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.

[1]  Yuichi Nakamura,et al.  Approximation of dynamical systems by continuous time recurrent neural networks , 1993, Neural Networks.

[2]  M. Gupta,et al.  Approximation of discrete-time state-space trajectories using dynamic recurrent neural networks , 1995, IEEE Trans. Autom. Control..

[3]  Yucai Zhu,et al.  Estimation of an N-L-N Hammerstein-Wiener model , 2002, Autom..

[4]  P. S. Sastry,et al.  Memory neuron networks for identification and control of dynamical systems , 1994, IEEE Trans. Neural Networks.

[5]  Kurt Hornik,et al.  Multilayer feedforward networks are universal approximators , 1989, Neural Networks.

[6]  Ken-ichi Funahashi,et al.  On the approximate realization of continuous mappings by neural networks , 1989, Neural Networks.

[7]  Kumpati S. Narendra,et al.  Identification and control of dynamical systems using neural networks , 1990, IEEE Trans. Neural Networks.

[8]  D. Westwick,et al.  Separable Least Squares Identification of Nonlinear Hammerstein Models: Application to Stretch Reflex Dynamics , 2001, Annals of Biomedical Engineering.

[9]  P. Werbos,et al.  Beyond Regression : "New Tools for Prediction and Analysis in the Behavioral Sciences , 1974 .

[10]  Ching-Hung Lee,et al.  Identification and control of dynamic systems using recurrent fuzzy neural networks , 2000, IEEE Trans. Fuzzy Syst..

[11]  Ah Chung Tsoi,et al.  Discrete time recurrent neural network architectures: A unifying review , 1997, Neurocomputing.

[12]  Petre Stoica,et al.  Estimation of the parameters of a bilinear model with applications to submarine detection and system identification , 2007, Digit. Signal Process..

[13]  Nikita Barabanov,et al.  Stability analysis of discrete-time recurrent neural networks , 2002, IEEE Trans. Neural Networks.

[14]  W. R. Cluett,et al.  Linearizing feedforward-feedback control of pH processes based on the Wiener model , 2005 .

[15]  Chia-Feng Juang,et al.  A recurrent self-organizing neural fuzzy inference network , 1997, Proceedings of 6th International Fuzzy Systems Conference.