Adaptive fuzzy control for a class of nonlinear time-delay systems with unknown control direction

A fuzzy robust adaptive control design scheme is developed for a class of uncertain nonlinear system represented by input-output models with time-delay. The Control Direction of the system is unknown. By on-line approximating the unknown nonlinear functions with fuzzy logic systems and using Nussbaum control gain technique, the control law and the update law are constructed. Based on the Lyapunov stability theory, it is proved that with the proposed control law and update laws, the closed-loop system is guaranteed to be stable and the tracking error converges with a desired precision. A simulation example is presented to demonstrate the method.