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

• Published in: IEEE transactions on fuzzy systems Vol. 28; no. 10; pp. 2581 - 2591
• Main Authors: Wu, Huai-Ning, Zhang, Xiu-Mei
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.10.2020; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Actuators; Biological system modeling; Boundary control; Control systems; Control theory; Feedback control; Fuzzy control; Fuzzy systems; Hilbert space; Liapunov functions; Linear matrix inequalities; Mathematical model; mean square exponential stability; Nonlinear control; Nonlinear systems; Operators (mathematics); Output feedback; Partial differential equations; Stability; Stability analysis; stochastic partial differential equations (SPDEs); Stochastic processes; Stochastic systems; Takagi–Sugeno (T–S) fuzzy model
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2019.2941698

This article investigates a fuzzy boundary control problem of a class of stochastic nonlinear systems modeled by the Itô-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.