Event-Driven-Modular Adaptive Backstepping Optimal Control for Strict-Feedback Systems through Zero-Sum Differential Games

Abstract

This paper addresses the event-driven-modular optimal tracking control problem for nonlinear strict-feedback systems with external disturbances. Through the backstepping feedforward control, the optimal tracking problem is transformed into an equivalent optimal regulation problem of affine tracking error system. Subsequently, adaptive dynamic programming technique is introduced to generate the optimal feedback controller, and solve the optimization problem of two-player zero-sum differential game. A single critic neural network is constructed to evaluate the associated cost function online, where the novel weight updating law is derived based on the gradient-descent technique. The resulting event-triggered closed-loop system, modeled as an impulsive system, is proved to be asymptotically stable by Lyapunov theory. Finally, the reliability and effectiveness of the theoretical results is validated by numerical simulation examples.