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Wavelet-based identification and control design for a class of nonlinear systems. (English) Zbl 1137.93318

Summary: We extend the wavelet networks for identification and \(H_{\infty}\) control of a class of nonlinear dynamical systems. The technique of feedback linearization, supervisory control and \(H_{\infty}\) 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.

MSC:

93B30 System identification
93B36 \(H^\infty\)-control
42C40 Nontrigonometric harmonic analysis involving wavelets and other special systems
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