Adaptive fuzzy-neural control for uncertain time-delayed systems

In this paper, a novel adaptive fuzzy-neural control (AFNC) scheme for uncertain dynamical systems is proposed to suppress the effects caused by multiple time-delayed state uncertainties, unmodeled dynamics, and disturbances. Each delayed uncertainty is assumed to be bounded by an unknown gain. A reference model with the desired amplitude and phase properties is given to construct an error model. A fuzzy-neural (FN) system is used to represent the unknown controlled system from the strategic manipulation of the model following tracking errors. The proposed AFNC scheme uses two on-line estimations, which allows for the inclusion of identifying the gains of the delayed state uncertainties and training the weights of the FN system simultaneously. Stability and robustness of the AFNC scheme is analyzed in Lyapunov sense. It is shown that the proposed control scheme can guarantee parameter estimation convergence and stability robustness of the closed-loop system. The performance of the proposed scheme is evaluated through the simulation results. Simulations are given to show the validity and confirm the performance of the proposed scheme.