Fuzzy observer-based adaptive control for a class of nonlinear systems with unknown time delays

An observer-based adaptive fuzzy control is presented for a class of nonlinear systems with unknown time delays. State observer is first designed, and then based on the observed states the controller is designed via adaptive fuzzy control method. Both the designed observer and controller are independent of the time delays. 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 functions. Based on Lyapunov stability theory, the constructed observer-based controller and the closed-loop system is proved to be asymptotically stable. The designed control law is independent of the time delays and has a simple form with only one adaptive parameter vector, which is required to be updated on-line. Simulation results are presented to demonstrate the effectiveness of the proposed approach.