Robust H(infinity) control of multiple time-delay uncertain nonlinear system using fuzzy model and adaptive neural network

In this paper, a robust control method which combines fuzzy model-based control with adaptive neural network control is presented for a class of uncertain nonlinear system with multiple time-delay. The fuzzy T-S model with multiple time-delay is adopted for the approximate modeling of the nonlinear system with some unknown uncertainties, and fuzzy-model-based H(infinity) control law is designed by means of LMI method. A full adaptive RBF neural network is added to the fuzzy H(infinity) control in order to guarantee the robust stability of the controlled system. The effect of the unknown uncertainties and the error caused by fuzzy modeling can be overcome by adaptive tuning of the weights, centers and widths of the RBF neural network on line, and no constraint or matching conditions are required. The stability of the designed closed-loop system is thus proved. The proposed method is applied to a multiple time-delay nonlinear chaotic system and the simulation results show that the proposed method cannot only stabilize the chaos systems, but has strong robustness against uncertainties and external disturbance.