ABSTRACT The objective of this paper is to develop a variable learning rate for neural modeling of multivariable nonlinear stochastic system. The corresponding parameter is obtained by gradient descent method optimization. The effectiveness of the suggested algorithm applied to the identification of behavior of two nonlinear stochastic systems is demonstrated by simulation experiments.
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nullA. Errachdi, I. Saad and M. Benrejeb, "Neural Modeling of Multivariable Nonlinear Stochastic System. Variable Learning Rate Case," Intelligent Control and Automation, Vol. 2 No. 3, 2011, pp. 167-175. doi: 10.4236/ica.2011.23020.
 K. Kara, “Application des Réseaux de Neurones à l’identification des Systèmes Non Linéaire,” Thesis, Con- stantine University, 1995.
 S. R. Chu, R. Shoureshi and N. Tenorio “Neural Networks for System Identification,” IEEE Control System Magazine, Vol. 10, No. 3, 1990, pp. 31-35.
 S. Chen and S. A. Billings, “Neural Networks for Non-linear System Modeling and Identification,” Inernational Journal of Control, Vol. 56, No. 2, 1992, pp. 319-346.
 N. N. Karabutov, “Structures, Fields and Methods of Iden- tification of Nonlinear Static Systems in the Conditions of Uncertainty,” Intelligent Control and Automation (ICA), Vol. 1, No. 1, 2010, pp. 1-59.
 D. C. Psichogios and L. H. Ungar, “Direct and Indirect Model-Based Control Using Artificial Neural Networks,” Industrial and Engineering Chemistry Research, Vol. 30, No. 12, 1991, pp. 25-64.
 A. Errachdi, I. Saad and M. Benrejeb, “On-Line Identifycation Method Based on Dynamic Neural Network,” International Review of Automatic Control, Vol. 3, No. 5, 2010, pp. 474-479.
 A. M. Subramaniam, A. Manju and M. J. Nigam, “A Novel Stochastic Algorithm Using Pythagorean Means for Minimization,” Intelligent Control and Automation, Vol. 1, No. 1, 2010, pp. 82-89.
 D. Sha and B. Bajic, “On-Line Adaptive Learning Rate BP Algorithm for MLP and Application to an Identification Problem,” Journal of Applied Computer Science, Vol. 7, No. 2, 1999, pp. 67-82.
 A. Errachdi, I. Saad and M. Benrejeb, “Neural Modelling of Multivariable Nonlinear System. Variable Learning Rate Case,” 18th Mediterranean Conference on Control and Automation, Marrakech, 2010, pp. 557-562.
 P. Borne, M. Benrejeb and J. Haggege, “Les Réseaux de Neurones. Présentation et Application,” Editions Technip, Paris, 2007.
 S. Chabaa, A. Zeroual and J. Antari, “Identification and Prediction of Internet Traffic Using Artificial Neural Net-Works,” Journal of Intelligent Learning Systems & Applications, Vol. 2, No. 1, 2010, pp. 147-155.
 M. Korenberg, S. A. Billings, Y. P. Liu and P. J. Mcllroy, “Orthogonal Parameter Estimation Algorithm for Non-linear Stochastic Systems,” International Journal of Control, Vol. 48, No. 1, 1988, pp. 346-354.
 A. Errachdi, I. Saad and M. Benrejeb, “Internal Model Control for Nonlinear Time-Varying System Using Neural Networks,” 11th International Conference on Sciences and Techniques of Automatic Control & Computer Engineering, Anaheim, 2010, pp. 1-13.
 D. Sha, “A New Neural Networks Based Adaptive Model Predictive Control for Unknown Multiple Variable No-Linear systems,” International Journal of Advanced Mechatronic Systems, Vol. 1, No. 2, 2008, pp. 146-155.
 R. P. Brent, “Fast Training Algorithms for Multilayer Neural Nets,” IEEE Transactions on Neural Networks, Vol. 2, No. 3, 1991, pp. 346-354.
 R. A. Jacobs, “Increase Rates of Convergence through Learning Rate Adaptation,” IEEE Transactions on Neural Networks, Vol. 1, No. 4, 1988, pp. 295-307.
 D. C. Park, M. A. El-Sharkawi and R. J. Marks, “An Adaptively Trained Neural Network,” IEEE Transactions on Neural Networks, Vol. 2, No. 3, 1991, pp. 334-345.
 P. Saratchandran, “Dynamic Programming Approach to Optimal Weight Selection in Multilayer Neural Networks,” IEEE Transactions on Neural Networks, Vol. 2, No. 4, 1991, pp. 465-467. doi:10.1109/72.88167