Boundary Control for Stochastic Reaction--Diffusion System Cascaded With an ODE System
研究了随机反应扩散系统与常微分系统级联时的控制问题，提出结合边界控制和状态反馈的混合策略，确保系统均方指数稳定，并考虑了不确定性和抗干扰性能。
The control problems are investigated for a stochastic reaction–diffusion system (SRDS) cascaded with an ordinary differential system (ODS). We propose a novel hybrid control strategy that combines boundary control for the SRDS with state feedback control for the ODS. The primary objective is to ensure the cascaded system achieves mean-square exponential stability (<italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">MSES</i>). Our research offers a flexible framework for stability analysis and control synthesis in cascaded systems, applicable regardless of the ODS’s inherent stability. We further explore the system’s robust stabilization with uncertainties and its <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty } $</tex-math> </inline-formula> performance to quantify disturbance-rejection capabilities. The key innovations include the development of a unified control framework that accommodates both stable and unstable ODE subsystems, the design of boundary control inputs that ensure MSES even in the presence of parameter uncertainties, and the application of matrix inequality techniques to simplify controller design. The effectiveness of the proposed control strategies is demonstrated by three numerical examples.