Boundary Static Output Feedback Control for Nonlinear Stochastic Parabolic Partial Differential Systems via Fuzzy-Model-Based Approach

Abstract

This article investigates a fuzzy boundary control problem of a class of stochastic nonlinear systems modeled by the Ito-type parabolic stochastic partial differential equation (SPDE). Initially, a Takagi–Sugeno fuzzy SPDE model is proposed to accurately represent the nonlinear SPDE system. Then, on the basis of the infinite-dimensional infinitesimal operator, a fuzzy boundary static output feedback controller is developed in terms of a set of linear matrix inequalities to locally exponentially stabilize the resulting system in the mean square sense. By using an approximation argument and constructing a Lyapunov function for the mild solution, the local mean square exponential stability of the closed-loop system is proved. Meanwhile, the closed-loop well-posedness analysis is also given by virtue of the semigroup theory. Finally, a simulation study on a Belousov–Zhabotinsky reaction–diffusion system with random parameter variation is presented to illustrate the effectiveness of the proposed method.