Adaptive fuzzy control of nonlinear time-delay systems

This paper is concerned with the problem of adaptive fuzzy control for nonlinear systems with an unknown time delay and unknown control gain. Using an appropriate Lyapunov-Krasovskii functional, uncertainty of the unknown time delay is compensated for, and then the Fuzzy logic system in Mamdani type is utilized to approximate the unknown nonlinear function. By the use of Lyapunov stability theorem, 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 neighborhood of the desired reference signal. An advantage of the proposed control scheme lies in that only an adaptive parameter is needed to be updated online. Simulation results show the effectiveness of the proposed scheme.