Fuzzy Control with Pole Assignment and Variance Constraints for Continuous-time Perturbed Takagi-Sugeno Fuzzy Models: Application to Ship Steering Systems

• Published in: International journal of control, automation, and systems Vol. 17; no. 10; pp. 2677 - 2692
• Main Authors: Chang, Wen-Jer, Lin, Yan-Horng, Du, Jialu, Chang, Chin-Ming
• Format: Journal Article
• Language: English
• Published: Bucheon / Seoul Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers 01.10.2019; Springer Nature B.V; 제어·로봇·시스템학회
• Subjects: Algorithms; Constraints; Control; Control stability; Control systems design; Control theory; Controllers; Covariance; Engineering; Fuzzy control; Fuzzy systems; Intelligent Control and Applications; Linear matrix inequalities; Mathematical analysis; Matrix methods; Mechatronics; Nonlinear systems; Pole placement; Robotics; Robust control; Stability analysis; Steering; Stochastic systems; Variance; 제어계측공학; Takagi-Sugeno fuzzy model; robust control; state variance constraint; pole placement constraint; Output variance constraint
• ISSN: 1598-6446; 2005-4092
• DOI: 10.1007/s12555-018-0917-9

The stability analysis and controller design of stochastic systems have become much more important because the stochastic behaviors usually exist in practical nonlinear systems. In this paper, a robust fuzzy controller design approach is proposed with multiple constraints, including state variance constraints, output variance constraints, and pole placement constraints. At first, nonlinear systems are expressed as the Takagi-Sugeno fuzzy model, and the parallel distributed compensation method is applied to design the robust fuzzy controllers. Next, considering the stability analysis and the performance constraints of perturbed Takagi-Sugeno fuzzy models, Lyapunov conditions are developed based on covariance control theory, pole placement theory and robust control theory. By constructing the stability conditions with multiple constraints, the proposed fuzzy control problem can be effectively transferred into the linear matrix inequality problem. It can be solved by the convex optimal programming algorithm. At last, a nonlinear ship steering system is selected to verify the effectiveness and applicability of the proposed robust fuzzy controller design method.