Aiming to address the stealthy cyber attacks faced by multiarea interconnected power systems, this article proposes a new decentralized resilient predictive load frequency control (LFC) scheme, which has several prominent features, such as privacy preservation, active attack detection, network blocking defense, and attack tolerance. Compared with the relevant studies in the literature, the novelty of these features is specifically demonstrated by: 1) a dynamic scaling and masking method is constructed to achieve the real-time dynamic protection of network transmission data, which not only enables a closed-loop cyber privacy preservation against eavesdropping attacks, but also guarantees the effectiveness of active detection of attack appearance and disappearance; 2) a scaled one-step-ahead predictive interpolation control strategy is further proposed to achieve dynamic privacy preservation of control algorithm, and to apply a check-before-use mechanism to avoid the false data injected by the stealthy attacks to be loaded into the actuator; and 3) an active attack defense method with fail-safe feature is constructed to block the attacks from penetrating the actuator from the input transmission channels, while providing some finite-time open-loop control capability to suboptimally regulate the LFC before the attacks disappear. A case study of a three-area power system is given to validate the effectiveness of the proposed LFC method.

This paper investigates the robust consensus scheme for a specific type of leader-follower multi-agent systems (MASs) in the context of a human-cyber-physical interactive system. The system encounters frequent communication challenges characterized by packet loss and data leakage. To address these challenges, the paper proposes a secure decentralized scheme that leverages game theory to determine optimal policies in a zero-sum game. The scheme utilizes the adaptive dynamic programming (ADP) method, which involves a decentralized iterative process. The paper demonstrates that the generated sequence exhibits exponential convergence and provides the maximum iteration number based on the convergence error. To mitigate data leakage among players, the scheme incorporates a secure operation that involves encrypted data. This integration seamlessly combines data conversion and encryption-decryption into decentralized computation. Finally, the paper presents a simulation example to validate the efficacy of the consensus scheme.

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

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

The wind energy, as a kind of renewable energy resources, has the potential to replace traditional fossil fuels. However, its intermittent power output can incur frequency instability due to the instantaneous unbalance between power generation and load demand. To smooth the penetration of wind energy, this paper presents a robust cooperative load frequency control (LFC) strategy for multi-area power systems, which is a hierarchical control approach. For the low-level wind turbine control, this paper adopts model predictive control (MPC) method to achieve the rated wind power tracking. In the meantime, an improved event-triggered scheme (ETS) considering multiple historic released signals is employed to relieve the computational burden of MPC. For the high-level cooperative LFC, this paper incorporates the robust performance index in the control synthesis to suppress the impact of intermittent wind power on frequency stability. In addition, to address the underlying shift of the steady-state operating point caused by the intermittent wind power supply, this paper improves the commonly used small-signal LFC model by adding an uncertain matrix, which reasonably explains the possible change of system parameters and extends the applicability of the traditional LFC model. Simulations are done on a four-area power system, and the results verify the efficacy of the presented event-triggered scheme and the robust cooperative LFC approach.Note to Practitioners—To promote the penetration of wind energy into power systems, this work explores a robust cooperative LFC approach under multi-agent structure to ensure the stability of the system, aiming at extending the applicability of existing approaches. The proposed approach is hierarchical. At the rated wind power tracking level, the MPC is employed to handle constraints associated with actuating devices, such as heterogeneous convertors. Simultaneously, an improved ETS considering multiple historic triggered signals is integrated in the MPC to reduce the computational burden. At the power system level, the robust performance index is incorporated in the control design to smooth the impacts of intermittent wind power on frequency stability. Additionally, the study accounts for the potential shift of the steady-state operating point and improves the traditional small-signal LFC model by adding an uncertain matrix, which can better explain the variation of system parameters and is more applicable in practical power system engineering. Simulation results demonstrate that the proposed robust cooperative LFC approach can effectively maintain the system frequency within the admissible range under the high penetration of wind energy, whereas the traditional PI controller falls short in this regard.

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

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

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

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

In this paper, a novel synchronization learning scheme is proposed for secure communication, where the signal transmission architecture with a chaotic encryption process is considered. Firstly, to realize the information security in communication, the original signals are encrypted by fractional order dynamics from the sender, and decrypted by receiver to achieve synchronization. For the process, a hybrid order dynamic optimization is constructed, where the fractional order and the integer order systems are modeled as constraints. Secondly, a transformation formula is developed to convert these constraints into new integer order dynamics, and the equivalence between two dynamic optimizations is obtained. Thirdly, to obtain the synchronization solution, a new iterative learning algorithm is designed, and the adaptive dynamic programming is successfully embedded into the solving process. Finally, we apply the proposed synchronization scheme into the secure image transmission, and the simulation results demonstrate the effectiveness and practicality successfully.

This article investigates the robust fault estimation (FE) scheme for a class of discrete-time nonlinear dynamics subject to simultaneous bounded disturbances, sensor and actuator/process faults through the T–S fuzzy method. By constructing an augmented system that contains sensor faults as part of its state, a dissipativity-based FE observer is proposed to achieve sensor and actuator/process faults reconstruction. Combine with the fuzzy Lyapunov function method and dissipativity theory, some brand-new conditions with slack scalars and matrices are attained to ensure that observation error systems are strictly$(\mathcal {R},\mathcal {W},\mathcal {S}) -\delta -$dissipative. Besides, to improve the transient FE performance, regional pole placement problem is also considered in FE observer design. It is worth mentioning that different from some existing results which assume that actuator faults occur in a constant form, the method given in this article is suitable for more types of faults such as time-varying ones. By two simulation experiments, the validity and practicability of the proposed FE observer are fully illustrated.

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

Aiming at the deep-sea submarine search and rescue problem, this paper proposes a universally applicable submarine position prediction model and search model. The position prediction of the submersible is realized by Kalman filtering and dynamics modeling. Meanwhile, Monte Carlo method is used to construct the initialized population of the motion trajectory and optimize the search path step by step by iterative genetic algorithm. In this paper, the optimal search path is taken as the objective, the main ship SAR trajectory is simulated, and the probability of the diver is fitted as a function of time and cumulative search results. For the multiple submersible search and rescue problem, this paper proposes two possible search and rescue schemes and compares the search and rescue time. Then we propose the optimal multi-objective dynamic search and rescue method. In addition, this paper adopts the G1-entropy weight-coefficient of variation combined assignment method to evaluate different search devices and creatively adopts the CRITIC method to secondary assign the weights obtained from different evaluation methods to select the optimal search device. Finally, sensitivity and robustness analysis are also carried out in this paper.

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

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

In the complex practical engineering systems, many interferences and attacking signals are inevitable in industrial applications. This article investigates the reinforcement learning (RL)-based resilient control algorithm for a class of Markovion jump systems with completely unknown transition probability information. Based on the Takagi-Sugeno logical structure, the resilient control problem of the nonlinear Markovion systems is converted into solving a set of local dynamic games, where the control policy and attacking signal are considered as two rival players. Combining the potential learning and forecasting abilities, the new integral RL (IRL) algorithm is designed via system data to compute the zero-sum games without using the information of stationary transition probability. Besides, the matrices of system dynamics can also be partially unknown, and the new architecture requires less transmission and computation during the learning process. The stochastic stability of the system dynamics under the developed overall resilient control is guaranteed based on the Lyapunov theory. Finally, the designed IRL-based resilient control is applied to a typical multimode robot arm system, and implementing results demonstrate the practicality and effectiveness.

The consensus problem of general linear multiagent systems (MASs) is studied under switching topologies by using observer-based event-triggered control method in this article. On the basis of the output information of agents, two kinds of novel event-triggered adaptive control schemes are designed to achieve the leaderless and leader-follower consensus problems, which do not need to utilize the global information of the communication networks. Finally, two simulation examples are introduced to show that the consensus error converges to zero and Zeno behavior is eliminated in MASs. Compared with the existing output feedback control research, one of the significant advantages of our methods is that the controller protocols and triggering mechanisms do not rely on any global information, are independent of the network scale, and are fully distributed ways.

This article is concerned with observer-based fault estimation (FE) and tolerant controller design for a series of discrete-time Takagi-Sugeno (T-S) fuzzy stochastic systems. There exist multiple time-varying state delays, intermittent sensor and actuator faults, nonlinear dynamics, and exogenous disturbances in the systems. Compared with the results of the existence, this approach suggested in this article is more flexible and feasible. By means of the FE information, a novel fuzzy adaptive descriptor observer is developed to obtain the error dynamics. Then, an active observer-based fault-tolerant controller is designed to stabilize the closed-loop fuzzy system. Furthermore, a set of delay-dependent sufficient conditions are provided by the fuzzy Lyapunov function with the way of linear matrix inequalities (LMIs), which has less conservatism compared with the ones of the existing observers and fault-tolerant controllers. Finally, a simulation example is shown to illustrate the advantages and effectiveness of this approach depicted in this article.

In this article, a novel parallel tracking control optimization algorithm is first proposed for partially unknown fuzzy interconnected systems. In the existing standard optimal tracking control, the bounded or nonasymptotic stable reference trajectory will lead the feedback control not converging to zero, which causes the performance index infinite and invalid. By using the precompensation technique, in this article, the working feedback control is considered as a reconstructed dynamic with the virtual control and a new augmented fuzzy interconnected tracking system is built, thus that the performance index is valid for optimal control. Then, combining the integral reinforcement learning (RL) method and decentralized control design, the novel integral RL parallel algorithm is first developed to solve the tracking controls for interconnected systems, which relax the requirements of exact matrices information Aikand Bikduring the solving process. Both the convergence and stability of the designed control optimization scheme are guaranteed by theorems. Finally, the new parallel tracking algorithm for interconnected systems is verified through the dual-manipulator coordination system and simulation results demonstrate the effectiveness.

This article investigates the adaptive resilient event-triggered control for rear-wheel-drive autonomous (RWDA) vehicles based on an iterative single critic learning framework, which can effectively balance the frequency/changes in adjusting the vehicle's control during the running process. According to the kinematic equation of RWDA vehicles and the desired trajectory, the tracking error system during the autonomous driving process is first built, where the denial-of-service (DoS) attacking signals are injected into the networked communication and transmission. Combining the event-triggered sampling mechanism and iterative single critic learning framework, a new event-triggered condition is developed for the adaptive resilient control algorithm, and the novel utility function design is considered for driving the autonomous vehicle, where the control input can be guaranteed into an applicable saturated bound. Finally, we apply the new adaptive resilient control scheme to a case of driving the RWDA vehicles, and the simulation results illustrate the effectiveness and practicality successfully.

This article addresses the decentralized control problem of continuous-time nonlinear large-scale interconnected systems by the means of echo state network (ESN). The interconnected terms between the subsystems are treated as the disturbances added to the system dynamics, then the control problem is solved by the proposed robust controllers. By designing a cost function for the nominal subsystems, the robust controller is obtained by solving optimal controllers. The stability of the interconnected systems is proved by a composite Lyapunov function. The online adaptive dynamic program (ADP) method is employed to solve the transformed optimal problem, where a single ESN is utilized to approximate the critic cost and control policy. The optimal control policies of all the isolated subsystems are obtained simultaneously. The closed-loop stability of the feedback nominal systems is also proved, in a uniformly ultimately boundedness (UUB) manner. In the simulation, a large-scale interconnected system with four subsystems is provided to verify the effectiveness of the proposed decentralized controllers.

This article is concerned with the optimal tracking control problem of the coupled Markov jump system (CMJS) by using the reinforcement learning (RL) technique. Based on the conventional optimal tracking architecture, an offline tracking iteration algorithm is first designed to solve the coupled algebraic Riccati equation that can hardly be solved by mathematical methods directly. To overcome the crucial requirements and existing shortcomings in the offline tracking method, a novel integral RL (IRL) tracking algorithm is first proposed for CMJS, which develops a transition-probability-free optimal tracking control scheme with a reconstructed augmented system and discounted cost function. Both the requirements of transition probability πij and system matrix Ai are avoided via the designed IRL algorithm. The stability and convergence of the novel schemes are proved by the Lyapunov theory, and the tracking objective is achieved as desired. Finally, we apply the designed algorithms in a fourth-order Markov jump control problem and the stochastic mass, spring, and damper system to track continuous sinusoidal waveforms, and the simulation results are provided to show the effectiveness and applicability.

In this paper, fault estimation (FE) and fault-tolerant control (FTC) are investigated for Takagi-Sugeno (T-S) fuzzy systems with multiple time-varying delays as well as actuator and sensor faults. Local nonlinear models and external disturbances are also considered. Inspired by the information from the (k-1)th induction FE, a novel observer is addressed to establish the kth error dynamics. The k-step induction FE observer can weaken the effect from input disturbances caused by the derivatives of actuator faults and can perform better FE subject to sensor and actuator faults and multiple time delays simultaneously. Compared with the existing results, the proposed observer can realistically better show the sizes and shapes of the actuator and sensor faults. In addition, according to online information from the k-step FE, an active dynamic output feedback fault-tolerant controller is proposed to make the closed-loop fuzzy system asymptotically stable. Moreover, the fuzzy Lyapunov-Krasovskii functional is developed by introducing some free-weighting matrices such that the delay dependent sufficient conditions are given in the form of a set of linear matrix inequalities (LMIs) with less conservatism for the existence of observer and fault-tolerant controller. At last, two simulation examples are given to prove the advantages and effectiveness of the approach given in this paper.

In this paper, a novel event-sampled robust optimal controller is proposed for a class of continuous-time constrained-input nonlinear systems with unknown dynamics. In order to solve the robust optimal control problem, an online data-driven identifier is established to construct the system dynamics, and an event-sampled critic-only adaptive dynamic programming method is developed to replace the conventional time-driven actor-critic structure. The designed online identification method runs during the solving process and is not applied as a priori part for the solutions, which simplifies the architecture and reduces computational load. The proposed robust optimal control algorithm tunes the parameters of critic-only neural network (NN) by event-triggering condition and runs in a plug-n-play framework without system functions, where fewer transmissions and less computation are required as all the measurements received simultaneously. Based on the novel design, the stability of system and the convergence of critic NN are demonstrated by Lyapunov theory, where the state is asymptotically stable and weight error is guaranteed to be uniformly ultimately bounded. Finally, the applications in a basic nonlinear system and the complex rotational-translational actuator problem demonstrate the effectiveness of the proposed method.

In this paper, by incorporating the event-triggered mechanism and the adaptive dynamic programming algorithm, a novel near-optimal control scheme for a class of unknown nonlinear continuous-time non-zero-sum (NZS) differential games is investigated. First, a generalized fuzzy hyperbolic model based identifier is established, using only the input-output data, to relax the requirement for the complete system dynamics. Then, under the event-based framework, the coupled Hamilton-Jacobi equations are derived for the multiplayer NZS games. Then, the adaptive critic design method is employed to approximate the optimal control policies; thus, an identifier-critic architecture is developed to obtain the event-triggered controller. By the virtue of the Lyapunov theory, a state-dependent triggering condition, which is different from the existing works, is developed to achieve the stability of the closed-loop control system both for the continuous and jump dynamics. Finally, two numerical examples are simulated to substantiate the feasibility of the analytical design.

In this paper, a fuzzy reinforcement learning (RL)-based tracking control algorithm is first proposed for partially unknown systems with actuator faults. Based on Takagi-Sugeno fuzzy model, a novel fuzzy-augmented tracking dynamic is developed and the overall fuzzy control policy with corresponding performance index is designed, where four kinds of actuator faults, including actuator loss of effectiveness and bias fault, are considered. Combining the RL technique and fuzzy-augmented model, the new fuzzy integral RL-based fault-tolerant control algorithm is designed, and it runs in real time for the system with actuator faults. The dynamic matrices can be partially unknown and the online algorithm requires less information transmissions or computational load along with the learning process. Under the overall fuzzy fault-tolerant policy, the tracking objective is achieved and the stability is proven by Lyapunov theory. Finally, the applications in the single-link robot arm system and the complex pitch-rate control problem of F-16 fighter aircraft demonstrate the effectiveness of the proposed method.

This paper addresses the problems of fault estimation and fault-tolerant control for switched fuzzy stochastic systems with actuator fault and sensor fault. A novel observer is proposed to estimate the system states, actuator, and sensor faults, simultaneously. The proposed observer can be treated as an extension of the traditional proportional-integral observer. The estimation information is utilized to design the fault-tolerant controller. Based on the piecewise Lyapunov function and the average dwell time, a set of linear matrix inequalities can be achieved, which ensure that the closed-loop system is mean-square exponentially stable with a weighted H∞performance level. At last, two simulation examples are provided to illustrate the effectiveness of the proposed approach.