Adaptive Tracking Control of Switched Stochastic Non-Linear Systems With Full State Constraints: A MDADT Switching Method

Abstract

This article proposes an adaptive tracking control scheme for a class of switched stochastic non-linear systems subject to full state constraints (FSCs). A unified framework is established by integrating the adaptive backstepping technique with barrier Lyapunov functions (BLFs) to address the time-varying full state constraints (TFSCs). Accordingly, utilizing the theorem of stochastic non-linear systems, a new adaptive state feedback control scheme is developed for a class of switching signals with the mode-dependent average dwell time (MDADT) property. The proposed adaptive controller is mode-dependent while the adaptive laws are mode-independent so as to facilitate an easy deployment of the controller. It is rigorously proven that all signals in the closed-loop system are bounded in probability, the tracking error converges to a bounded compact set, and the TFSCs are not violated. Finally, simulation examples are conducted to validate the effectiveness of the controller.