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

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.

Sliding Mode Control of a Class of Hybrid-Switched Systems with Disturbances

“…Theorem 2. Consider the system (4) and the sliding surface function (5). If the SMC law is designed as (27), the system state trajectory can reach the quasi-sliding mode domain…”

“…Switched system can simplify the mathematical model of the system, minimize the computational complexity and enhance the real-time efficiency of the system. It has been widely used in different fields, such as PI control of vehicle transmission [1], flight control system [2], power electronics system [3,4], network control system [5][6][7], and has attracted great attention from researchers. In the switched system, the switching signal indicates how each subsystem operates, and it is the core factor that determines the stable operation of the system.…”