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

Xiaohe Wan and Yan Li ()
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Xiaohe Wan: Jinan Campus (Swinburne College), Shandong University of Science and Technology, Jinan 250031, China
Yan Li: Jinan Campus (Swinburne College), Shandong University of Science and Technology, Jinan 250031, China

Mathematics, 2024, vol. 12, issue 7, 1-22

Abstract: 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.

Keywords: backstepping technique; adaptive fuzzy control; unknown hysteresis; nonlinear stochastic switched systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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