On Learning Wavelet Control for Affine Nonlinear Systems

Function Approximation has been proven to be an effective approach when dealing with nonlinear dynamics. Among numerous function approximation methods, wavelet network shows unique advantage in terms of its orthonormality and multi-layer resolution properties, which enable the on-line tuning or closed-loop tuning for the wavelet network structure. Using such a constructive wavelet network, an adaptive iterative learning control approach was proposed for finite interval tracking problems [1]. In this work, the adaptive learning control approach with wavelet approximation (denoted by learning wavelet control or LWC) is applied two general classes of plants affine-in-input. One class is with nonlinear unknown input coefficient, and the other class is in cascade form. With the help of Lyapunov method, the learning convergence properties of the adaptive learning control system can be analyzed while the wavelet network undergoes on-line structure adaptation.