Constrained Control for a Class of TS Fuzzy Systems

• Published in: IEEE transactions on fuzzy systems Vol. 31; no. 1; pp. 348 - 353
• Main Authors: Tiko, Souhail, Mesquine, Fouad
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.01.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Behavioral sciences; Closed loops; Constraints; Control systems design; Fuzzy systems; Liapunov functions; line integral Lyapunov function (LILF); Lyapunov methods; PD control; Saturation; Stability; Stability analysis; stabilization; Symmetric matrices; Takagi–Sugeno (TS); Writing
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2022.3182775

This article investigates handling control constraints in the controller design phase for a class of Takagi-Sugeno (TS) fuzzy systems. Line integral Lyapunov function (LILF) is used to reduce the conservativeness compared to common quadratic Lyapunov function (CQLF) and fuzzy Lyapunov function (FLF). Two cases, namely unsaturating and saturating control, are studied. First, an inclusion condition is set to guarantee the behavior in a region where control constraints violation does not occur. For the second case, the saturation may take effect and is allowed. Thanks to the saturation function, convex writing to outrun the nonlinearity inconvenience. For both cases, stabilizing design procedures are proposed such that closed-loop stability and its linked performances are not affected. Furthermore, the proposed conditions enlarge the domain of stability as possible. Hence, comparisons are made with other approaches to show the effectiveness of our approach.