Sliding-mode surface-based adaptive actor-critic optimal control for switched nonlinear systems with average dwell time

Abstract

This paper studies the problem of sliding-mode surface (SMS)-based adaptive optimal control for a class of continuous-time switched nonlinear systems with average dwell time (ADT) via using an actor-critic (AC) reinforcement learning (RL) strategy. By developing a specific cost function related to SMS, the original control problem is equivalently transformed into the problem of finding a series of optimal control policies. Then, the error terms separated from the Hamilton-Jacobi-Bellman (HJB) equation are integrated into a function, which effectively reduces the influence of some repeated magnifications caused by approximation errors. Besides, the solution to the HJB equation is identified by the SMS-based AC neural networks (NNs), where the actor and critic NNs are developed to carry out the RL strategy simultaneously. The actor updating law is to implement control actions based on the system output, while the critic updating law is required to assess the current control action and feedback to the actor. Based on the Lyapunov stability theory, the applicability of the proposed adaptive AC optimal control method is verified to guarantee the boundedness of all signals in the considered closed-loop switched nonlinear systems. Finally, a simulation examples is given to illustrate the effectiveness of the proposed adaptive optimal control method.