Adaptive Mamdani Fuzzy Backstepping Control for a Class of Strict-feedback Nonlinear Time-varying Delay Systems

This paper presents an adaptive Mamdani fuzzy control scheme for a class of uncertain strict-feedback nonlinear systems with unknown time-varying delays. Within this scheme, fuzzy logic systems are used to approximate nonlinear functions and the developed adaptive fuzzy controller is recursively designed via backstepping technique and Lyapunov-Krasovskii functionals, which not only significantly compensate for the unknown time-varying delays but also, avoids controller singularity problem. The proposed adaptive fuzzy controller guarantees that all signals in the closed-loop system are uniformly ultimately bounded, while tracking error converges to a small neighborhood of the origin. The main advantages of the proposed controller are that the designed control law is time-delay independent and only one adaptive parameter is required to be updated online. Simulation results are presented to verify the effectiveness of the proposed scheme.