Adaptive Fuzzy-Neural Control for a class of Nonlinear Time-Delay Systems using a State Observer

n this paper, an observer-based adaptive fuzzy-neural control is presented for a class of nonlinear systems with unknown time delays. The state observer is first designed, and then the controller is designed via the adaptive fuzzy-neural control method based on observer states. Both the designed observer and controller are independent of time delays. Using an appropriate LyapunovKrasovskii functional, the uncertainty of the unknown time delay is compensated, and then the fuzzyneural system is utilized to approximate the unknown nonlinear functions. Based on the Lyapunov stability theory, the constructed observer-based controller and the closed-loop system are 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 to be updated on-line. Simulation results are presented to demonstrate the effectiveness of the proposed approach.