A Hammerstein-Wiener recurrent neural network with universal approximation capability

This paper presents a Hammerstein-Wiener recurrent neural network with a parameter learning algorithm for identifying unknown dynamic nonlinear systems. The proposed recurrent neural network resembles the conventional Hammerstein-Wiener model that consists of a dynamic linear subsystem embedded between two static nonlinear subsystems. There are two novelties in our network: 1) the three subsystems are integrated into a single recurrent neural network whose output is the nonlinear transformation of a linear state-space equation; 2) the well-developed linear theory can be applied directly to the linear subsystem of the trained network to analyze its characteristics. In addition, we utilized the Stone-Weierstrass theorem to demonstrate the proposed network possesses the universal approximation capability. Finally, a computer simulation and comparisons with some existing models have been conducted to demonstrate the effectiveness of the proposed network and its parameter learning algorithm.