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Modelling and Simulation in Engineering
Volume 2008, Article ID 343940, 8 pages
Research Article

Stability Analysis of Neural Networks-Based System Identification

Research Unit on Intelligent Control, Design and Optimization of Complex Systems (ICOS), National Engineering School of Sfax (ENIS), University of Sfax, BP W, 3038 Sfax, Tunisia

Received 28 January 2008; Revised 23 April 2008; Accepted 12 June 2008

Academic Editor: Petr Musilek

Copyright © 2008 Talel Korkobi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper treats some problems related to nonlinear systems identification. A stability analysis neural network model for identifying nonlinear dynamic systems is presented. A constrained adaptive stable backpropagation updating law is presented and used in the proposed identification approach. The proposed backpropagation training algorithm is modified to obtain an adaptive learning rate guarantying convergence stability. The proposed learning rule is the backpropagation algorithm under the condition that the learning rate belongs to a specified range defining the stability domain. Satisfying such condition, unstable phenomena during the learning process are avoided. A Lyapunov analysis leads to the computation of the expression of a convenient adaptive learning rate verifying the convergence stability criteria. Finally, the elaborated training algorithm is applied in several simulations. The results confirm the effectiveness of the CSBP algorithm.