Event-Triggered H∞ Tracking Control of Nonlinear Systems via Reinforcement Learning Method

Abstract

In this paper, the H ∞ tracking control problem of continuous-time nonlinear system is investigated. An event-triggered adaptive optimal tracking control scheme is developed based on the reinforcement learning method. By constructing an augmented system and introducing a discounted cost function, the corresponding event-driven tracking Hamilton-Jacobi-Isaacs (HJI) equation is derived, which provides the solution of the H ∞ tracking control problem. Since the event-triggered tracking HJI equation is a nonlinear partial difference equation in essence, it is hard to be solved analytically. To overcome this difficulty, a novel reinforcement learning algorithm is proposed to learn the solution of derived event-triggered tracking HJI equation in which a critic network is employed to approximate the optimal cost function on-line without the requirement of initial admissible control policy. It is worthy to mention that the developed event-triggered tracking controller is updated only at the event-triggered instants, which can greatly decrease the controller update frequency and reduce the communication burden by contrast to the time-triggered one. The stability of closed-loop system is demonstrated by the Lyapunov theory. Simulation results validate the effectiveness of proposed event-triggered tracking control scheme.