Event-driven H_∞ control with critic learning for nonlinear systems.

Abstract

In this paper, we study an event-driven H_∞ control problem of continuous-time nonlinear systems. Initially, with the introduction of a discounted cost function, we convert the nonlinear H_∞ control problem into an event-driven nonlinear two-player zero-sum game. Then, we develop an event-driven Hamilton-Jacobi-Isaacs equation (HJIE) related to the two-player zero-sum game. After that, we propose a novel event-triggering condition guaranteeing Zeno behavior not to happen. The triggering threshold in the newly proposed event-triggering condition can be kept positive without requiring to properly choose the prescribed level of disturbance attenuation. To solve the event-driven HJIE, we employ an adaptive critic architecture which contains a unique critic neural network (NN). The weight parameters used in the critic NN are tuned via the gradient descent method. After that, we carry out stability analysis of the hybrid closed-loop system based on Lyapunov's direct approach. Finally, we provide two nonlinear plants, including the pendulum system, to validate the proposed event-driven H_∞ control scheme.