Adaptive Pareto Optimal Control of T–S Fuzzy System with Input Constraints and Its Application

• Published in: International journal of fuzzy systems Vol. 24; no. 2; pp. 967 - 988
• Main Authors: Li, Hu, Song, Bao, Tang, Xiaoqi, Xie, Yuanlong, Zhou, Xiangdong
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022; Springer Nature B.V
• Subjects: Adaptive control; Artificial Intelligence; Business metrics; Computational Intelligence; Constraints; Controllers; Design; Design criteria; Design optimization; Engineering; Feedback control; Fuzzy control; Fuzzy systems; H-infinity control; Linear matrix inequalities; Management Science; Mathematical analysis; Multiple objective analysis; Operations Research; Optimal control; Optimization; Pareto optimum; Permanent magnets; Preferences; State feedback; Synchronous motors; T–S fuzzy system; Input saturation; Permanent magnet synchronous motor; Pareto optimal; Multi-objective problem
• ISSN: 1562-2479; 2199-3211
• DOI: 10.1007/s40815-021-01180-0

This paper proposes an adaptive Pareto optimal control scheme for a general class of multi-objective T–S fuzzy systems subject to input constraints. Firstly, the fuzzy state feedback controller is employed to close the augmented system. Then, based on linear matrix inequality (LMI), a novel multi-objective optimizer is proposed for pre-regulation of the control gains to simultaneously minimize H 2 / H ∞ performance. Utilizing a polytopic representation, sufficient conditions to ensure the stability of the input constrained system are derived in the proposed optimizer. Furthermore, the resultant design criteria are relaxed by utilizing the membership-function-dependent analysis and the parameterized LMI technologies. Besides, under uncertain working conditions, the interactive fuzzy decision-maker with the reduced computation burden is designed to online schedule Pareto optimal control gains. Finally, simulations and experiments implemented on a permanent magnet synchronous motor system validate the effectiveness and applicability of the proposed scheme.