Wavelet-based identification and control design for a class of nonlinear systems

In this paper, we extend the wavelet networks for identification and H_∞ control of a class of nonlinear dynamical systems. The technique of feedback linearization, supervisory control and H_∞ control are used to design an adaptive control law and also the parameter adaptation laws of the wavelet network are developed using a Lyapunov-based design. By some theorems, it will be proved that even in the presence of modeling errors, named network error, the stability of the overall closed-loop system and convergence of the network parameters and the boundedness of the state errors are guaranteed. The applicability of the proposed method is illustrated on a nonlinear plant by computer simulation.