Adaptive fuzzy tracking control for a class of perturbed strict-feedback nonlinear time-delay systems

This paper is concerned with the problem of adaptive fuzzy output tracking for a class of perturbed strict-feedback nonlinear systems with time delays and unknown virtual control coefficients. Fuzzy logic systems in Mamdani type are used to approximate the unknown nonlinear functions, then the adaptive fuzzy tracking controller is designed by using the backstepping technique and Lyapunov–Krasovskii functionals. The proposed adaptive fuzzy controller guarantees that all the signals in the closed-loop system are bounded and the system output eventually converges to a small neighborhood of the desired reference signal. An advantage of the proposed control scheme lies in that the number of the online adaptive parameters is not more than the order of the original system. Finally, two examples are used to demonstrate the effectiveness of our results proposed in this paper.