A new sliding mode-based learning control for uncertain discrete-time systems

A new sliding mode-based learning control scheme is developed for a class of uncertain discrete-time systems. In particular, a recursive-learning controller is designed to enforce the sliding variable vector to reach and retain in the sliding mode, and the system states are then guaranteed to asymptotically converge to zero. A recently introduced “Lipschitz-like condition” for sliding mode control systems, which describes the continuity property of uncertain systems, is further extended to the discrete-time case setting in this paper. The distinguishing features of this approach include: (i) the information about the uncertainties is not required for designing the controller, (ii) the closed-loop system exhibits a strong robustness with respect to uncertainties, and (iii) the control scheme enjoys the chattering-free characteristic. Simulation results are also given to demonstrate the effectiveness of the new control technique.