NONLINEAR SYSTEM IDENTIFICATION USING DISCRETE-TIME NEURAL NETWORKS WITH STABLE LEARNING ALGORITHM

Talel Korkobi, Mohamed Djemel, Mohamed Chtourou

Abstract

This paper presents a stable neural sytem identification for nonlinear systems. An input output discrete time representation is considered. No a priori knowledge about the nonlinearities of the system is assumed. 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 phenomenon during the learning process is avoided. A Lyapunov analysis is made in order to extract the new updating formulation which contain a set of inequality constraints. In the constrained learning rate algorithm, the learning rate is updated at each iteration by an equation derived using the stability conditions. As a case study, identification of two discrete time systems is considered to demonstrate the effectiveness of the proposed algorithm. Simulation results concerning the considered systems are presented.

References

  1. B. Egardt, 1979. Stability of adaptive controllers. in: Lecture Notes in Control and Information Sciences 20, Springer-Verlag, Berlin.
  2. Z. Feng, A.N. Michel, 1999. Robustness analysis of a class of discrete-time systems with applications to neural networks, in: Proceedings of American Control Conference, San Deigo, pp. 3479-3483.
  3. S.S. Ge, C.C. Hang, T.H. Lee, T. Zhang, 2001: Stable Adaptive Neural Network Control, Kluwer Academic, Boston.
  4. P. A. Ioannou, J. Sun, 2004. Robust Adaptive Control, Information Sciences 158, 31-147, Prentice-Hall, Upper Saddle River.
  5. L. Jin, M.M. Gupta, 1999. Stable dynamic backpropagation learning in recurrent neural networks, IEEE Trans. Neural Networks 10 (6) , 1321-1334.
  6. Z. P. Jiang, Y. Wang, 2001. Input-to-state stability for discrete-time nonlinear systems, Automatica 37 (2) , 857-869.
  7. E. B. Kosmatopoulos, M.M. Polycarpou, M.A. Christodoulou, P.A. Ioannou, 1995. High-order neural network structures for identification of dynamical systems, IEEE Trans. Neural Networks 6 (2), 431-442.
  8. M. M. Polycarpou, P.A. Ioannou 1992. Learning and convergence analysis of neural-type structured networks, IEEE Trans. Neural Networks 3 (1) ,39- 50.
  9. J. A. K. Suykens, J. Vandewalle, B. De Moor, 1997. NLq theory: checking and imposing stability of recurrent neural networks for nonlinear modelling, IEEE Trans. Signal Process (special issue on neural networks for signal processing) 45 (11) , 2682-2691.
  10. W. Yu, X. Li, 2001. Some stability properties of dynamic neural networks, IEEE Trans. Circuits Syst., Part I 48 (1) , 256-259.
  11. W. Yu, A.S. Poznyak, X. Li, 2001. Multilayer dynamic neural networks for nonlinear system on-line identification, Int. J. Control 74 (18), 1858-1864.
  12. E. Barn, 1992. Optimisation for training neural nets, IEEE Trans. Neural Networks 3 (2) , 232-240.
  13. Ching-Hang Lee and al, 2002. Control of Nonlinear Dynamic Systems Via adaptive PID Control Scheme with Daturation Bound, International Journal of Fuzzy Systems, Vol. 4 No. 4 ,922-927.
  14. K. S. Narendra and K. Parthasarathy, 1990. Identification and control of dynamical systems using neural networks, IEEE Transaction Neural Networks, vol.1, pp.4-27, Mar.
  15. J. D. Boskovic and K.S.Narendra 1995. Comparison of linear nonlinear and neural-network based adaptive controllers for a class of fed-batch fermentation process, Automatica, vol. 31, no. 6, pp. 537-547.
Download


Paper Citation


in Harvard Style

Korkobi T., Djemel M. and Chtourou M. (2008). NONLINEAR SYSTEM IDENTIFICATION USING DISCRETE-TIME NEURAL NETWORKS WITH STABLE LEARNING ALGORITHM . In Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO, ISBN 978-989-8111-30-2, pages 351-356. DOI: 10.5220/0001504403510356


in Bibtex Style

@conference{icinco08,
author={Talel Korkobi and Mohamed Djemel and Mohamed Chtourou},
title={NONLINEAR SYSTEM IDENTIFICATION USING DISCRETE-TIME NEURAL NETWORKS WITH STABLE LEARNING ALGORITHM},
booktitle={Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,},
year={2008},
pages={351-356},
publisher={SciTePress},
organization={INSTICC},
doi={10.5220/0001504403510356},
isbn={978-989-8111-30-2},
}


in EndNote Style

TY - CONF
JO - Proceedings of the Fifth International Conference on Informatics in Control, Automation and Robotics - Volume 1: ICINCO,
TI - NONLINEAR SYSTEM IDENTIFICATION USING DISCRETE-TIME NEURAL NETWORKS WITH STABLE LEARNING ALGORITHM
SN - 978-989-8111-30-2
AU - Korkobi T.
AU - Djemel M.
AU - Chtourou M.
PY - 2008
SP - 351
EP - 356
DO - 10.5220/0001504403510356