SciELO - Scientific Electronic Library Online

vol.14 issue1Is the Coordinated Clusters Representation an analog of the Local Binary Pattern?Fast Most Similar Neighbor (MSN) classifiers for Mixed Data author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand




Related links

  • Have no similar articlesSimilars in SciELO


Computación y Sistemas

Print version ISSN 1405-5546

Comp. y Sist. vol.14 n.1 México Jul./Sep. 2010




Real–time Discrete Nonlinear Identification via Recurrent High Order Neural Networks


Identificación No Lineal en Tiempo Real usando Redes Neuronales Recurrentes de Alto Orden


Alma Y. Alanis1, Edgar N. Sanchez2 and Alexander G. Loukianov2


1CUCEI, Universidad de Guadalajara, Apartado Postal 51–71, Col. Las Aguilas, C.P. 45080, Zapopan, Jalisco, Mexico.

2CINVESTAV, Unidad Guadalajara, Apartado Postal 31–438, Plaza La Luna, Guadalajara, Jalisco, C.P. 45091, Mexico. E–mail:


Article received on November 25, 2008
Accepted on March 23, 2009



This paper deals with the discrete–time nonlinear system identification via Recurrent High Order Neural Networks, trained with an extended Kalman filter (EKF) based algorithm. The paper also includes the respective stability analysis on the basis of the Lyapunov approach for the whole scheme. Applicability of the scheme is illustrated via real–time implementation for a three phase induction motor.

Keywords: Neural identification, Extended Kalman filtering learning, Discrete–time nonlinear systems, Three phase induction motor.



Este artículo trata el problema de identificación de sistemas no lineales discretos usando redes neuronales recurrentes de alto orden entrenadas con un algoritmo basado en el filtro de Kalman extendido (EKF). El artículo también incluye el análisis de estabilidad para el sistema completo, en las bases de la técnica de Lyapunov. La aplicabilidad del esquema se ilustra a través de la implementación en tiempo real para un motor de inducción trifásico.

Palabras clave: Identificación neuronal, Aprendizaje usando filtro de Kalman Extendido, Sistemas no lineales discretos, Motor de inducción trifásico.





The authors thank the support of PROMEP/103.5/09/3912 and CONACYT Mexico, through Project 103191Y. They also thank the very useful comments of the anonymous reviewers, which help to improve the paper.



1. Chui, C. K., & Chen, G. (1998). Kalman Filtering with Real–Time Applications. New York: Springer–Verlag.         [ Links ]

2. Cotter, N. E. (1990). The Stone–Weiertrass theorem and its application to neural networks. IEEE Transactions Neural Networks. 1(4), 290–295.         [ Links ]

3. Ge, S. S., Zhang, J. & Lee, T. H. (2004). Adaptive neural network control for a class of MIMO nonlinear systems with disturbances in discrete–time. IEEE Transactions on Systems, Man and Cybernetics, Part B, 34(4), 674–692.         [ Links ]

4. Ghosh, J. & Shin Y. (1992). Efficient High–Order Neural Networks for Classification and Function Approximation. International. Journal of Neural Systems, 3(4), 323–350.         [ Links ]

5. Grover, R., & Hwang, P. Y. C. (1992). Introduction to Random Signals and Applied Kalman Filtering. New York: John Wiley and Sons.         [ Links ]

6. Haykin, S. (1999). Neural Networks. A comprehensive foundation. New Jersey: Prentice Hall.         [ Links ]

7. Kim, Y. H., & Lewis, F. L. (1998). High–Level Feedback Control with Neural Networks. Singapore: World Scientific.         [ Links ]

8. Loukianov, A. G., Rivera, J. & Cañedo J. M. (2002). Discrete–time sliding mode control of an induction motor. 2002 IFAC 15th Triennial World Congress, Barcelone, Spain, 1074–1079.         [ Links ]

9. Narendra, K. S., & Parthasarathy, K. (1990). Identification and control of dynamical systems using neural networks. IEEE Transactions on Neural Networks, 1(1), 4–27.         [ Links ]

10. Rovithakis, G. A., & Christodoulou, M. A. (2000). Adaptive Control with Recurrent High –Order Neural Networks. New York: Springer Verlag.         [ Links ]

11. Sanchez, E. N., Alanis, A. Y. & Chen, G. (2004). Recurrent neural networks trained with Kalman filtering for discrete chaos reconstruction. Asian–Pacific Workshop on Chaos Control and Synchronization '04, Melbourne, Australia, 55–59.         [ Links ]

12. Sanchez, E. N., & Ricalde, L. J. (2003). Trajectory tracking via adaptive recurrent neural control with input saturation. International Joint Conference on Neural Networks'03, Portland, USA, vol.1, 359–364.         [ Links ]

13. Singhal, S., & Wu, L. (1989). Training multilayer perceptrons with the extended Kalman algorithm. In D. S. Touretzky (Ed.), Advances in Neural Information Processing Systems (133–140). San Mateo, CA: Morgan Kaufmann.         [ Links ]

14. Song, Y., & Grizzle, J. W. (1995). The extended Kalman Filter as Local Asymptotic Observer for Discrete–Time Nonlinear Systems. Journal of Mathematical systems, Estimation and Control, 5(1), 59–78.         [ Links ]

15. Yu, W., & Li, X. (2003). Discrete–time neuro identification without robust modification. IEE Proceedings Control Theory & Applications, 150(3), 311–316.         [ Links ]

16. Yu, W. (2004). Nonlinear system identification using discrete–time recurrent neural networks with stable learning algorithms. Information Sciences —Informatics and Computer Science: An International Journal, 158 (1), 131–147.         [ Links ]

Creative Commons License All the contents of this journal, except where otherwise noted, is licensed under a Creative Commons Attribution License