Adaptive Fuzzy Controller Design for a Class of Nonstrict-Feedback Nonlinear Time-Delay Systems with Unknown Hysteresis

In this paper, an adaptive back-stepping controller is designed for a class of nonstrict-feedback nonlinear time-varying delay systems with unknown hysteresis using fuzzy logic systems. Fuzzy logic systems are directly employed to approximate the unknown nonlinear functions. The adaptive-fuzzy controller is constructed by using the back-stepping technique and appropriate Lyapunov–Krasovskii functionals. The proposed controller guarantees that all the closed-loop signals are semiglobally uniformly ultimately bounded. The main advantage of this paper is that the proposed control design scheme does not need to construct the hysteresis inverse. Finally, the effectiveness of the proposed approach is shown by two simulation examples.