Event-triggered optimal control for discrete-time multi-player non-zero-sum games using parallel control

Adaptive sampling artificial-actual control for non-zero-sum games of constrained systems

Considering physical constraints encountered by actuators, this paper addresses the non-zero-sum game of continuous nonlinear systems with symmetric and asymmetric input constraints through aperiodic sampling artificial-actual control. Initially, the artificial system built by the improved Elman dynamic neural networks (EDNNs) has artificial-actual interaction with the physical system, which provides a new perspective for predicting the system state. By constantly learning and adjusting parameters, EDNNs can gradually approximate the dynamic behavior of the real system to achieve more effective control. Aiming at accommodating diverse input constraints, the non-quadratic value function constructed from a smoothly bounded function is devised. Then, the polynomial parameterized adaptive dynamic programming (ADP) is employed to approximate the solution of the coupled Hamilton-Jacobi equation (HJE), deriving optimal control laws for two players. To improve the efficiency of data communication, three adaptive sampling mechanisms including event-triggered mechanism (ETM) with relative threshold, dynamic ETM (DETM) and self-triggered mechanism (STM) are introduced in turn during the iterative learning process of control sequences. DETM further extends sampling intervals by incorporating internal dynamic variables, while STM determines the next trigger time through soft calculation without hardware monitoring. All three trigger modes can ensure the system stability while avoiding the Zeno phenomenon, and relevant proofs are given. Finally, the simulation validates the effectiveness of the designed algorithm and highlights the unique characteristics of each trigger mode.

Neural Adaptive H∞ Sliding-Mode Control for Uncertain Nonlinear Systems with Disturbances Using Adaptive Dynamic Programming

This paper focuses on a neural adaptive H∞ sliding-mode control scheme for a class of uncertain nonlinear systems subject to external disturbances by the aid of adaptive dynamic programming (ADP). First, by combining the neural network (NN) approximation method with a nonlinear disturbance observer, an enhanced observer framework is developed for estimating the system uncertainties and observing the external disturbances simultaneously. Then, based on the reliable estimations provided by the enhanced observer, an adaptive sliding-mode controller is meticulously designed, which can effectively counteract the effects of the system uncertainties and the separated matched disturbances, even in the absence of prior knowledge regarding their upper bounds. While the remaining unmatched disturbances are attenuated by means of H∞ control performance on the sliding surface. Moreover, a single critic network-based ADP algorithm is employed to learn the cost function related to the Hamilton-Jacobi-Isaacs equation, and thus, the H∞ optimal control is obtained. An updated law for the critic NN is proposed not only to make the Nash equilibrium achieved, but also to stabilize the sliding-mode dynamics without the need for an initial stabilizing control. In addition, we analyze the uniform ultimate boundedness stability of the resultant closed-loop system via Lyapunov's method. Finally, the effectiveness of the proposed scheme is verified through simulations of a single-link robot arm and a power system.

Event-Triggered Near-Optimal Control for Unknown Discrete-Time Nonlinear Systems Using Parallel Control

This article uses parallel control to investigate the problem of event-triggered near-optimal control (ETNOC) for unknown discrete-time (DT) nonlinear systems. First, to achieve parallel control, an augmented nonlinear system (ANS) with an augmented performance index (API) is proposed to introduce the control input into the feedback system. The control stability relationship between the ANS and the original system is analyzed, and it is shown that, by choosing a proper API, optimal control of the ANS with the API can be seen as near-optimal control of the original system with the original performance index (OPI). Second, based on parallel control, a novel event-triggered scheme is proposed, and then a novel ETNOC method is developed using the time-triggered optimal value function of the ANS with the API. The control stability is proved, and an upper bound, which is related to the design parameter, is provided for the actual performance index in advance. Then, to implement the developed ETNOC method for unknown DT nonlinear systems, a novel online learning algorithm is developed without reconstructing unknown systems, and neural network (NN) and adaptive dynamic programming (ADP) techniques are employed in the developed algorithm. The convergence of the signals in the closed-loop system (CLS) is shown using the Lyapunov approach, and the assumption of boundedness of input dynamics is not required. Finally, two simulations justify the theoretical conjectures.