Model-based recurrent neural network for modeling nonlinear dynamic systems

A model-based recurrent neural network (MBRNN) is introduced for modeling dynamic systems. This network has a fixed structure that is defined according to the linearized state-space model of the plant. Therefore, the MBRNN has the ability to incorporate the analytical knowledge of the plant in its formulation. With its original topology intact, the MBRNN can then be trained to represent the plant nonlinearities through modifying its nodes' activation functions, which consist of contours of Gaussian radial basis functions (RBFs). Training in MBRNN involves adjusting the weights of the RBF's so as to modify the contours representing the activation functions. The performance of the MBRNN is demonstrated via several examples. The results indicate that it requires much shorter training than needed by ordinary recurrent networks. This efficiency in training is attributed to the MBRNN's fixed topology which is independent of training.

[1]  Roderick Murray-Smith,et al.  Extending the functional equivalence of radial basis function networks and fuzzy inference systems , 1996, IEEE Trans. Neural Networks.

[2]  U. R. Prasad,et al.  Back propagation through adjoints for the identification of nonlinear dynamic systems using recurrent neural models , 1994, IEEE Trans. Neural Networks.

[3]  C. Lee Giles,et al.  Rule Revision With Recurrent Neural Networks , 1996, IEEE Trans. Knowl. Data Eng..

[4]  James S. Albus,et al.  New Approach to Manipulator Control: The Cerebellar Model Articulation Controller (CMAC)1 , 1975 .

[5]  Pierre Roussel-Ragot,et al.  Training recurrent neural networks: why and how? An illustration in dynamical process modeling , 1994, IEEE Trans. Neural Networks.

[6]  Martin T. Hagan,et al.  Neural network design , 1995 .

[7]  R. R. Hocking.  The analysis and selection of variables in linear regression , 1976 .

[8]  Dragan Obradovic,et al.  On-line training of recurrent neural networks with continuous topology adaptation , 1996, IEEE Trans. Neural Networks.

[9]  Paul J. Werbos,et al.  Backpropagation Through Time: What It Does and How to Do It , 1990, Proc. IEEE.

[10]  W. Thomas Miller,et al.  Real-time application of neural networks for sensor-based control of robots with vision , 1989, IEEE Trans. Syst. Man Cybern..

[11]  Kwang Y. Lee,et al.  Diagonal recurrent neural networks for dynamic systems control , 1995, IEEE Trans. Neural Networks.

[12]  Thierry Denoeux,et al.  Initializing back propagation networks with prototypes , 1993, Neural Networks.

[13]  R. R. Hocking.  Developments in Linear Regression Methodology: 1959–l982 , 1983 .

[14]  Frank L. Lewis,et al.  Control of Robot Manipulators , 1993 .

[15]  Jay A. Farrell,et al.  A Computationally Efficient Algorithm for Training Recurrent Connectionist Networks , 1992, 1992 American Control Conference.

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

[17]  Chuen-Tsai Sun,et al.  Functional equivalence between radial basis function networks and fuzzy inference systems , 1993, IEEE Trans. Neural Networks.

[18]  Amir F. Atiya,et al.  Application of the recurrent multilayer perceptron in modeling complex process dynamics , 1994, IEEE Trans. Neural Networks.

[19]  Jude W. Shavlik,et al.  Knowledge-Based Artificial Neural Networks , 1994, Artif. Intell..

[20]  Kumpati S. Narendra,et al.  Gradient methods for the optimization of dynamical systems containing neural networks , 1991, IEEE Trans. Neural Networks.

[21]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .