Optimal Guaranteed Cost Sliding-Mode Control of Interval Type-2 Fuzzy Time-Delay Systems

• Published in: IEEE transactions on fuzzy systems Vol. 26; no. 1; pp. 246 - 257
• Main Authors: Li, Hongyi, Wang, Jiahui, Wu, Ligang, Lam, Hak-Keung, Gao, Yabin
• Format: Journal Article
• Language: English
• Published: IEEE 01.02.2018
• Subjects: Adaptive systems; Cost function; Fuzzy systems; Guaranteed cost control; interval type-2 (IT2) fuzzy systems; Sliding mode control; sliding-mode control (SMC); Symmetric matrices; time-delay systems; Uncertainty
• ISSN: 1063-6706; 1941-0034
• DOI: 10.1109/TFUZZ.2017.2648855

This paper is concerned with the optimal guaranteed cost sliding-mode control problem for interval type-2 (IT2) Takagi-Sugeno fuzzy systems with time-varying delays and exogenous disturbances. In the presence of the uncertain parameters hidden in membership functions, an adaptive method is presented to handle the time-varying weight coefficients reflecting the change of the uncertain parameters. A new integral sliding surface is presented based on the system output. By designing a novel adaptive sliding-mode controller, system perturbation or modeling error can be compensated, and the reachability of the sliding surface can be guaranteed with the ultimate uniform boundedness of the closed-loop system. Optimal conditions of an H 2 guaranteed cost function and an H ∞ performance index are established for the resulting time-delay control system. Finally, an inverted pendulum system represented by the IT2 fuzzy model is applied to illustrate the advantages and effectiveness of the proposed control scheme.