Adaptive Fuzzy Backstepping Control for Itô-Type Nonlinear Switched Systems Subject to Unknown Hysteresis Input

• Published in: Mathematics (Basel) Vol. 12; no. 7; p. 1070
• Main Authors: Wan, Xiaohe, Li, Yan
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.04.2024
• Subjects: Adaptive control; adaptive fuzzy control; Analysis; backstepping technique; Control; Controllers; Design; Differential calculus; Fuzzy algorithms; Fuzzy control; Fuzzy logic; Fuzzy sets; Fuzzy systems; Hysteresis; Influence; Investigations; Methods; Neural networks; Nonlinear control; nonlinear stochastic switched systems; Nonlinear systems; Nonlinear theories; Switches; Tracking errors; unknown hysteresis; China
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math12071070

The adaptive fuzzy backstepping control problem is studied for Itô-type nonlinear switched systems subject to unknown hysteresis input. Compared with existing works, the unknown hysteresis and stochastic disturbances are considered in the pure-feedback switched systems. The mean value theorem tackles the non-affine functions. The backstepping technique introduces an auxiliary virtual controller. In addition, the Nussbaum function is employed to solve the difficulty caused by the unknown hysteresis under arbitrary switching. Based on a fuzzy logic system and backstepping technique, a new adaptive control proposal is obtained, which ensures that the system states satisfy semiglobally uniformly ultimately bounded (SGUUB) in probability and that the tracking error converges to a region of the origin. Finally, we provide two examples to show the validity of the presented scheme.