Robust adaptive fuzzy control in the presence of external disturbance and approximation error

Robust direct and indirect adaptive fuzzy controllers are proposed for tracking control of a class of nonlinear SISO systems. The behavior of the adaptive law is investigated in the error state space when the perturbations are introduced in the adaptive fuzzy control system. A new adaptation scheme that can eliminate the effect of perturbations on the parameter adaptation is proposed. It is proved that all the signals in the closed-loop system are bounded in the presence of external disturbances and approximation error of the fuzzy logic system. The concept of persistent excitation is utilized to guarantee the convergence and the boundedness of adaptation parameters. It has also been observed that the convergence of parameters and tracking error could be smoother and faster with the proposed methods compared with the conventional adaptive fuzzy controllers. Two simulations have been conducted to demonstrate the effectiveness of the proposed controllers.