Nonlinear and Time Varying System Identification Using a Novel Adaptive Fully Connected Recurrent Wavelet Network

This paper presents a novel Adaptive Fully Connected Recurrent Wavelet Network (AFCRWN) for online identification of nonlinear dynamic and time varying systems. The AFCRWN inherits the architecture of fully connected recurrent neural network proposed by Williams & Zipser. Since the AFCRWN incorporates translated and dilated versions of scaling function and wavelet instead of global functions as activation functions of hidden neurons, this would lead to a significant improvement of network performance. An adaptive gradient based algorithm is used to adjust the shapes and weights of scaling functions and wavelets. Simulation results for modeling of different dynamic nonlinear and dynamic nonlinear and time varying systems are presented. Comparisons with a network of neurons with wavelets and a network of neurons with sigmoid functions are provided. Computer simulation results have successfully validated the superior performance of AFCRWN.