Control Design for Parabolic PDE Systems via T-S Fuzzy Model

被引：32
|
作者：
Li, Teng-Fei [1 ,2 ]
Chang, Xiao-Heng [1 ,2 ]
Park, Ju H. [3 ]
机构：
[1] Wuhan Univ Sci & Technol, Sch Informat Sci & Engn, Wuhan 430081, Peoples R China
[2] Wuhan Univ Sci & Technol, Engn Res Ctr Met Automat & Measurement Technol, Minist Educ, Wuhan 430081, Peoples R China
[3] Yeungnam Univ, Dept Elect Engn, Gyongsan 38541, South Korea
来源：
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS | 2022年 / 52卷 / 06期
基金：
中国国家自然科学基金; 新加坡国家研究基金会;
关键词：
Mathematical model; Asymptotic stability; Fuzzy control; Linear matrix inequalities; Control design; Boundary conditions; Thermal stability; linear matrix inequality (LMI); parabolic partial differential equation (PDE); Takagi-Sugeno (T-S) fuzzy systems; EQUATION;
D O I：
10.1109/TSMC.2021.3071502
中图分类号：
TP [自动化技术、计算机技术];
学科分类号：
0812 ;
摘要：
In this article, we investigate the parabolic partial differential equations (PDEs) systems with Neumann boundary conditions via the Takagi-Sugeno (T-S) fuzzy model. On the basis of the obtained T-S fuzzy PDE model, a novel fuzzy state controller which is associated with the boundary state of position and the mean value coefficient matrix derived through the mean value theorem of integral is designed to analyze the asymptotic stability of the parabolic PDE system. Without sampling the nonlinear parameter of the system, new stability conditions are deduced in the form of linear matrix inequalities (LMIs). Moreover, compared with the novel fuzzy state controller, more conservative conditions based on another fuzzy state controller are also provided. Finally, we explore the state-feedback controller into the Fisher equation as an application. Simulation results show that the proposed method is effective.
引用
收藏
页码：3671 / 3679
页数：9
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