constructed, which ensures a time interval between any adjacent switching. Furthermore, a dynamic event-triggered schema is established, which allows the occurrence of asynchronous switching phenomenon generated by switching and event-triggering. An event-triggering-based switching controller is designed so that the adaptive asymptotic tracking control problem is solvable even when input saturation and vanishing control gains arise. Finally, simulation results with theoretical analysis are presented to validate the feasibility of the control algorithm. Note to Practitioners—With the development of artificial intelligence techniques, the studies of switched nonlinear systems have received widespread attention. This investigation is motivated by the vanishing control gains problem for switched nonlinear systems. We propose a co-design of a hysteresis-type gain-dependent switching rule and an event-triggering-based switching controller for switched nonlinear systems under input saturation and vanishing control gains. In existing results, the designed control signal is required to enter into the systems everywhere, while we relax the restriction. An improved dynamic event-triggered adaptive control framework has been established to obtain less conservative conditions further, where the control gain is allowed to vanish at some points. This study presents the method for practitioners interested in adaptive control design.

This paper mainly concentrates on the issue of fixed-time cluster secure synchronization upon interlayer switching networks with DoS attacks, in which the DoS attacks may cause random damage to the nodes/edges in networks and then generate impulsive disturbances. To resist the attacks, one robust fixed-time discontinuous control strategy is proposed, such that all the nodes in interlayer switching networks can achieve the cluster secure synchronization even when the communication topology are disconnected or changed over time after being influenced by attacks. By using the Lyapunov method, several effective conditions for fixed-time cluster secure synchronization and the maximum convergence time near to the actual value are obtained. In view of the comparison principle, a suitable estimation method upon stability time for the switching networks is established, and the stability time is computable and controllable. Moreover, the correlation among attack intensity, connectivity network, impulsive interval, impulsive disturbance intensity and synchronization time is revealed. Simulation case is finally supplied to manifest the availability of the obtained outcomes.

This article addresses the zonotope-based ${\mathcal {L}}_{\infty }$ event-triggered control for switched positive systems with frequent asynchronism and interval uncertainties. In view of the advantages of zonotope in set description, we extend it to the set-based control, propose a novel zonotope-based control method, and further consider the typical model uncertainty and frequent asynchronism. First, by introducing a 1-norm-based event-triggered scheme, the time-varying state zonotope is established based on the closed-loop system and event-triggering conditions. Second, the dual convergence and ${\mathcal {L}}_{\infty }$ performance of the positive state zonotope is analyzed by defining suitable center and radius functions for matched and mismatched intervals, respectively. Then, the permissible mode-dependent average dwell time signals and asynchronous controllers are jointly designed to guarantee the stability and ${\mathcal {L}}_{\infty }$ performance for the underlying system. Finally, the effectiveness and advantages of the proposed method are demonstrated through a numerical example.

This article studies the adaptive fuzzy asynchronous (AFA) stabilization of discrete networked hidden stochastic semi-Markovian switching power systems under cyber attacks. Due to the complex network environment, cyber-attacks are taken into account, in which the fuzzy logic rule is adopted to describe the unknown deception attacks. Considering the mismatch mechanism between the controller and the system, an adaptive fuzzy controller runs asynchronously with the system, where the hidden semi-Markovian model is used to characterize the asynchronous mechanism. Based on the detected mode and the fuzzy logic rule, an AFA stabilizing controller is designed for the underlying system. Using the stochastic Lyapunov function related to the detected mode and system mode, sufficient criteria are given for the AFA controller design, ensuring that the underlying system is bounded stable in the mean square. Finally, the proposed scheme is verified by the simulated example.

This study investigates the synchronization of reaction-diffusion complex dynamical networks (CDNs) based on semi-Markov switching topology and an event-triggered protocol. The investigated model is rendered more practical via the introduction of a semi-Markov process for stochastic jump CDNs. Based on the internal dynamic variable history information, a dynamic-memory event-triggered strategy is proposed, wherein the primary novelty lies in its prior transmitted packets to enhance the control performance. This further reduces data transmission based on the dynamic threshold parameters. The Bessel-Legendre inequality is adopted to reduce the conservatism of the obtained results. In addition, sufficient synchronization conditions are established to ensure the stochastic stability of the error system for two different models (partial differential equations-and ordinary differential equations-based models). Furthermore, two examples are provided to illustrate the effectiveness of the theoretical results.

This work studies the novel sliding mode control (SMC) of discrete nonlinear stochastic switching models under semi-Markovian parameter and incomplete semi-Markovian kernel (SMK). The characteristic of nonlinear system is described by an interval type-2 fuzzy (IT2F) model that can be recognized as a collection of several type-1 fuzzy models. The uncertainties in system parameters is efficiently captured using the lower and upper grades of membership. Based on the mode-dependent Lyapunov function and incomplete SMK, sufficient conditions are proposed to ensure the stability of sliding dynamics. Moreover, an IT2F SMC law based on learning strategy is developed such that the state signals are guided onto the predetermined sliding region and the mode switchings-induced chattering is effectively reduced. Finally, the IT2F SMC strategy is validated through the simulation of truck-trailer model.

This article addresses synchronization control of switched complex network with unknown state and actuator fault. A mode-dependent proportional-integral intermediate observer is explored to estimate unknown elements with high-estimation accuracy. A hybrid controller is constructed to treat the asynchronous occurrence of impulses and switching moments. With the help of mode-dependent average dwell time and mode-dependent average impulsive interval, a mode-dependent criterion is established to guarantee the uniformly bounded synchronization performance. Two examples are simulated to deliver the effectiveness of the proposed method.

This article primarily studies the adaptive output-feedback consensus tracking control issue for nonlinear multiagent systems (MASs) with unknown control directions against deception attacks. First, a composite observer combining the state observer and the disturbance observer is developed to concurrently estimate the states of confronting deception attacks and unmeasurable disturbances. Moreover, to resolve the unknown gains resulting from deception attacks, the adaptive attack compensator is proposed. Furthermore, in view of the logarithm Lyapunov function in the final step of the design process and the intelligent approximation technique, a new composite-observer-based adaptive consensus tracking control strategy is constructed. The suggested control strategy ensures the boundedness of all the closed-loop signals while also achieving synchronous tracking of the leader's output by the followers. Last but not least, the effectiveness of the suggested control strategy is validated through two simulation examples.

In this article, the problem of adaptive dynamic event-triggered nonsingular predefined-time (PT) tracking control for a third-order fully heterogeneous vehicle platoon system is investigated. First, an improved nonsingular PT adaptive tracking controller is constructed by introducing a piecewise continuous function within the control signal in each step of the backstepping procedure, which avoids the singularity problem of the traditional PT control signals in the existing literature and guarantees the existence of the values for all the terms within the control signals in the real number field. Second, a class of universal barrier Lyapunov function (UBLF) is adopted to set restrictions on distance, which ensures that collisions are avoided and communication connectivity is maintained. In addition, based on a dynamic auxiliary variable, the communication resources are saved with the use of the dynamic event-triggered control scheme. Finally, through the PT stability criterion, it is proven that the PT stability of the whole vehicle platoon is ensured, and the effectiveness of the control algorithm is verified by the simulation results.

This article principally presents the adaptive fuzzy dynamic event-triggered output-feedback consensus tracking control problem for constrained nonlinear multiagent systems encountering false data injection attacks, using monotone tube boundary functions (MTBFs). First, the composite observer is designed to concurrently estimate the unpredictable system states and disturbances. Then, a novel parameter integration approach is constructed via the fuzzy approximation technique to reduce the computational burden, where the uncertainty terms (state errors, composite errors, fuzzy weights, and injection attacks) can be converted into a linear parameterized form with merely one unknown scalar. In addition, a set of MTBFs is designed to prevent the excessive overshoot or jitter of system errors in the transient-state performance. Furthermore, an adaptive dynamic event-triggered control strategy is constructed on the basis of the auxiliary dynamic variable. All the closed-loop signals are shown to be bounded, and the followers can achieve the synchronous tracking of the leader's output. In the end, the simulation results demonstrate the efficiency of the proposed control strategy.

This study is devoted to the observer-based sliding mode control (SMC) for discrete nonlinear semi-Markov jump models with incomplete sojourn information and application to the quarter-car suspension model. The nonlinear plant with parameter uncertainty is represented by an interval type-2 fuzzy model, where the membership functions of the fuzzy rules are related to the system mode. Since sojourn information is challenging to obtain in practice, the sojourn time probability density function is considered to be incompletely available. The considered system is more general, not only relaxing the traditional assumption that all the sojourn time probability density functions are completely available, but also covering completely available sojourn time probability density functions as a special case. The main innovation is that an observer-based SMC scheme is designed, which makes the discrete nonlinear models have better dynamic performance, and realizes the reachability of discrete quasi-sliding mode. By the interval type-2 fuzzy and classical Lyapunov function, the mean-square stability criterion of the semi-Markov jump models is constructed employing additional matrix variables. Then, an observer-based SMC mechanism is constructed to achieve the reachability of the quasi-sliding mode. Ultimately, the proposed method is validated by a two-degree-freedom quarter-car suspension model.

The bipartite formation allows agents to achieve two formation structures in opposite directions and finds wide applications in social as well as natural situations. This article investigates the fast finite-time bipartite formation control problem for time-delay nonlinear multiagent systems operating in an obstacle environment. A fuzzy adaptive formation control strategy is proposed utilizing the leader-following method, under which the desired formation is achieved at a fast convergence rate. Since the practical actuator output is usually limited and susceptible to faults, its antisaturation and fault-tolerance capacities are thus considered in the controller construction. Moreover, an obstacle avoidance mechanism is embedded in the control strategy utilizing the artificial potential field method, ensuring the security operation of the formation. An improved Lyapunov–Krasovskii functional is constructed for the stability analysis, which makes full use of the time-delay information of the system. The fast finite-time convergence of the formation error system and the feasibility of obstacle avoidance behavior are verified with the Lyapunov stability theory and the designed energy function. Finally, the proposed control strategy is applied to the bipartite formation control task of a mobile robot swarm, and sufficient simulation results are presented to demonstrate the effectiveness of the theoretical analysis.

This paper proposes an adaptive robust preview control method for path tracking in tractor-trailer trucks, aiming to effectively mitigate trailer sway and attenuate stochastic disturbances while adapting to variable vehicle velocity and path curvature. First, we establish the path tracking control system for the tractor-trailer truck, incorporating the hitch angle and hitch angle rate into the system state to minimize trailer sway. On this basis, an adaptive robust preview control method is developed, integrating feedforward and feedback control to improve tracking performance and robustness. The feedforward controller is designed to proactively minimize tracking errors. In the feedback control, an adaptive observer-based$H_{\infty } $robust feedback controller is developed to limit the effects of stochastic disturbances, where an innovative preview distance model, considering variable vehicle velocity and path curvature, is applied to achieve preview control. Then, based on the$H_{\infty } $theory, the design criterion of the proposed feedback controller is established, where bilinear matrix inequality (BMI) is transformed into linear matrix inequality (LMI) to solve the observer and controller gains. Additionally, the fuzzy algorithm is performed to enable the feedback controller to adapt to variable velocity. Finally, we evaluate the effectiveness of the proposed method using a hardware-in-the-loop platform. Simulation results confirm its superior robustness and performance compared to the existing baseline control method.

Neural network adaptive iterative learning control (ILC) is developed in this article to treat strict-feedback nonlinear systems with unknown state delays and input saturation. These delays are treated by constructing the Lyapunov-Krasovskii (L-K) functions for each subsystem. A command filter is employed to avoid the derivative explosion caused by continuous differentiation of the virtual controller. Corresponding auxiliary systems are designed and integrated into the backstepping procedure to compensate input saturation and the unimplemented part of the filter. Hyperbolic tangent functions and radial basis function neural networks (RBF NNs) are employed to treat singularity and related unknown terms, respectively. The convergence of the resultant strict-feedback systems is ensured in the framework of composite energy function (CEF). Finally, a simulation example is adopted to substantiate the validity of the proposed algorithm.

Robust resilient control is promising and effective since it can combat gain perturbations in control system design. In this article, finite-time resilient control is investigated for the networked Markov switched nonlinear systems (NMSNSs). Both additive and multiplicative feedback gain perturbations with randomly occurring manners are considered during the controller design to improve its tolerance of inaccurate controller implementation. The mode information that is partially available to the controller is incorporated into the design. With the help of the fuzzy-logic method, fuzzy resilient output-feedback controllers are established to cope with the gain perturbations and immeasurable system states. Then, by developing a novel switching model, relaxed conditions compared with the existing results are obtained which guarantee the finite-time boundedness (FTB) of NMSNSs. Based on the FTB analysis, a fuzzy design algorithm is proposed via a new separation approach to obtain the controller gains. Eventually, simulations are conducted via a multimode robotic arm system to validate the achieved results.

In this work, via proposing a novel$\tan $-type asymmetric barrier Lyapunov function (ABLF), we developed a command filtered adaptive fault tolerant control scheme for a class of uncertain nonlinear systems with predefined-time asymmetric and time-varying output constraints. First, such a class of constraints under interest is more practical. Unlike most of the existing constraints that need to be addressed at the moment of inception, the initial value requirement of the constrained object in this work is released. A predefined setting time can be installed in advance through the implementation of a shifting function embedded within the proposed ABLF. Second, the problem of unknown actuator faults is considered where the actuator faults can be both multiplicative and additive. Third, by combining the command filter and backstepping techniques, a twice-transformation design method is presented to construct the desired controller, under which the errors between the virtual control laws and the outputs of the command filters can be compensated thoroughly. Aside from avoiding the “explosion of complexity” issue, the designed controller also achieves the requisite tracking performance. Meanwhile, under such controller, the effect of the actuator faults can be estimated. Finally, the validity of the given scheme is evaluated through the use of a practice example.

This article investigates the adaptive neural network (NN) tracking control problem for nonlinear networked control systems (NCSs) with finite-time prescribed performance (FTPP) subject to intermittent denial-of-service (DoS) attacks. It is noticeable that when the DoS attacker is active, the controller does not receive any information, which makes the controller fail to work. To tackle the challenge, an adaptive NN switching state observer is first built to estimate the unmeasurable states. Second, an FTPP function is constructed to boost the transient and steady-state performances of NCSs. Third, under the framework of the backstepping technique, an adaptive command filter is established by combining the dynamic adaptive technique with the switching state observer, which handles the “complexity explosion” problem and improves the robustness of NCSs. Besides, it is rigorously proved mathematically that the boundedness of all signals in the closed-loop system and the designed controller compels the tracking error to fall into the predefined boundary within a finite time. Finally, an application-oriented example of the single-link robotic arm system is utilized to demonstrate the viability of the proposed control method.

This paper investigates the attack-compensated output control problem for a class of Markov jump cyber-physical systems (MJCPSs) subject to mismatched modes. A sub-domain-awareness adaptive probabilistic event-triggered mechanism (APETM) is innovatively developed to fully enhance the control performance of the networked control system. Here, sub-domain-awareness means the network’s communication ability, which may be affected by time delay and network resource. To defend against the cyber-attacks imposed on the communication channel, a predictor-based compensator is constructed to mitigate the impact of attacks on the control performance. Different from the existing works, the mismatch degree between the controller and the system, governed by a random variable obeying any discrete-time distribution over$[0, 1]$, is changing dynamically. A mismatched output feedback controller is designed based on the APETM and attack-compensator, and an augmented closed-loop system is obtained. Both time delay-and triggering threshold-dependent Lyapunov functionals are introduced to perform the asymptotical stability analysis. With a separation technique, a solving algorithm is provided which converts the non-convex analysis conditions into traceable ones. Finally, simulations are conducted to validate the proposed results through a mass-spring-damping system model.Note to Practitioners—Cyber-physical systems (CPSs) have found many applications in the fields such as smart grid, gas distribution systems, and automated manufacturing systems. The open communication network deployed in CPSs face two main challenges including the security of data transmission and the efficiency of resource utilization. Owing to the practical environment and other factors, system parameters may change abruptly, which can be well defined by a Markov model. In the resultant Markov jump system, it is typically assumed that the mode mismatch degree between the controller and the system remains the same, which is unrealistic in a time-varying network environment. Motivated by these observations, this paper investigates the secure output control of Markov jump CPSs (MJCPSs) subject to mismatched modes and unknown cyber-attacks. An adaptive probabilistic event-triggered mechanism is innovatively proposed, which compared with the existing mechanisms strikes a higher level balance between the communication burden and the control performance. And attack-compensated mismatched output controllers are developed to stabilize MJCPSs and meanwhile preserve the security level. Finally, a mass-spring-damping system is adopted to verify the application effectiveness of the proposed results. Note that communication traffic control and secure control are finely involved based on CPSs, making our proposed results more applicable to practical systems.

A distributed adaptive secure control algorithm is proposed for asynchronous switching nonlinear multi-agent systems (MASs) in pure-feedback form while considering the sensor attacks and actuator faults, which eliminates the effect of attack signals, actuator faults and uncertainties without knowing the sign of the control gain functions. Since the system states measured by the sensors are corrupted by the malicious attacker, only the post-attack system states can be obtained. Thus, an improved coordinate transformation is constructed by using the post-attack system states and a backstepping method based on the improved coordinate transformation is developed to solve the consensus tracking control problem of the researched systems under sensor attacks. The common Lyapunov function is designed to ensure the stability of all asynchronous switching subsystems of each agent. In the end, a simulation example is presented to illustrate the theoretical results’ validity.Note to Practitioners—This paper deal with the distributed adaptive secure consensus tracking control problem for asynchronous switching nonlinear MASs, whose models can describe many phenomena in nature such as biological processes, robot team formation and sensor networks. It is extremely challenging to achieve the tracking control problem of the researched asynchronous switching nonlinear system in an unsafe network environment, where the unknown sensor attacks signals, actuator faults coefficients, and randomly switched non-affine nonlinearities exist together for the followers. Furthermore, the control design and stability analysis of the researched system is based on the common Lyapunov approach, which makes the developed approach more engineering oriented.

This article presents a co-design method of dynamic periodic event-triggering mechanism (DPETM) and output-based control law for networked control systems (NCSs) subject to inevitable imperfections such as limited network resources, exogenous disturbances and successive packet dropouts. The developed DPETM has the potential to make full use of scarce network resources compared to the periodic sampled-data control on the one hand, and is natural for practical digital platforms instead of a discretized version of continuous event-triggered control (CETC) one the other hand. In this paper, the whole closed-loop system is modeled a unified hybrid system by incorporating bilateral DPETM, successive packet dropouts effects and external disturbances, and an improved hybrid Lyapunov function is constructed for stability analysis. Based on the hybrid framework, some sufficient conditions are presented to guarantee$\mathcal {L}_{2}$-stability of the system while tolerating a maximum allowable number of successive packet dropouts (MANSD). Furthermore, new linear matrix inequality (LMI) conditions for co-design of control law and triggering strategy are derived by introducing some constraints with the free variables and a modified Young’s inequality. In addition, this paper considers two scenarios relating to whether an acknowledgment scheme is employed or not. Finally, the effectiveness of the proposed method is verified by two illustrated examples and comparative studies. Note to Practitioners—With the increasing requirement for reducing unnecessary waste of communication resources in modern industries, it is necessary to consider an alternative paradigm of the time-triggered control. In many digital control applications such as smart power grid, vehicle and remote surgery, the control tasks are often executed periodically, which makes it difficult for the theoretical results of CETC to be directly applied to practical digital platforms. The DPETM proposed in this paper, which only verifies the triggering conditions periodically at each sampling instant, is more suitable for practical digital platforms such as time-sliced embedded architectures compared to CETC. This paper investigates the stability problem for NCSs with DPETM subject to packet dropouts. Different from most of the existing literature on randomness of packet loss, this paper focuses on impact of the continuity of packet dropouts on system performance. Based on the hybrid framework and the Lyapunov approach, a co- design methodology of triggering condition and control law is proposed to ensure that the system satisfies the desired performance and can admit a MANSD.

This paper investigates the deferred output constraint (DOC) issues of high-order random nonlinear systems. The DOC indicates that the system output is constrained within a given range after the system running for a period of time, rather than being constrained at the beginning. This leads to an obstacle that the well used barrier Lyapunov function method is invalid because it is not defined at the initial stage. For this reason, a prescribed-time scaling function and a barrier function are introduced. Then, to more accurately describe the disturbances in nature, this paper considers a more common stochastic process than white noise, which is called colored noise. In addition, a dynamic-memory event-triggered mechanism (DMETM) that takes into account the influence of historical information of internal dynamic variables on trigger conditions is proposed to reduce the waste of communication resources. With the assistance of Lyapunov stability theory and backstepping approach, it is shown that our developed DMETM-based control scheme can guarantee that all signals are bounded in the presence of colored noises. Ultimately, two simulation examples are included to demonstrate the effectiveness of the proposed theory.Note to Practitioners—Since higher-order nonlinear systems can describe nonlinear features in system dynamics, some complex actual systems such as induction motorcycles and space vehicles can be modeled as such systems. In engineering applications, controlled systems are usually affected by random noises from external environment, thus colored noises are introduced in this paper. Compared with white noises, colored noises can describe disturbances in nature more accurately and reasonably. In addition, to ensure that practical systems such as car operation systems and robotic arm systems can work safely, their DOC issues need to be considered. However, the traditional barrier Lyapunov functions (BLFs) cannot solve the DOC problems because they are not defined in the initial stage, hence the prescribed-time scaling and barrier functions are proposed. Meanwhile, to circumvent the problem of limited communication bandwidth, a DMETM with delay terms of internal variables is devised.

This paper investigates the adaptive finite-time consensus tracking control problem for a class of nonlinear nonstrict-feedback multi-agent systems (MASs) with output constraints. Firstly, to deal with the output constraints problem, an improved tan-type nonlinear mapping (NM) function is presented for the first time. Then, the singularity problem that exists in finite-time control is successfully avoided by employing a novel switching function. A modified tracking error involving the dependent variable of the designed NM function is constructed to guarantee that the outputs of all agnets achieve consensus tracking simultaneously and satisfy the constraints requirement. In addition, a switching threshold event-triggered control (ETC) strategy is applied to design controller for each agent, which combines the advantages of fixed threshold strategy and relative threshold strategy, and saves system communication resources well. The developed distributed adaptive finite-time control protocol ensures that all the signals in the closed-loop system are bounded and the consensus tracking control is achieved in finite time. Finally, the effectiveness of the designed control strategy is verified by a simulation experimentNote to Practitioners—Due to the wide application of nonlinear MASs in practice, such as unmanned aerial vehicles (UAVs) formation control, robots formation control and so on, the adaptive finite-time consensus tracking control problem for a class of nonlinear nonstrict-feedback MASs is studied in this paper. In practical applications, the practical fast finite-time strategy can effectively increase the system convergence, the NM method not only solves the output constraints problem well, but also overcomes the conservativeness of traditional barrier Lyapunov functions. Then, in order to reduce the communication burden of the nonlinear MASs, a switching threshold ETC is considered. In addition, the system model and backstepping technology used in this paper are general and practical.

This work proposes an adaptive neural network asymptotic tracking control strategy, capable of ensuring flexible fixed-time prescribed transient behavior for switched nonlinear systems with external disturbances and input saturation. Unlike most existing prescribed performance controls with input constraints that ignore the contradiction in fulfilling the input constraint and the output constraint, the proposed strategy realizes a trade-off between them by constructing a modified fixed-time prescribed performance function. The performance function boundary will increase with the error between the actual input and the desired control input, which can sacrifice the user-specified performance while saturation exists and fix it while no saturation exists, lowering the risk of singularity. Together with the designed performance function, a Zeno-free event-triggered controller is built to enforce that the output error converges asymptotically and satisfies the performance function boundaries within a fixed time. Besides, the complexity explosion problem is circumvented through the command-filtered technique. Finally, two case studies are provided to validate the established control strategy.Note to Practitioners—Due to physical restrictions, there are various system input and output constraints in practical engineering, which severely hampers the application of both traditional and cutting-edge control algorithms, particularly in the chemical, boiler, robot, and other sectors. Regrettably, the existing approaches only consider input and output constraints separately and assume that they can be implemented simultaneously, which is unrealistic in many practical systems. Hence, this work focuses on developing a novel adaptive fixed-time prescribed performance control strategy by introducing a modification signal, which can not only comprehensively balance input and output constraints but also achieve the asymptotic tracking of the system output. Meanwhile, an event-triggered mechanism is introduced to deal with the problem of limited communication bandwidth.

This paper investigates a zero-sum game (ZSG)-based fault-tolerant tracking control problem for a class of interconnected nonlinear systems, in which the faults of each subsystem can affect the other subsystems through couplings. First, a static control policy is developed to transform the fault-tolerant tracking control problem into a ZSG problem of a deduced error system, where the controllers and the faults are regarded as players with opposite interests. Then, based on the sliding mode control technology and the concept of hierarchical design, a novel robust control policy is proposed to regulate the tracking error while minimizing a special cost function. Subsequently, a critic neural network (NN) is trained online to derive the solution of the coupling HJI equation. The critic NN weights are tuned on the basis of the gradient descent approach as well as the historical stored data, such that the persistence of excitation conditions are no longer required. Finally, a simulation example is presented to demonstrate the validity of the proposed control strategy.Note to Practitioners—Since complex modern engineering systems are difficult to be controlled by a single component, the research on adaptive control of interconnected nonlinear systems has become the mainstream trend. In addition, for the practical applications of interconnected systems, fault problems are becoming more common. These faults may make the system difficult to operate normally. Hence, how to guarantee the normal work of the control system when subject to faults has become a hot topic. Furthermore, several engineering applications often take production cost as an important index, and thus it is necessary to design a control strategy that can achieve control objectives with the minimum cost. This paper discusses the optimal fault-tolerant control problem for interconnected nonlinear systems. Meanwhile, a hierarchical sliding-mode control mechanism is designed to improve system robustness.

The issue of adaptive protocol-based control is studied for nonhomogeneous stochastic semi-Markov jump systems with denial-of-service (DoS) attacks. As a result of cyber attacks occurring during networked information transmission, the security controller design for the underlying nonhomogeneous semi-Markov jump systems becomes significantly more complicated. Different from the existing self-triggered strategy, an adaptive self-triggered strategy is proposed to reduce the updating frequency of the controller by adjusting the on-line threshold. The main novelty lies in constructing an appropriate adaptive self-triggered strategy to realize better dynamic performance, overcoming the difficulty caused by DoS attacks. By using the algebraic relationship among transition probability, probability distribution function, and probability density function, the time-varying transition rate is expressed based on the semi-Markov process. According to adaptive self-triggered strategy and DoS attacks, stochastic stability conditions are established. Furthermore, the desired adaptive self-triggered controller gains are derived to realize the stochastic stability for the corresponding system. Finally, the boost converter circuit model is carried out to ensure the feasibility of the proposed theoretical results.

The sliding mode control (SMC) is addressed for discrete-time semi-Markov switching slow sampling singularly perturbed models. Under only the part known semi-Markov kernel, the$\varepsilon $-dependent sliding function is designed for the underlying system. Based on the upper bound of the sojourn time of each system mode, sufficient conditions are obtained for mean-square stability. Then, a strategy to estimate the upper bound of the singularly perturbed parameter is given under an incomplete semi-Markov kernel. Moreover, an appropriate SMC scheme is synthesized to drive the system states onto the pre-specified sliding region. An inverted pendulum model is adopted to verify the practicability of the proposed strategy.

This article investigates the extended dissipative finite-time boundedness (ED-FTB) problem for fuzzy switched systems under deception attacks. To improve the network resource efficiency, a multidomain probabilistic event-triggered mechanism (MDPETM) is proposed. The mode mismatched phenomenon is modeled based on the switching delay information between the controller mode and the system mode. To extract the true signal generated by the MDPETM, a virtual delay concept is developed. The constraint that the controller and the system must have the same premise variables is removed. Based on the MDPETM, mismatched fuzzy state feedback controllers are first devised which may not share the same modes with the system. Then, by establishing fuzzy basis and controller mode-dependent Lyapunov functionals, sufficient criteria free of nonlinear terms existing in the literature are derived, which ensure the ED-FTB of the closed-loop system under admissible delays and deception attacks. Finally, an application-oriented one-link robotic arm system is utilized to validate the theoretical results.

In this study, asynchronous sliding-mode control (SMC) for discrete-time networked hidden stochastic jump systems subjected to the semi-Markov kernel (SMK) and cyber attacks is investigated. Considering the statistical characteristic of the SMK, which is challenging to acquire in engineering, this study recognizes the SMK to be incomplete. Due to the mode mismatch between the original system and the control law in the operating process, a hidden semi-Markov model is proposed to describe the considered asynchronous situation. The main aim of this study is to construct an asynchronous SMC mechanism based on an incomplete SMK framework under the condition of random denial-of-service attacks so that the resulting closed-loop system can realize the mean-square stability. By virtue of the upper bound of the sojourn time in each mode, innovative techniques are developed for mean-square stability analysis under an incomplete SMK. Furthermore, an asynchronous SMC scheme is designed to achieve the reachability of the quasi-sliding mode. Finally, the effectiveness is verified using an electronic throttle model.

This article introduces an adaptive dynamic event-triggered technique for addressing the output tracking control problem of uncertain switched nonlinear systems with prescribed performance. First, a switching dynamic event-triggered mechanism (SDETM) is established to alleviate network burden and conserve computational resources. A notable aspect is the inclusion of asynchronous switching between the switching subsystems and controllers. Second, a state-dependent switching law ensuring a dwell-time constraint is designed, which avoids the frequent switching phenomenon within any finite time interval. Third, an SDETM and an adaptive dynamic event-triggered controller are developed to confine the output tracking error within predefined decaying boundaries, while ensuring that all the signals of the closed-loop switched system remain within bounded regions. Finally, the validity and applicability of the developed control scheme are demonstrated through a one-link manipulator example.

The present study proposes an adaptive fuzzy tracking control strategy for switched nonlinear systems, capable of effectively addressing false data injection (FDI) attacks and input saturation, while achieving flexible prescribed performance control as well as semi-global uniform ultimate boundness for the resultant system. Compared to the previous work, the provided control strategy exhibits two notable strengths: 1) it introduces a novel modified fixed-time pregiven performance function to effectively balance input saturation and output constraint and 2) the detrimental impacts resulting from FDI attacks are successfully mitigated by implementing the fuzzy logic systems approximation technique in the backstepping procedure. A set of switching fuzzy observers are established to estimate the unobservable states while a first-order differential filter is utilized to handle the complexity explosion problem. Finally, the mass-spring-damper system is given to substantiate the developed approach.

In this paper, an adaptive fuzzy bipartite formation tracking control strategy of nonlinear multi-agent systems (MASs) is developed under a directed communication topology. Fuzzy logic systems are utilized to approximate the unknown nonlinear dynamics. Then, considering MASs with both cooperative and competitive relationships, the proposed bipartite formation tracking strategy allows each agent to operate according to their specific advantages. By employing a nonlinear state transformation function, the original constrained outputs of the MASs are converted into unconstrained ones. Meanwhile, a prescribed-time shifting function is introduced to handle the deferred output constraints, by which the singularity problem generated from the denominator of nonlinear state transformation functions is avoided. In addition, considering the communication bandwidth is limited, a distributed dynamic self-triggered control (DSTC) mechanism is constructed to improve the transmission efficiency. Different from the traditional self-triggered control strategy, the proposed DSTC strategy allows triggered intervals to be adjusted dynamically according to bipartite formation tracking errors, which enables the DSTC strategy to compromise communication burdern and system performances dynamically. Finally, two simulation examples are given to illustrate the validity of the proposed control scheme.

This article is concerned with the mismatched quantized$H_{\infty }$output-feedback control of fuzzy Markov jump systems via a dynamic guaranteed cost triggering scheme. An event generator and a quantizer are set up at the sensor-to-controller side and the controller-to-actuator side, respectively. The quantization scheme is presented in terms of a multichannel configuration with different decoder/encoder parameters. A guaranteed cost dynamic event-triggered mechanism is built on instantaneous and averaged triggering errors, output cost, and preset bounds. A composite controller consisting of a static output-feedback and a nonlinear compensation is constructed to meet the desired system performance. Based on the Lyapunov stability theory, sufficient conditions are obtained such that the closed-loop system is stochastically stable with the prescribed$H_{\infty }$performance. A structural vertex separation technique and Finsler's Lemma are employed to decouple the control gain, the quantizer parameters, and the Lyapunov variable. Finally, the validity of proposed scheme is verified by a circuit example.

This article explores a novel singularity-free command-filtered adaptive fuzzy finite-time tracking control algorithm for the flexible robotic manipulator with dead-zone input. First, by considering the influence of the residual term in two cases, a novel practical finite-time stability criterion is presented, and the settling time is more accurately characterized, which is applied to the design of the flexible robotic manipulator. The unknown nonlinear function in the robotic manipulator is handled by employing an intelligent estimation technique based on fuzzy logic systems. Unlike the related finite-time work, a new adaptive command-filtered finite-time controller is constructed by fusing a piecewise continuous function in each step of the backstepping process, such that the singularity of the control signal of the finite-time results is completely circumvented. Further, the mathematical model of the dead zone is delicately reconstructed such that the dead-zone input can be rigorously designed using effective mathematical techniques. Finally, the robotic manipulator system demonstrates the validity of the designed finite-time algorithm.

This article studies the$H_\infty$control problem for fuzzy switched cyber-physical systems (FSCPSs) subject to denial-of-service (DoS) attacks. An observer state-dependent switching signal is designed using the multiple Lyapunov function technology under the unavailable system states. When DoS attacks occur, the information transmission involving the sensor and controller data is corrupted. Under the designed switching signal, the subsystem with the lowest energy is selected in both the DoS sleeping interval and the DoS activated interval. First, a switching technique is introduced to deal with a DoS attack behavior. The$H_\infty$control problem of the considered FSCPS is divided into two cases for handling: the presence and absence of DoS attacks. Then, a fuzzy switching observer and an observer-based fuzzy switching controller are proposed to guarantee the solvability of the$H_\infty$control problem for FSCPSs with DoS attacks. Finally, a simulation example demonstrates the effectiveness and usefulness of the proposed fuzzy switching control strategy for FSCPSs subject to DoS attacks.

This article focuses on the problem of resilient event-triggered$H_{\infty }$filtering for networked switched Takagi–Sugeno (T-S) fuzzy systems in the presence of Denial-of-Service (DoS) attacks. To improve the utilization efficiency of communication resources and resist the influence of attacks, the resilient mode-dependent event-triggered strategy (ETS) is proposed to determine the necessary data transmission. Different from the existing ETSs for the switching linear systems, the proposed strategy not only removes the two adjacent trigger instants that are strictly less than the average dwell time constraint but also releases data immediately at the end of the attack to mitigate its side effects. Based on the transmitted switching signal and measurable output, the switching fuzzy filter is constructed to estimate the target signal. Unlike the traditional switching filter design, the transmission signals are affected by intermittent interruption of DoS attacks and ETS leads to the asynchronous behavior of system mode and filter mode, which increases the difficulty of filtering error system analysis and filter design. To overcome this challenge, a novel multiple Lyapunov function related to attack signals, system modes, and filter modes is established to analyze the exponential stability and$H_{\infty }$performance of the estimation error system. Furthermore, co-design methods regarding filter gains and event-triggered parameters are given. Finally, simulation results are carried out to substantiate the feasibility of the proposed approach.

This article studies the hierarchical sliding-mode surface (HSMS)-based adaptive optimal control problem for a class of switched continuous-time (CT) nonlinear systems with unknown perturbation under an actor-critic (AC) neural networks (NNs) architecture. First, a novel perturbation observer with a nested parameter adaptive law is designed to estimate the unknown perturbation. Then, by constructing an especial cost function related to HSMS, the original control issue is further converted into the problem of finding a series of optimal control policies. The solution to the HJB equation is identified by the HSMS-based AC NNs, where the actor and critic updating laws are developed to implement the reinforcement learning (RL) strategy simultaneously. The critic update law is designed via the gradient descent approach and the principle of standardization, such that the persistence of excitation (PE) condition is no longer needed. Based on the Lyapunov stability theory, all the signals of the closed-loop switched nonlinear systems are strictly proved to be bounded in the sense of uniformly ultimate boundedness (UUB). Finally, the simulation results are presented to verify the validity of the proposed adaptive optimal control scheme.

In this article, the resilient adaptive intermittent output feedback control is investigated for a class of uncertain strict-feedback nonlinear systems under unknown sensor deception attack. The underlying problem is rather challenging not only because the system contains mismatched uncertainties, the output information is corrupted by an additional attack signal, and only the intermittent false output is available for control design, but also because the virtual control terms are nondifferentiable due to the utilization of event triggering. To circumvent these obstacles, we construct a new fuzzy state estimator via intermittent false output and fuzzy-logic systems (FLSs), which, in conjunction with a new set of error surfaces employing the false and estimated state information, allows a novel observer-based resilient adaptive intermittent control strategy to be developed. The results of the proposed resilient adaptive output event-triggered control shown that the stabilization errors converge to a vicinity of the origin, and all the signals of the overall system remain bounded. Numerical simulations confirm the efficiency of the proposed methodology.

In this article, a novel adaptive self-triggered controller is constructed to handle the fault-tolerant control problem for nonlinear system with input dead zone through a funnel function method: 1) the actuator failure and the dead-zone nonlinearity are fully analyzed for the modeling purpose, we transform the system into a new model; 2) the self-triggered scheme is set up to update the control signals, which effectively economizes communication resources; 3) due to the existence of unknown control gains and unknown nonlinear functions, the adaptive neural network funnel controllers are designed, such that the tracking error is confined within the funnel boundary and all the signals of the closed-loop system are semi-globally uniformly ultimately bounded; and 4) finally, the applicability of the acquired control algorithm is demonstrated via a rigid robot manipulator system.

The security problem for a kind of switched nonlinear systems with denial-of-service (DoS) attacks is addressed here with a novel event-triggered neural network (NN) adaptive control technique. The provided event-triggered control algorithm, compared to the current output feedback control schemes on continuous-time systems, not only conserves communication resources but also defends against DoS attacks throughout the system stabilization process. First, a novel adaptive NN switching observer is proposed by examining the stability of each subsystem in the sleep and active intervals of the attack, which makes the standard backstepping controller workable even in the DoS attacks scenario. Further, an event-triggered secure control strategy is established by creating a common coordinate transformation, which ensures the bound of all the signals in the resultant system under arbitrary switching and prevents the occurrence of Zeno behavior. A first-order filter is developed to fix the complexity explosion problem in backstepping design. Finally, a continuous stirred tank reactor example is presented to support the established method.

This article investigates the finite time bumpless transfer fuzzy control problem for Markovian jump fuzzy systems (MJFSs) via an observer-based bumpless transfer fuzzy control approach. Neither the measurability of system states nor the availability of all transition rates for each subsystem is required. A bumpless transfer index with a continuous reference input is derived to characterize the transient jumping behavior of MJFSs caused by an observer-based fuzzy jumping controller. First, a Markovian jump fuzzy model is employed to describe the more general practical situations. Second, by introducing a fuzzy state observer, an observer-based bumpless transfer fuzzy jumping controller is established, and a sufficient condition is developed such that the finite time fuzzy control issue for MJFSs is solvable while ensuring the bumpless transfer index. Finally, two simulation examples are provided to verify the utilizability of the acquired method.

An adaptive neural bipartite tracking control approach is proposed for nonlinear multi-agent systems in this article. In contrast to previous results, it is worth noting that this paper considers a cooperative-competitive relationship in multi-agent systems, which stands for a more common situation. In this paper, a distributed self-triggered communication strategy is designed to improve the transmission efficiency of the whole system. In addition, the designed controller can compensate the actuator failure and dead-zone nonlinearity, and increases the system fault-tolerance. The proposed method ensures the boundedness of all signals of the closed-loop system and the bipartite tracking performance. The effectiveness of the proposed method is verified by two simulation examples.Note to Practitioners—Since complex modern engineering systems are difficult to be controlled by a single component, the cooperative control mode of multi-agent systems has become the mainstream trend. For multi-agent systems with cooperative-competitive relationships, the unique bipartite consensus will allow each agent to better complete the control objectives according to their respective advantages. In addition, for engineering systems such as automated manufacturing systems and transportation systems, fault problems are becoming more commonplace. These faults may make the system difficult to operate normally, and then affect the project progress. Therefore, how to guarantee the normal work of the control system when subject to faults has become a key topic. On the other hand, the channel bandwidth of the actual communication system is limited, and frequent updating of control signals will produce huge communication pressure in the traditional control scheme. Hence, it is challenging to design a control strategy that can achieve system stability and reduce communication resources simultaneously. This paper discusses the bipartite fault-tolerant control problem for nonlinear multi-agent systems. Meanwhile, a distributed adaptive self-triggered mechanism is designed to save communication resources.

This article addresses the finite-time dissipative fuzzy state estimation for Markov jump systems under mixed cyber attacks. A probabilistic event-triggered mechanism (PETM) is proposed to reduce the unwanted network traffic by using the statistic information of network-induced delays. The dual asynchronizations characterized by asynchronous modes and mismatched premise variables are tackled simultaneously. Under the PETM, Takagi-Sugeno (T-S) fuzzy state estimators are first constructed based on the imperfect measurements subject to mixed cyber attacks and exogenous disturbances. Less conservative criteria relying on both fuzzy rules and jumping modes are established to achieve the strictly (Q,S,R) - ϑ -dissipative finite-time state estimation performance. Furthermore, a synthesis algorithm is derived to calculate the fuzzy state estimator gains by virtue of an improved matrix decoupling technique. Finally, two examples are utilized to validate the effectiveness and advantage of the proposed results.

In this study, the output-feedback control (OFC) strategy design problem is explored for a type of Takagi-Sugeno fuzzy singular perturbed system. To alleviate the communication load and improve the reliability of signal transmission, a novel stochastic communication protocol (SCP) is proposed. In particular, the SCP is scheduled based on a nonhomogeneous Markov chain, where the time-varying transition probability matrix is characterized by a polytope-structure-based set. Different from the existing homogeneous Markov SCP, a nonhomogeneous Markov SCP depicts the data transmission in a more reasonable manner. To detect the actual network mode, a hidden Markov process observer is addressed. By virtue of the hidden Markov model with partly unidentified detection probabilities, an asynchronous OFC law is formulated. By establishing a novel Lyapunov-Krasovskii functional with a singular perturbation parameter and a nonhomogeneous Markov process, a sufficient condition is exploited to guarantee the stochastic stability of the resulting system, and the solution for the asynchronous controller is portrayed. Eventually, the validity of the attained methodology is expressed through a practical example.

The finite-time event-triggered stabilization is studied for a class of discrete-time nonlinear Markov jump singularly perturbed models with partially unknown transition probabilities (TPs). T-S fuzzy strategy is adopted to characterize the related nonlinear Markov jump singularly perturbed models. The control objective is to make sure that the system states remain within a bounded domain during a fixed-time interval. First, a mode-dependent event-triggered scheme is constructed to reduce the communication burden and save the network bandwidth. On that basis, by using a new Lyapunov function, a developed finite-time stability criterion is derived for the corresponding system to avoid an ill-conditioned issue due to a small singular perturbation parameter. Moreover, the mode-dependent fuzzy controller gain and the event-triggered parameter are co-designed under the framework of partially unknown TPs. Finally, the feasibility of the main results is provided to verify the finite-time event-triggered control strategy.

The event-triggered sliding-mode control (SMC) for discrete-time networked Markov jumping systems (MJSs) with channel fading is investigated by means of a genetic algorithm. In order to reduce resource consumption in the transmission process, an event-triggered protocol is adopted for networked MJSs. A key feature is that the signal transmission is inevitably affected by fading phenomenon due to delay, random noise, and amplitude attenuation in a networked environment. With the aid of a common sliding surface, an event-triggered SMC law is designed by adjusting the system network mode. Under the framework of stochastic Lyapunov stability, sufficient conditions are constructed to ensure the mean-square stability of the closed-loop networked MJSs, and the sliding region is reached around the specified sliding surface. Moreover, based on the iteration optimizing accessibility of objective function, an effective SMC approach under genetic algorithm is proposed to minimize the convergence region around the sliding surface. Finally, the effectiveness of the proposed method is proved by the F-404 aircraft model.

In this article, a novel switched observer-based neural network (NN) adaptive control algorithm is established, which addresses the security control problem of switched nonlinear systems (SNSs) under denial-of-service (DoS) attacks. The considered SNSs are described in lower triangular form with external disturbances and unmodeled dynamics. Note that when an attack is launched in the sensor-controller channel, the controller will not receive any message, which makes the standard backstepping controller not workable. To tackle the challenge, a set of NN adaptive observers are designed under two different situations, which can switch adaptively depending on the DoS attack on/off. Further, an NN adaptive controller is constructed and the dynamic surface control method is borrowed to surmount the complexity explosion phenomenon. To eliminate double damage from DoS attacks and switches, a set of switching laws with average dwell time are designed via the multiple Lyapunov function method, which in combination with the proposed controllers, guarantees that all the signals in the closed-loop system are bounded. Finally, an illustrative example is offered to verify the availability of the proposed control algorithm.

Nonsmooth nonlinear systems can model many practical processes with discontinuous property and are difficult to be stabilized by classical control methods like smooth nonlinear systems. This article considers the output-feedback adaptive neural network (NN) control problem for nonsmooth nonlinear systems with input deadzone and saturation. First, the nonsmooth input deadzone and saturation is converted to a smooth function of affine form with bounded estimation error by means of the mean-value theorem. Second, with the help of approximation theorem and Filippov's differential inclusion theory, the given nonsmooth system is converted to an equivalent smooth system model. Then, by introducing a proper logarithmic barrier Lyapunov function (BLF), an output-feedback adaptive NN strategy is set up by constructing an appropriate observer and adopting the adaptive backstepping technique. A new stability criterion is established to guarantee that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, comparative simulations through Chua's oscillator are offered to verify the effectiveness of the proposed control algorithm.

This article investigates the problem of reachable set control for a class of discrete-time Takagi–Sugeno fuzzy singular Markov jump systems (T–S FSMJSs) with time-varying delay and disturbance for the first time. By designing the state feedback and output feedback controllers, and based on the Lyapunov functional, two new sufficient conditions for the reachable set control are established. The state feedback and output feedback controller gains are obtained by optimizing the iterative algorithm. Then, all the state trajectories of the closed-loop T–S FSMJSs are contained by the intersection of ellipsoids. Finally, two examples with practical application background are presented to show the validity and usability of the proposed methods.

This article investigates the hierarchical sliding-mode surface (HSMS)-based adaptive critic tracking control problem for nonlinear multiplayer zero-sum games (ZSGs). First, a generalized fuzzy hyperbolic model-based identifier is employed to approximate the unknown nonlinear functions. According to the derived data-driven model, a static control policy is proposed to transform the considered optimal tracking control problem into an optimal regulation control problem of an induced error system. Subsequently, based on sliding mode control technology and the concept of hierarchical design, a novel optimal feedback control policy is developed to regulate the tracking error by minimizing a performance index function related to the HSMS. The solution to the Hamilton–Jacobi–Isaacs equation of nonlinear multiplayer ZSGs is obtained via the HSMS-based critic neural network. Furthermore, the historical stored data are utilized to conquer the difficulty associated with the persistence of excitation conditions. Based on Lyapunov stability theory, it is strictly proven that the tracking error and the critic neural network weight are uniformly ultimately bounded. Finally, two examples are presented to demonstrate the effectiveness of the proposed control scheme.

This article investigates the finite-time secure filter design of fuzzy switched cyber-physical systems equipped with a resource-constraint network that may undergo false data injection attacks (FDIAs). To strike a higher level balance between the resource consumption and filtering performance, a multidomain probabilistic event-triggered mechanism (MDPETM) is initially developed. And the mode mismatched phenomenon between the filter and the system is characterized through a delayed switching signal. Based on the MDPETM and a virtual delay partitioning approach, fuzzy mismatched secure filters are first devised whose modes could differ from the system. Then, filter-mode-dependent Lyapunov functionals are created to obtain new sufficient criteria such that the filtering error achieves finite-time boundedness with extended dissipativity subject to admissible FDIAs. The filter gains are obtained by solving a set of convex optimization problems. Finally, an application-oriented example is employed to test the effectiveness and advantages of the proposed results.

The security control of a vehicle platoon depends on the network topology and communication quality. Denial of service (DoS) attacks force vehicle formations to destabilize by disrupting digital communications between vehicles. To this end, this paper develops a resilient distributed event-triggered security control strategy to resist the malicious impact of DoS attacks on connected vehicles. By designing a distributed event-triggered mechanism based on sampled data, the controller updating frequency is reduced, thereby promoting utilization rate of network resources. Since the end of the attack is not the sampling instant, this may prolong the duration of the attack. To overcome this problem, a switched sampled-data scheme is proposed to ensure that the control signal acts on the system immediately when the attack ends. Then, a switched system model with artificial delay is established to capture the sampling period, event triggering mechanism and DoS attack purpose. With the analysis methods of switched system and time-delay system, sufficient conditions are obtained to guarantee the same safe distance and speed between vehicles, so that the connected vehicle system can achieve the desired tracking effect. A co-design approach is given with respect to controller gains and triggering parameter. Finally, simulation and experimental studies are provided to demonstrate the effectiveness of the proposed security control method.

In this work, a neural-networks (NNs)-based adaptive asymptotic tracking control scheme is presented for a class of uncertain nonstrict feedback nonlinear systems with time-varying full-state constraints. First, we construct a novel exponentially decaying nonlinear mapping to map the constrained system states to new system states without constraints. Instead of the traditional barrier Lyapunov function methods, the feasible conditions which require the virtual control signals satisfying the constraint requirements are removed. By employing the Nussbaum design method to eliminate the effect of unknown control gains, the general assumption about the signs of the unknown control gains is relaxed. Then, the nonstrict feedback form of the system can be pulled back to the strict feedback form through the basic properties of radial basis function NNs. Simultaneously, the intermediate control signals and the desired controller are constructed by the backstepping process and the Nussbaum design method. The designed controller can ensure that all signals in the whole closed-loop system are bounded without the violation of the constraints and hold the asymptotic tracking performance. In the end, a practical example about a brush dc motor driving a one-link robot manipulator is given to illustrate the effectiveness of the proposed design scheme.

This article concentrates on the discrete-time sliding mode control (DTSMC) problem for uncertain networked semi-Markovian switching systems (S-MSSs) under random denial-of-service (DoS) attacks. The semi-Markovian kernel (SMK) approach is utilized such that the switching among different modes is mutually governed by the transition probability and the sojourn-time distribution function. Considering randomly occurring DoS attacks, a sliding mode function related to the attack probability is constructed to analyze the impact of malicious attacks. Then, sufficient conditions under the equivalent DTSMC law are derived in view of the$\sigma $-error mean square stability criterion. Furthermore, the synthesis problem of the proposed DTSMC law ensures that the resulting closed-loop system dynamics can be driven onto the prespecified sliding region within a limited time. Finally, an electronic throttle control system is shown to validate the proposed algorithm.

This article addresses the fixed-time control problem for high-order nonlinear systems with unknown nonlinear functions and asymmetric output constraint. First, a continuous state-feedback controller is constructed by revamping the adding a power integrator technique (API), which guarantees that the system output does not exceed the pregiven asymmetric output constraint boundary. Second, with the barrier Lyapunov function (BLF) method and the backstepping technique, a fixed-time stability criterion is constructed. It is rigorously proven that the closed-loop systems are fixed-time stable by the Lyapunov theory. The proposed BLF can not only deal with the symmetric output constraint but also cover the traditional logarithm-type BLF as a special case. Finally, a practical application example of the boiler–turbine unit system is offered to certify the availability of the proposed control algorithm.

This article studies the decentralized event-triggered control problem for a class of constrained nonlinear interconnected systems. By assigning a specific cost function for each constrained auxiliary subsystem, the original control problem is equivalently transformed into finding a series of optimal control policies updating in an aperiodic manner, and these optimal event-triggered control laws together constitute the desired decentralized controller. It is strictly proven that the system under consideration is stable in the sense of uniformly ultimate boundedness provided by the solutions of event-triggered Hamilton-Jacobi-Bellman equations. Different from the traditional adaptive critic design methods, we present an identifier-critic network architecture to relax the restrictions posed on the system dynamics, and the actor network commonly used to approximate the optimal control law is circumvented. The weights in the critic network are tuned on the basis of the gradient descent approach as well as the historical data, such that the persistence of excitation condition is no longer needed. The validity of our control scheme is demonstrated through a simulation example.

The fault detection issue is investigated for complex stochastic delayed systems in the presence of positivity constraints and semi-Markov switching parameters. By choosing a mode-dependent fault detection filter (FDF) as a residual generator, the corresponding fault detection is formulated as a positive [Formula: see text] filter problem. Attention is focused on the design of a mode-dependent FDF to minimize the error between the residual signal and the fault signal. The designed FDF features good sensitivity of the faults and robustness against the external disturbances. Subsequently, by means of the linear copositive Lyapunov functional (LCLF), stochastic stability is proposed to satisfy an expected [Formula: see text]-gain performance. Some solvability conditions for the desired mode-dependent FDF are established with the help of a linear programming approach. Finally, an application example of a data communication network model is provided to demonstrate the effectiveness of the theoretical findings.

This article focuses on the bumpless transfer$H_{\infty }$anti-disturbance control problem for switching Markovian LPV systems under a hybrid switching law. A parameter-dependent multiple piecewise disturbance observer-based bumpless transfer control strategy is put forward to reject multiple disturbances and reduce switching bumps. First, a hybrid switching law making full use of determinacy and randomness is proposed to improve the bumpless transfer anti-disturbance level by introducing a fixed dwell time in random switching. Second, a generalized bumpless transfer anti-disturbance specification is given to describe the switching quality at the switching points of switching Markovian LPV systems. Third, a solvability condition is established for the bumpless transfer$H_{\infty }$anti-disturbance control problem, and a parameter-dependent multiple piecewise disturbance observer-based bumpless transfer controller is designed. Finally, an application example has been supplied to demonstrate the availability of the developed method.

This article investigates the$H_{\infty }$stochastic tracking control problem for uncertain fuzzy Markovian hybrid switching systems by using a fuzzy switching dynamic adaptive control approach. The long and the short is to construct multiple piecewise stochastic Lyapunov functions which provide an effective tool for designing hybrid switching law and fuzzy switching dynamic adaptive law. A hybrid switching law, including both stochastic switching and deterministic switching, is designed to represent more general switching scenarios, which can improve the$H_{\infty }$adaptive tracking performance through offering a running time before stochastic switching for the adaptive control strategy to work well. A fuzzy switching dynamic adaptive control technique is developed such that all signals of the tracking error equation are bounded, and the system state trajectory tracks the reference model state trajectory under a disturbance attenuation level as closely as possible. Finally, an application study verifies the effectiveness of the acquired methods.

This article focuses on the$H_{\infty }$adaptive tracking problem of uncertain switched systems. A key point of the study is to set up a multiple piecewise Lyapunov function framework which provides an effective tool for designing an adaptive switching controller consisting of a state-feedback and time-driven switching signal and a time-driven adaptive law. The proposed switching signal guarantees the solvability of the$H_{\infty }$adaptive tracking problem for uncertain switched systems. Significantly, it provides plenty of adjusting time for the adaptive tracking control strategy to damp the transient caused by switching and avoids frequent switching. A novel time-driven adaptive switching controller is established such that the tracking error asymptotically converges to zero and all the signals in the error dynamic system are bounded under an achieved disturbance attenuation level. The solvability criterion ensuring an$H_{\infty }$adaptive tracking performance is established for the uncertain switched systems, where the solvability of the$H_{\infty }$adaptive tracking problem for individual subsystems is not required. Finally, the proposed method is applied to the electro-hydraulic unit.

A policy-iteration-based algorithm is presented in this article for optimal control of unknown continuous-time nonlinear systems subject to bounded inputs by utilizing the adaptive dynamic programming (ADP). Three neural networks (NNs), called critic network, actor network, and quasi-model network, are utilized in the proposed algorithm to give approximations of the control law, the cost function, and the function constituted by partial derivatives of value functions with respect to states and unknown input gain dynamics, respectively. At each iteration, based on the least sum of squares method, the parameters of critic and quasi-model networks will be tuned simultaneously, which eliminates the necessity of separately learning the system model in advance. Then, the control law is improved by satisfying the necessary optimality condition. Then, the proposed algorithm's optimality and convergence properties are exhibited. Finally, the simulation results demonstrate the availability of the proposed algorithm.

This study proposes the time-/event-triggered adaptive neural control strategies for the asymptotic tracking problem of a class of uncertain nonlinear systems with full-state constraints. First, we design a time-triggered strategy. The effect caused by the residuals of the estimation via radial basis function (RBF) neural networks (NNs), and the reasonable upper bounds on the first derivative of the reference signal and the derivative of each virtual control, can be eliminated by designing appropriate adaptive laws and utilizing the basic properties of RBF NNs. Moreover, the construction of the barrier Lyapunov functions (BLFs) in this work ensures the compliance of the full-state constraints and also holds the asymptotic output tracking performance. Then, based on the time-triggered strategy, we further design a relative threshold event-triggered strategy. The proposed event-triggered adaptive neural controller can solve the main control objective of this work, that is: 1) the full-state constraint requirements of the system are not violated and 2) the output signal asymptotically tracks the reference signal. Compared with the traditional method, the event-triggered strategy can improve the utilization of communication channels and resources and has greater practical significance. Finally, an example of single-link robot under the proposed two strategies illustrates the validity of the constructed controllers.

This paper investigates the asynchronous event-triggered state-feedback control for discrete-time nonlinear singular Markov jump systems subject to reachable set bounding and stochastic cyber-attacks. An event-triggered mechanism is introduced to regulate data transmission and save network resources. While this mechanism brings advantages, it also causes that the mode information of the system and the controller are not synchronized. On the other hand, network communication has brought convenience to signal transmission, and it has also resulted in the network channel being in an open and unreliable environment, which is vulnerable to cyber-attacks. In order to solve these problems, the secure asynchronous controller is designed to effectively resist the influence of attacks. In addition, by using the reachable set analysis approach, the constructed controller ensures that the estimation error is within the boundary of the ellipsoid, and the existence conditions of the required controller are given by solving the linear matrix inequalities. Finally, a simulation example is given to illustrate the effectiveness of the theoretical results.

In this article, the issue of positive$\mathcal {L}_{1}$filter design is investigated for positive nonlinear stochastic switching systems subject to the phase-type semi-Markov jump process. Many complicated factors, such as semi-Markov jump parameters, positivity, T–S fuzzy strategy, and external disturbance, are taken into consideration. Practical systems under positivity constraint conditions and unpredictable structural changes are characterized by positive semi-Markov jump systems (S-MJSs). First, by the key properties of the supplementary variable and the plant transformation technique, phase-type S-MJSs are transformed into Markov jump systems (MJSs), which means that, to an extent, these two kinds of stochastic switching systems are mutually represented. Second, with the help of the normalized membership function, the associated nonlinear MJSs are transformed into the local linear MJSs with specific T–S fuzzy rules. Third, by choosing the linear copositive Lyapunov function (LCLF), stochastic stability (SSY) criteria are given for the corresponding system with$\mathcal {L}_{1}$performance. Some solvability conditions for positive$\mathcal {L}_{1}$filter are constructed under a linear programming framework. Finally, an epidemiological model illustrates the effectiveness of the theoretical findings.

This article investigates the input–output finite-time stability (IO-FTS) for nonlinear hidden semi-Markov switching systems (S-MSSs) via the asynchronous sliding mode control (SMC) approach. Under the assumption that a detector is set up to estimate the mode value, the mode of the original system is not directly accessible. The asynchrony between the system and controller is described as a hidden semi-Markov model (HSMM). Many practical factors, such as semi-Markov switching parameters, finite-time interval, asynchronous phenomenon, uncertain parameters, and nonlinearity, are taking into account during the SMC design process. We aim to design an efficient finite-time asynchronous SMC scheme under a hidden semi-Markov switching effect. A novel sliding switching surface (SSS) is constructed, in which the SMC law rises asynchronously with original S-MSSs. Then, by means of finite-time stability, an asynchronous SMC law is synthesized to guarantee that the associated hidden S-MSSs fulfill the reaching condition within a finite time. Furthermore, sufficient conditions are derived in view of the IO-FTS of sliding mode dynamics under the framework of a novel inequality lemma. Results are given for the application of this control design method to a single-link robot arm model (SLRAM).

This paper addresses the finite-time event-triggered control problem for nonlinear semi-Markovian switching cyber-physical systems (S-MSCPSs) under false data injection (FDI) attacks. Compared with the traditional time-triggered mechanism, the proposed event-triggered scheme (ETS) can effectively avoid network resource waste. Considering the network-induced delay in the modeling, a closed-loop system model with time delay is established in the unified framework. By the use of a mode-dependent piecewise Lyapunov-Krasovskii functional (LKF), stochastic finite-time stability (SFTS) criteria are established for the resultant closed-loop system. Then, some solvability conditions are established for the desired finite-time controller in light of a linear matrix inequality framework. Finally, an application example of vertical take-off and landing helicopter model (VTOLHM) is provided to demonstrate the effectiveness of the theoretical findings.

In this article, the sliding mode control (SMC) design is studied for a class of stochastic switching systems subject to semi-Markov process via an adaptive event-triggered mechanism. Network-induced communication constraints, semi-Markov switching parameters, and uncertain parameters are considered in a unified framework for the SMC design. Due to the constraint of measuring transducers, the system states always appear with unmeasurable characteristic. Compared with the traditional event-triggered mechanism, the adaptive event-triggered mechanism can effectively reduce the number of triggering than the static event-triggered mechanism. During the data transmission of network communication systems, network-induced delays are characterized from the event trigger to the zero-order holder. The aim of this work is to design an appropriate SMC law based on an adaptive event-triggered communication scheme such that the resulting closed-loop system could realize stochastic stability and reduce communication burden. By introducing the stochastic semi-Markov Lyapunov functional, sojourn-time-dependent sufficient conditions are established for stochastic stability. Then, a suitable SMC law is designed such that the system state can be driven onto the specified sliding surface in a finite-time region. Finally, the simulation study on boost converter circuit model (BCCM) illustrates the effectiveness of the theoretical findings.

We study the exponential stability of discrete-time neural networks (NNs) with a time-varying delay which contains a few intermittent large delays (LDs). By modeling the considered discrete-time NN as a discrete-time switched NN which contains two subsystems and one of them may be unstable over the LD periods (LDPs), switching techniques are employed to analyze the problem. Delay-dependent exponential stability conditions to check the frequency and the length of the LDs allowed for guaranteeing the exponential stability are proposed by applying a novel Lyapunov-Krasovskii functional (LKF) with LDP-based terms, Wirtinger-based summation inequality, and reciprocally convex combination technique. Based on these conditions, associated evaluation algorithms are developed. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.

Event-triggered communication mechanism (ETCM) provides an efficient way to reduce unwanted network traffic. This article studies the co-design of an ETCM and an annular finite-time (AFT) H∞filter for networked switched systems (NSSs). First, the AFT definition and ETCM are presented. Second, a set of mode-dependent average dwell-time (MADT) switching rules is given. By resorting to a delay-dependent Lyapunov functional approach, some feasible AFT H∞filters are designed. Third, it is proved that the filtering error system (FES) has a good performance in attenuating the external disturbances. Finally, the feasibility of the developed method is verified via simulation.

This article studies the problem of adaptive fuzzy fixed-time decentralized control for nonlinear interconnected systems with stochastic disturbances and unknown nonlinearities. In control design, fuzzy logic systems are utilized to identify the unknown nonlinear functions. Combining stochastic fixed-time Lyapunov stability theory with adaptive backstepping control technique, a fuzzy adaptive fixed-time decentralized control design algorithm is developed by adopting smooth projection operator. It is proved that all the state variables of the closed-loop system are globally fixed-time stable in probability. Finally, both numerical and practical examples are provided to elucidate the feasibility of the proposed control algorithm.

Finite-time synchronization (FTS) is discussed for delayed semi-Markov switching neural networks (S-MSNNs) with quantized measurement, in which a logarithmic quantizer is employed. The stochastic phenomena of structural and parametrical changes are modeled by a semi-Markov process whose transition rates are time-varying to depend on the sojourn time. Practical systems subject to unpredictable structural changes, such as quadruple-tank process systems, are described by delayed S-MSNNs. A key issue under the consideration is how to design a feedback controller to guarantee the FTS between the master system and the slave system. For this purpose, by using the weak infinitesimal operator, sufficient conditions are constructed to realize FTS of the resulting error system over a finite-time interval. Then, the solvability conditions for the desired finite-time controller can be determined under a linear matrix inequality framework. Finally, the theoretical findings are illustrated by the quadruple-tank process model.

This article investigates the problem of the decentralized adaptive output feedback saturated control problem for interconnected nonlinear systems with strong interconnections. A decentralized linear observer is first established to estimate the unknown states. Then, an auxiliary system is constructed to offset the effect of input saturation. With the aid of graph theory and neural network technique, a decentralized adaptive neuro-output feedback saturated controller is designed in a nonrecursive manner. A sufficient criterion is established to achieve the uniform ultimate boundedness (UUB) of the closed-loop system. An application example of autonomous underwater vehicle (AUV) is provided to verify the effectiveness of the developed algorithm.

This article considers the problem of event-triggered optimal control for discrete-time switched nonlinear systems with constrained control input. First, an event-triggered condition is given to make the closed-loop switched system asymptotically stable. Second, a novel method, event-triggered heuristic dynamic programming (ETHDP), is applied to derive the optimal control policy. Two neural networks (NNs) are utilized to approximate the value function and control law, respectively. When the event-triggered condition is violated, the weights of the two NNs are updated, which can decrease the networks calculation and transmission load notably. A proof of the convergence of the ETHDP is also carried out. Finally, the effectiveness of the proposed method is verified by an example.

In this article, the issue of adaptive neural fault-tolerant control (FTC) is addressed for a class of uncertain switched nonstrict-feedback nonlinear systems with unmodeled dynamics and unmeasurable states. In such a system, the uncertain nonlinear parts are identified by radial basis function (RBF) neural networks (NNs). Also, with the help of the structural characteristics of RBF NNs, the violation between the nontsrict-feedback form and backstepping method is tackled. Then, based on the small-gain technique, input-to-state practical stability (ISpS) theory, and common Lyapunov function (CLF) approach, an adaptive fault-tolerant tracking controller with only three adaptive laws is developed by designing an observer. It is shown that the designed controller can ensure that all the closed-loop signals are bounded under arbitrary switching, while the tracking error can converge to a small area of the origin. Finally, two simulation examples are provided to demonstrate the feasibility of the suggested control approach.

This paper concerns a positive G1 observer for positive nonlinear semi-Markovian switching systems (MSSs) via the expansion of Taylor formula and the fuzzy Lyapunov function approach, in which semi-Markovian switching parameters, positivity, Takagi-Sugeno (T-S) fuzzy, and external disturbance are all considered in a unified framework. A fuzzy Lyapunov function approach with less conservativeness is introduced into the research of positive systems. In the system under consideration, positive S-MSSs with the semi-Markovian process can describe more complex systems in a practical control process. The main motivation of this paper is that the practical system subject to positivity and abrupt changes can be described by positive nonlinear S-MSSs, which always needs to consider the external disturbance. First, by using the normalized membership function approach, positive nonlinear S-MSSs can be represented by local positive T-S fuzzy S-MSSs. Second, by constructing the fuzzy Lyapunov function, some sufficient conditions are proposed for stochastic stability and G1-gain performance analysis, respectively. Then, a positive G1 observer in a novel standard linearprogramming condition is designed to guarantee the resulting closed-loop augmented system is positive and stochastically stable with a required G1-gain performance. Finally, a practical example about the epidemiological model is introduced to show the effectiveness of the main theory.

In this paper, the problem of asynchronous finite-time filtering issue is addressed for a class of Markov jump nonlinear systems with incomplete transition rate. The so-called asynchronization means that the filter's modes do not synchronize with the system's modes. Both the stochastic finite-time boundedness (FTBs) problem and the stochastic input-output finite-time stability (IO-FTSy) problem are involved. By resorting to the mode-dependent Lyapunov function approach and the matrix inequality techniques, some interesting results are derived to verify the properties of the stochastic FTBs and the stochastic IO-FTSy of the asynchronous filtering error system. The asynchronous filter parameters can be reduced to the solvability of some convex optimization problems. Finally, a single-link robot arm and a tunnel diode circuit are applied to elucidate the proposed algorithms.

In this paper, a decentralized adaptive neural network proportional-integral (PI) tracking control scheme is proposed for interconnected nonlinear systems with input quantization and dynamic uncertainties. This algorithm is underpinned by the use of the dynamic signal, graph theory, and function recombination to deal with the difficulties existing in the nontriangular form, unmodeled dynamics, and unknown interconnected terms. Recalling the backstepping method and neural network approximation technology, a new PI tracking controller characterized by simple structure and easy implementation is developed which ensures that all the closed-loop signals are uniformly ultimately bounded. The effectiveness of the obtained controller is exemplified via a numerical example and an application to an inverted pendulum.

This article investigates the exponential stability of generalized neural networks (GNNs) with a time-varying delay. Different from the literatures on the similar topic, the considered time delay contains a few intermittent large-delay periods (LDPs). A new approach is proposed to determine how frequent and how long the LDPs are allowed for guaranteeing the exponential stability by using switching techniques. The GNN is first modeled as a switched time-delay system which may include an unstable subsystem. Then, based on a novel Lyapunov–Krasovskii functional with LDP-based terms, a delay-dependent exponential stability criterion and associated evaluation algorithm are developed. Finally, two numerical examples are provided to show the effectiveness of the proposed method.

In this article, the issue of$\mathscr {L}_{1}$control design is addressed for a class of delayed stochastic jump systems subject to semi-Markov jump parameters. The stochastic jump systems in the presence of positivity constraints are described by positive semi-Markov jump systems (S-MJSs). By constructing new linear Lyapunov functional dependent double integral, some sojourn-time-dependent sufficient conditions are established to realize the corresponding stochastic stability with a prescribed$\mathscr {L}_{1}$-gain performance index. Then, a switching controller via gain matrix decomposition is designed to achieve positivity and stochastic stabilization with a prescribed$\mathscr {L}_{1}$-gain performance, which can be solved with the help of linear programming approach. Finally, the virus mutation treatment model verifies the effectiveness of the theoretical results.

The problem of asymptotic tracking control for a class of uncertain switched nonlinear systems under fuzzy approximation framework is solved in this paper. Superior to most existing results based on fuzzy adaptive control strategy that can only achieve bounded error tracking performance, our proposed control scheme can guarantee the local asymptotic tracking performance for the uncertain switched nonlinear systems under consideration. This is accomplished by constructing a nonsmooth Lyapunov function and introducing a novel discontinuous controller with dynamic feedback compensator in the design procedure. Meanwhile, some concepts, such as differential inclusion and set-valued map, are introduced to theoretically verify the local asymptotic tracking performance of the systems with our proposed controller. With the help of set-valued Lie derivative, the common virtual control functions, the desired controller, and the adaptive laws can be precisely constructed. Finally, simulation results are given to show the effectiveness of the proposed method.

This article investigates the problem of sliding mode control (SMC) for semi-Markov switching systems (S-MSSs) with quantized measurement in finite-time level. The transition between different subsystems obeys a stochastic semi-Markov process related to nonexponential distribution. Additionally, due to the sensor information constraints, the state vectors are not always measurable in practice. Moreover, compared with existing results in literature, the output quantization is first considered for finite-time SMC problem via a logarithmic quantizer. Our attention is to design an appropriate finite-time SMC law to attenuate the influences of parametrical uncertainty and external disturbance onto the overall performance of the system under consideration. First, by the key points of stochastic semi-Markov Lyapunov function and observer design theory, a desired SMC law is constructed to guarantee that the system trajectories can arrive at the specified sliding surface (SSS) within an assigned finite-time level. Then, ST-dependent sufficient conditions are established to ensure the required finite-time boundedness performance including both reaching phase and sliding motion phase. Finally, the applicability of the proposed results is demonstrated by a single-link robot arm model.

This study investigates the problem of adaptive decentralized tracking control for a class of interconnected nonlinear systems with input quantization, unknown function, and time-delay, where the time-delay and interconnection terms are supposed to be bounded by some completely unknown functions. An adaptive decentralized tracking controller is constructed via the backstepping method and neural network technique, where a sliding-mode differentiator is presented to estimate the derivative of the virtual control law and reduce the complexity of the control scheme. On the basis of Lyapunov analysis scheme and graph theory, all the signals of the closed-loop system are uniformly ultimately bounded. Finally, an application example of an inverted pendulum system is given to demonstrate the effectiveness of the developed methods.

In this paper, the problems of stability and l2-gain analysis are investigated for discrete-time switched systems with mode-dependent average dwell time (DT). By proposing a novel multiple discontinuous Lyapunov function (MDLF) approach, the conditions of stability and weighted l2-gain are established for nonlinear systems. Next, the corresponding results for linear switched systems are also proposed by using MDLF. It turns out that our proposed results provide smaller bounds on the DT. Some simulation results are given to show the validity of our approaches.

Point stabilization control of wheeled inverted pendulum (WIP) vehicles remains a challenge because of the existing nonholonomic and underactuated characteristics. This paper proposes a point stabilization control method for the WIP vehicle based on motion planning, where a point-to-point motion is achieved by performing pivot steering and longitudinal motion successively to avoid the nonholonomic constraint. Specifically, to handle the underactuated problem, a kinematic coupling-based longitudinal trajectory planning approach is presented, by which both precise longitudinal movement and stability of vehicle body can be guaranteed. Moreover, a mathematical model of parameters optimization problem is deduced with strict analysis, and then the particle swarm optimization algorithm is used to obtain the appropriate trajectory parameters, which ensures the good performance of the trajectory planning method. On this basis, the point stabilization of the WIP vehicle can be effectively realized through a commonly used proportional-integral-derivative control approach. Numerical simulation and experimental study are both conducted to demonstrate the feasibility and effectiveness of the proposed method.

This paper investigates the problems of backstepping control for a class of nonsmooth nonlinear systems. With the help of set-valued functions (or maps) and set-valued derivatives, a new Lyapunov criterion is developed for nonsmooth systems. The concept of semi-globally uniformly ultimately bounded (SGUUB) stability that is widely used for smooth nonlinear systems in lower triangular form is, for the first time, applied to the nonsmooth case, and such a concept provides a theory foundation for the subsequent backstepping control design. Then, two types of continuous controllers are designed based on the backstepping technique and adaptive neural network (NN) algorithm. In the light of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions, the system under investigation is first transformed into an equivalent model. Then, the first type of controller can be efficiently designed by using the traditional backstepping technique. On the other hand, when the unknown uncertainty is taken into account in the equivalent systems, another type of controller is designed based on adaptive NN control strategy. It is proved that in both cases, all the closed-loop signals are SGUUB by using our proposed controllers. Finally, a numerical example with two types of controllers is supplied to show the availability of the provided control schemes.

This paper proposes a solution to adaptive output-feedback control for a class of nonsmooth nonlinear systems. First, the concept of semiglobally uniformly ultimately bounded (SGUUB) stability that has been widely used for smooth nonlinear systems with lower triangular systems is extended to the nonsmooth systems. Then by resorting to set-valued maps and set-valued derivatives, a new Lyapunov criterion ensuring the SGUUB stability is developed for nonsmooth nonlinear systems, which establishes the theory foundation for the subsequent backstepping control design. With the help of Cellina approximate selection theorem and smooth approximation theorem for Lipschitz functions, the system under investigation is first transformed into an equivalent model. In the sequel, exploring some efficient techniques, an adaptive fuzzy output-feedback controller is constructed for the systems under consideration by utilizing an appropriate observer and the approximation ability of fuzzy systems. Finally, a numerical example is given to show the effectiveness of the proposed control method.

This paper is concerned with the event-triggered finite-time control problem for networked switched linear systems by using an asynchronous switching scheme. Not only the problem of finite-time boundedness, but also the problem of input-output finite-time stability is considered in this paper. Compared with the existing event-triggered results of the switched systems, a new type of event-triggered condition is proposed. Sufficient conditions are established to guarantee the event-based asynchronous closed-loop systems are both finite-time bounded and input-output finite-time stable. A set of event-triggered finite-time bounded and input-output finite-time stabilizing controllers are designed under the asynchronous control scheme. It is revealed that the triggered thresholds determine the number of sampling points transmitted to the controller, and the smaller triggered parameters indicate the less-sampled data needed to be transmitted to the controller under the event-triggered scheme. Finally, a boost converter circuit is applied to bring out the advantages of the proposed control scheme.

In this paper, a new adaptive approximation-based tracking controller design approach is developed for a class of uncertain nonlinear switched lower-triangular systems with an output constraint using neural networks (NNs). By introducing a novel barrier Lyapunov function (BLF), the constrained switched system is first transformed into a new system without any constraint, which means the control objectives of the both systems are equivalent. Then command filter technique is applied to solve the so-called "explosion of complexity" problem in traditional backstepping procedure, and radial basis function NNs are directly employed to model the unknown nonlinear functions. The designed controller ensures that all the closed-loop variables are ultimately boundedness, while the output limit is not transgressed and the output tracking error can be reduced arbitrarily small. Furthermore, the use of an asymmetric BLF is also explored to handle the case of asymmetric output constraint as a generalization result. Finally, the control performance of the presented control schemes is illustrated via two examples.

This paper deals with adaptive neural tracking control design for a class of switched high-order stochastic nonlinear systems with unknown uncertainties and arbitrary deterministic switching. The considered issues are: 1) completely unknown uncertainties; 2) stochastic disturbances; and 3) high-order nonstrict-feedback system structure. The considered mathematical models can represent many practical systems in the actual engineering. By adopting the approximation ability of neural networks, common stochastic Lyapunov function method together with adding an improved power integrator technique, an adaptive state feedback controller with multiple adaptive laws is systematically designed for the systems. Subsequently, a controller with only two adaptive laws is proposed to solve the problem of over parameterization. Under the designed controllers, all the signals in the closed-loop system are bounded-input bounded-output stable in probability, and the system output can almost surely track the target trajectory within a specified bounded error. Finally, simulation results are presented to show the effectiveness of the proposed approaches.

In this paper, the problem of the global finite-time adaptive stabilization for nonlinearly parametrized systems with multiple unknown control directions is addressed. Different from the previous results, the control directions of the considered systems are completely unknown. Adopting the adding a power integrator design technique, we develop an adaptive switching controller with a tuning parameter. Due to control directions unknown, a novel logic switching regulation is established based on Lyapunov function method to overcome this main obstacle. According to this switching rule, the design parameter is tuned online in a switching way. With the help of the obtained adaptive switching controller, the global finite-time stability of the closed-loop systems is shown. To verify the effectiveness of the control algorithm, a simulation example is presented.

This paper proposes an adaptive sliding mode control method for a class of nonstrict-feedback nonlinear systems where some widely used restrictions on system structure are relaxed. Based on the calculus principle, the original system is first transformed into a new defined system. Then, by using sliding mode control technology and the concept of hierarchical design, a series of control signals are sequentially designed for the new defined system where radial basis function neural networks are used to approximate the unknown functions. Based on the Lyapunov stability theory, the closed-loop system together with the proposed sliding surfaces is proved to be uniformly ultimately bounded under our designed adaptive neural controller. The main contributions of this paper lie in that some strict restrictions on uncertain system functions are removed; a hierarchical control method is proposed for the considered systems, which can avoid the problem of “causes and consequences” that may be encountered by using traditional backstepping design method; and the proposed control method is also available for underactuated nonlinear systems. Finally, simulation results demonstrate the effectiveness of the proposed design techniques.

In this paper, the problem of stochastic input-to-state stability (SISS) is investigated for a class of stochastic switched nonlinear systems. A sufficient condition is first derived to estimate an upper bound on a stochastic process. Based on that, the SISS problem is addressed for stochastic nonlinear systems be virtue of the indefinite Lyapuno function approach. For the convenience of simulation, the SISS property of stochastic switched nonlinear systems i further analyzed by the average dwell-time technique. An illustrative example together with numerical simulatio s is presented to demonstrate the efficiency of the proposed results.

The finite time tracking problem is considered for robotic manipulators with unknown dynamic friction, bounded disturbances and unmodeled dynamics. A global relay switching control scheme with finite time convergence is proposed. For general finite time variable structure controller, the control signals may escape to infinity in finite time when the initial states of the system are in some specified area, causing the singularity phenomena of the closed-loop system. The design scheme for finite time tracking control uses a two-phase switching control method so that the boundedness of the control signal is guaranteed and the singularity phenomena is avoided.

In this paper, the exponential stability is considered for a class of switched systems containing both stable and unstable subsystems with impulsive effect by using the matrix measure concept and average dwell time approach. The authors show that if the average dwell time and the ratio of the total activation time (of those subsystems) with negative matrix measure to the total activation time (of those subsystems) with nonnegative matrix measure are both chosen appropriately large, the exponential stability of a desired degree is guaranteed. Under a similar condition, the robust exponential stability problem for a class of switched systems with impulsive effect and structure perturbations is also studied. Simulations validate the main results.