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

• Published in: Communications in nonlinear science & numerical simulation Vol. 143; p. 108633
• Main Authors: Zhou, Wei-Jie, Wu, Kai-Ning, Wu, Yong-Xin
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2025
• Subjects: Boundary control; Markovian switching; Mean square exponential stability; Sliding mode control; Stochastic reaction–diffusion systems; Boundary control; Stochastic reaction–diffusion systems; Sliding mode control; Markovian switching; Mean square exponential stability
• ISSN: 1007-5704
• DOI: 10.1016/j.cnsns.2025.108633

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. •A novel observer-based mode-dependent SMS and SMBCr are proposed to ensure the stabilization.•The finite-time reachability is addressed for stochastic systems.•For UMSRDS, the SMBC based on the boundary output observer is presented.