System identification using wavelet neural networks

In this paper, a wavelet-based neural network (WNN) is introduced for nonlinear system identification. The structure of the WNN is similar to that of multi-layer perceptron (MLP), except that here the activation function of the hidden nodes is replaced by a wavelet function. It will be proved that any function f ϵ L²(Rⁿ) can be approximated on any bounded domain by the WNN. Employing the MLP-like architecture, the proposed WNN is a powerful tool to handle high dimensional problems. A robust adaptive weight updating law based on Lyapunov stability theory is proposed for dynamical system identification. It is proved that the identification error and weights of the network are bounded even in the presence of modeling error. Simulation results demonstrate the effectiveness of the proposed identification methodology.