Echo State versus Wavelet Neural Networks: Comparison and Application to Nonlinear System Identification

Abstract

This paper examines two popular neural networks that have been successfully utilized in a wide variety of applications: echo state networks (ESN) and wavelet neural networks (WNN). It introduces innovations in the structure of ESN that result in major improvements in their performance. By adding a feedforward component to the networks, and by tuning their weights using recursive least squares, we can drastically reduce the number of hidden layer neurons while reducing their error. We demonstrate the improvement in the performance of ESN and compare their performance to that of WNN by application to the identification of an un-manned vehicle. Different ESN and WNN are utilized to identify the model of the vehicle and examine the effects of adding a feedforward term to ESN and WNN. Simulation results shows that adding a feedforward term to ESN and WNN can reduce the number of hidden nodes drastically while reducing the identification error of ESN. Because the number of internal units in ESN can be very high for nonlinear systems, adding this term makes ESN more suitable for online identification and control applications. Our results show that, even though both networks yield acceptable performance, ESN outperform WNN in terms of accuracy but have a slightly higher computational cost.