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This paper develops a novel guaranteed cost control (GCC) approach under the event-triggered mechanism for completely unknown systems using integral reinforcement learning (IRL) algorithm. First, based on the adaptive dynamic programming (ADP) method, the GCC problem is addressed by transforming it into the optimal control problem. Second, without using the accurate information of system dynamics, a model-free data-based GCC approach is designed via IRL algorithm. Moreover, for the purpose of reducing the waste of communication resources, a GCC algorithm is presented under the event-triggered mechanism for completely unknown system by utilizing the explorized IRL algorithm. The critic–actor–disturbance neural networks (NNs) are applied to approximate near optimal solution. In addition, the weight estimations of NNs are tuned synchronously according to the designed novel triggering condition. Furthermore, the stability analysis of the controlled system is given by utilizing the Lyapunov principle. Finally, the simulation results are presented to verify the feasibility of the designed approach. [ABSTRACT FROM AUTHOR]

In this article, the problems of robust reliable H∞ optimization control for discrete‐time nonlinear systems with or without time‐delay subject to faults are investigated. A static state feedback controller is explored for Takagi–Sugeno fuzzy systems against nonlinear dynamics, exogenous disturbances, and model uncertainties. In contrast to the design of conventional controllers, the proposed controller is easier and more flexible. The Lyapunov function is utilized to assure the stability of the closed‐loop systems. Besides, linear matrix inequalities are utilized to derive the sufficient conditions by MATLAB toolbox. Finally, two simulation examples are shown to validate the feasibility of the suggested approach. [ABSTRACT FROM AUTHOR]

This article presents a novel event-driven guaranteed cost control method for nonlinear systems subject to actuator faults. For the purpose of handling the problem of actuator faults and obtaining the event-driven approximate optimal guaranteed cost control approach for general nonlinear dynamics, the reinforcement learning (RL) algorithm is utilized to develop a sliding-mode control (SMC) strategy. To begin with, the unknown faults can be estimated by designing a fault observer. Meanwhile, an SMC technique is presented aiming at countering the effect of abrupt faults. In addition, the optimal performance of the equivalent sliding mode dynamics is considered, then an event-driven guaranteed cost control mechanism is implemented by using RL principle. In the control process, a general cost function, which has a simpler structure, is given to reduce the computation complexity. At the same time, a modified cost function is approximated to obtain optimal guaranteed cost control by using a single critic neural network (NN). In addition, a modified weight update law for critic NN is presented to relax the persistence of excitation (PE) condition. Moreover, a newly triggering condition, which is easy to be implemented, is designed, and the critic NN update law makes sure that the system states are stable. Furthermore, in light of the Lyapunov analysis, it is demonstrated that the developed event-driven control method guarantees the uniformly ultimately bounded (UUB) property of all the signals. Finally, three simulation results are given to validate the designed control method. [ABSTRACT FROM AUTHOR]

Summary: In this article, a novel neural network (NN) optimal control approach using adaptive critic designs is developed for nonlinear discrete‐time (DT) systems with time delays. First, to eliminate the delay term of control input, a time‐delay matrix function is developed by designing a M network. Furthermore, the cost function is approximated by the critic NN, and the control signal can be obtained directly by using the information of critic NN according to the equilibrium condition. In addition, to shorten the learning time and reduce the computational burden in the control process, a novel control strategy with less adjustable parameters for the time‐delay DT nonlinear systems is proposed in this article, in which the norm of the weight estimations of critic NN is updated to generate a novel long‐term performance function. The proposed control algorithm using adaptive critic designs has the advantage of reducing adaptive learning parameters and lessening calculative burden. The Lyapunov stability analysis shows that the time‐delay DT controlled systems can be uniformly ultimately bounded stable. Finally, three simulations are presented to demonstrate the control performance of the developed method. [ABSTRACT FROM AUTHOR]

This paper is concerned with online adaptive control strategy for a class of unknown nonlinear discrete-time systems with time delays. The main objective is to establish an online adaptive control strategy based on reinforcement learning (RL) algorithm, so that the nonquadratic performance index can be minimized and the closed-loop system with time delays is stable. In order to simplify the control systems with time delays, a time delay function is designed to eliminate the term of control delays. Then, the online adaptive control algorithm via RL is presented to approach the reasonable control law and optimizes the long-term performance function. On the basis of the Lyapunov theory, it is proved that the design of online adaptive controller is effective and all the signals of control system are ultimately uniformly bounded. The simulation results indicate the validity and feasibility of the proposed adaptive control strategy. [ABSTRACT FROM AUTHOR]

• Firstly, a novel FTC strategy involved with event-triggered mechanism and ISMC method is proposed for nonlinear systems subject to actuator failures. The proposed control method can make the nonlinear systems stable, as well as lower the frequency of network communication of the controlled systems, and therefore avoid the waste of system resources. • Secondly, inspired by Vrabie and Lewis (2009)[35] and Liu et al. (2020)[36], the proposed control method is presented to drive an event-based H ∞ control policy by applying RL algorithm without requiring a stable initial control law, which is necessary in the implemen-tation of event-triggered RL-based control approaches developed in Adib and Braun (2019)[25], Liu et al. (2019)[29], Wang et al. (2019)[33] and Vrabie et al. (2009)[34]. • Thirdly, since the phenomenon of input constraints often exists in nonlinear practical control systems, different from Liu et al. (2019)[29], Liu et al. (2021)[37], Han et al. (2020)[38] and Liu et al. (2020)[39], the event-triggered H ∞ control strategies is developed for nonlinear system dynamics subject to actuator failures. This paper investigates guaranteed cost control (GCC) problem for nonlinear systems subject to input constraints and disturbances by utilizing the reinforcement-learning (RL) algorithm. Firstly, by establishing a modified Hamilton–Jacobi–Bellman (HJI) equation, which is difficult to be solved, a model-based policy iteration (PI) GCC algorithm is designed for input-constrained nonlinear systems with disturbances. Moreover, without requiring any knowledge of system dynamics, by designing an auxiliary system with a control law and an auxiliary disturbance policy, an online model-free GCC approach is developed by utilizing integral reinforcement learning (IRL) algorithm. To implement the proposed control algorithm, the actor and disturbance NNs are constructed to approximate the optimal control input and worst-case disturbance policy, while the critic NN is utilized to approximate optimal value function. Further, a synchronization weight update law is developed to minimize the NN approximation residual errors. The asymptotic stability of controlled systems is analyzed by applying the Lyapunov's method. Finally, the effectiveness and feasibility of the proposed control method are verified by two nonlinear simulation examples. [ABSTRACT FROM AUTHOR]

• The proposed control scheme can solve the coupled HJ equations online and forward in time without the requirement of initial stabilizing control policies through adding a novel term of only relying on value function V(x) on the weight tuning law of critic NN for each player in this paper. • In this paper, due to the introduction of Osgood condition, a more general condition than Lipschitz condition, the uniqueness of the solution of the system is obtained. So the requirement of the nonlinear term f (x) is greatly relaxed by using Osgood condition, which makes the nonlinear term f (x) is not limited to a function of the first degree, but can be quadratic, cubic, N-degree. • Compared with the works in [23, 30] and [31], the assumptions that g(x) and k(x) are bounded functions are removed, which can also be reflected in the subsequent simulation. • In [23], the system state and the weight estimation errors of critic NNs are uniformly ultimately bounded (UUB), where the boundary contains constants and the errors generated by the NNs. However, in our paper, the boundary is only related to the errors generated by the NNs themselves. Further, when the error is small enough or even tend to zero, the system is asymptotically stable. In this paper, a single network adaptive dynamic programming (ADP) control method is presented to obtain the nearly optimal control policies for the non-zero sum (NZS) differential game problem of the autonomous nonlinear system. The Osgood condition, instead of the traditional Lipschitz condition, is firstly introduced to policy iteration to guarantee the existence and uniqueness of the solution of the dynamic nonlinear systems and to weaken the limited conditions of nonlinear dynamic functions f (x) , g (x) and k (x). Moreover, this adaptive control pattern finds in real-time approximations of the optimal value and the non-zero sum Nash-equilibrium, while also ensuring the uniform ultimate ε -boundedness of the closed-loop system. Further, as the number of hidden-layer neurons tends to infinite, the approximation errors converge to zero. As a result, the closed-loop system is asymptotically stable. Finally, the effectiveness of the proposed near-optimal control pattern is verified by a simulation example. [ABSTRACT FROM AUTHOR]

Abstract This paper focuses on studying the distributed leader-following consensus problem of heterogeneous second-order time-varying nonlinear multi-agent systems (HSTN_MASs) under directed switching topology. Firstly, based on the relative position and relative velocity measurements among neighborhood agents, a class of distributed tracking protocols are proposed. Then the state transformations are provided to solve the time-varying nonlinearity and translate the leader-following problem into the stabilization control problem. By constructing the topology-dependent Lyapunov function and choosing appropriate time-varying regulation factor and coupling strength, it is shown that the exponential tracking of HSTN_MASs can be achieved. Moreover, this paper discusses the distributed leaderless consensus problem of HSTN_MASs. Finally, several simulation examples are given to illustrate the validity of theoretical results. [ABSTRACT FROM AUTHOR]