Performance enhancement of a Fourier/Hopfield neural network for nonlinear periodic systems representation

Nonlinear periodic systems arise in many important practical applications including systems with multirate sampling. System identification in such applications is possible by representing the system in terms of basis functions of our choice. Fourier basis functions are the natural choice when identifying periodic systems. In this paper, we examine the performance of a three-layer Fourier/Hopfield network designed for system identification. We study the effect of network parameters such as absolute and relative error tolerances, discretization step size, and the saturation level of the activation function on the performance of the network and propose a new approach for their selection. We demonstrate our approach through a numerical example.