Adaptive-triggered H∞ sliding-mode optimal control for nonlinear input-limited systems

Abstract

This paper concentrates on the $H_{\infty }$ sliding mode optimal control (SMOC) problem for nonlinear systems with mismatched interference and constrained input. Firstly, an adaptive-triggered strategy for the discontinuous control part is employed, which can suppress input interference and the separated matched disturbances. Also, the system trajectories are guaranteed to converge to the sliding manifold. Moreover, the adaptive-triggered strategy is optimized into self-triggered strategy with the aim to avoid the real-time measurement of triggered conditions, and the minimum time interval is obtained to prevent Zeno phenomenon. Subsequently, the optimal $H_{\infty }$ control problem of sliding motion turns into a two-person ZS game issue. To derive the solutions of event-trigger HJI equation, an adaptive dynamic programming (ADP) algorithm with critic-only structure is implemented to obtain the optimal control online. Furthermore, by utilizing the Lyapunov technique, the uniformly ultimately bounded (UUB) conditions about system state and the weight estimation error are obtained. At last, simulation outcomes are analyzed to validate the effectiveness of the control strategy.