A Hammerstein-Wiener Recurrent Neural Network with Frequency-Domain Eigensystem Realization Algorithm for Unknown System Identification

Abstract

This paper presents a Hammerstein-Wiener recurrent neural network (HWRNN) with a systematic identification algorithm for identifying unknown dynamic nonlinear systems. The proposed HWRNN resembles the conventional Hammerstein-Wiener model that consists of a linear dynamic subsystem that is sandwiched in between two nonlinear static subsystems. The static nonlinear parts are constituted by feedforward neural networks with nonlinear functions and the dynamic linear part is approximated by a recurrent network with linear activation functions. The novelties of our network include: 1) the structure of the proposed recurrent neural network can be mapped into a state-space equation; and 2) the state-space equation can be used to analyze the characteristics of the identified network. To efficiently identify an unknown system from its input-output measurements, we have developed a systematic identification algorithm that consists of parameter initialization and online learning procedures. Computer simulations and comparisons with some existing models have been conducted to demonstrate the effectiveness of the proposed network and its identification algorithm.