Observer-based sliding mode boundary control of uncertain Markovian stochastic reaction–diffusion systems

Abstract

This paper deals with the robust mean square exponential stabilization for uncertain Markovian stochastic reaction–diffusion systems (UMSRDS) via the observer-based sliding mode boundary control (SMBC). First, a suitable boundary-output-based observer is constructed for estimating the unknown system states. Next, to process the impact of Markovian switching, a mode-dependent integral sliding mode surface (SMS) is established, on which the closed-loop system is mean square robust exponentially stable. Furthermore, an observer-based sliding mode boundary controller (SMBCr) is designed to guarantee the almost sure reachability of the predefined SMS. Then, a mode-dependent condition is provided to ensure the robust mean square exponential stability of the closed-loop system. Finally, the proposed method is applied to a CPU thermal model to illustrate the effectiveness of theoretical results.