Event-Triggered $H_\infty $ Control for Continuous-Time Nonlinear System via Concurrent Learning

Abstract

In this paper, the ${H}_{\infty }$ optimal control problem for a class of continuous-time nonlinear systems is investigated using event-triggered method. First, the ${H}_{\infty }$ optimal control problem is formulated as a two-player zero-sum (ZS) differential game. Then, an adaptive triggering condition is derived for the ZS game with an event-triggered control policy and a time-triggered disturbance policy. The event-triggered controller is updated only when the triggering condition is not satisfied. Therefore, the communication between the plant and the controller is reduced. Furthermore, a positive lower bound on the minimal intersample time is provided to avoid Zeno behavior. For implementation purpose, the event-triggered concurrent learning algorithm is proposed, where only one critic neural network (NN) is used to approximate the value function, the control policy and the disturbance policy. During the learning process, the traditional persistence of excitation condition is relaxed using the recorded data and instantaneous data together. Meanwhile, the stability of closed-loop system and the uniform ultimate boundedness (UUB) of the critic NN’s parameters are proved by using Lyapunov technique. Finally, simulation results verify the feasibility to the ZS game and the corresponding ${H}_{\infty }$ control problem.