SciELO - Scientific Electronic Library Online

vol.18 issue2Internal State Identification for Black Box SystemsSliding Mode Control Applied to a Mini-Aircraft Pitch Position Model 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.18 n.2 México Apr./Jun. 2014 

Artículos regulares


Trajectory Tracking for Chaos Synchronization via PI Control Law between Roosler-Chen


Seguimiento de trayectorias para sincronización de caos vía ley de control PI entre Roosler-Chen


Joel Perez Padron, Jose Paz Perez Padron, Francisco Rodriguez Ramirez, and Angel Flores Hernandez


Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Nuevo León (UANL), Monterrey, Mexico.,,



This paper presents an application of adaptive neural networks based on a dynamic neural network to trajectory tracking of unknown nonlinear plants. The main methodologies on which the approach is based are recurrent neural networks and Lyapunov function methodology and Proportional-Integral (PI) control for nonlinear systems. The proposed controller structure is composed of a neural identifier and a control law defined by using the PI approach. The new control scheme is applied via simulations to Chaos Synchronization. Experimental results have shown the usefulness of the proposed approach for Chaos Production. To verify the analytical results, an example of a dynamical network is simulated and a theorem is proposed to ensure tracking of the nonlinear system.

Keywords: Dynamic neural networks, chaos production, chaos synchronization, trajectory tracking, Lyapunov function stability, PI control.



Este artículo presenta la aplicación de redes neuronales adaptables, basada sobre una red neuronal dinámica, para seguimiento de trayectorias de plantas no lineales desconocidas. La principal metodología, sobre el cual la aproximación es basada, son redes neuronales recurrentes, metodología de las funciones de Lyapunov y control Proporcional-Integral (PI) para sistemas no lineales. La estructura del controlador propuesto es compuesta de un identificador neuronal y una ley de control definida usando la aproximación PI. El nuevo esquema de control es aplicado vía simulación para sincronización de caos. Resultados experimentales han mostrado la utilidad del enfoque propuesto para la producción de caos. Para verificar el resultado analítico, un ejemplo de una red dinámica es simulado y un teorema es propuesto para asegurar el seguimiento del sistema no lineal.

Palabras clave: Red neuronal dinámica, producción de caos, sincronización de caos, seguimiento de trayectorias, estabilidad de funciones de Lyapunov, control PI.





1. Gupta, M.M. & Rao, D.H. (Eds.) (1994). Neuro-Control Systems, Theory and Applications. IEEE Press, Piscataway, N.J., USA.         [ Links ]

2. Hunt, G.I. & Warwick, K. (Eds.) (1995). Neural Networks Engineering in Dynamic Control Systems. Springer Verlang, New York, USA.         [ Links ]

3. Poznyak, A.S., Yu, W., Sanchez, E.N., & Perez, J.P. (1999). Nonlinear adaptive trajectory tracking using dynamic neural networks. IEEE Trans. on Neural Networks, 10(6), 1402-1411.         [ Links ]

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

5. Suykens K., Vandewalle, L., & De Moor, R. (1996). Artificial Neural Networks for Modelling and Control of Nonlinear Systems. Kluwer academic Publishers, Boston, USA.         [ Links ]

6. Rovitahkis, G.A. & Christodoulou, M.A. (2000). Adaptive Control with Recurrent High-Order Neural Networks. Springer Verlang, New York, USA.         [ Links ]

7. Poznyak, A.S., Sanchez, E.N., & Yu, W. (2000). Differential Neural Networks for Robust Nonlinear Control. World Scientific, USA.         [ Links ]

8. Isidori, A. (1995). Nonlinear Control Systems. 3rd Ed., Springer Verlang, New York, USA,1995.         [ Links ]

9. Hill, D.J. & Moylan, P. (1996). The Stability of nonlinear dissipative systems. IEEETrans. on Auto. Contr., vol. 21, 708-711.         [ Links ]

10. Basar, T. & Bernhard, P. (1995). H-Infinity Optimal Control and Related Minimax Design Problems. Birkhauser, Boston, USA.         [ Links ]

11. Krstic, M. & Deng, H. (1998) Stabilization of Nonlinear Uncertain Systems. Springer Verlang, New York, USA.         [ Links ]

12. Sanchez, E.N., Perez, J.P. & Chen, G. (2001). Using dynamic neural control to generate chaos: An inverse optimal control approach. Int. J. Bifurcation and Chaos.         [ Links ]

13. Sanchez, E.N., Perez, J.P., Ricalde, L., & Chen, G. (2001). Trajectory tracking via adaptive neural control. In Proceeding of IEEE Int. Symposium on Intelligent Control, Mexico City, pp. 286-289.         [ Links ]

14. Sanchez, E.N., Perez, J.P., Ricalde, L., & Chen, G. (2001). Chaos production and synchronization via adaptive neural control. In Proceeding of IEEE Conference on Decision and Control, Orlando, Fl, USA.         [ Links ]

15. Ioannou, P.A. & Sun, J. Robust Adaptive Control. PTR Prentice-Hall, Upper Saddle River, NJ 07458.         [ Links ]

16. Astrom, K.J. & Wittenemark, B. (1989). Adaptive Control. Addison-Wesley Publishing Company.         [ Links ]

17. Perez P., J., Perez, J.P., Soto, R., Flores, A., Rodriguez, F., & Meza, J.L. (2012). Trajectory Tracking Using PID Control Law for Two-Link Robot Manipulator via Adaptive Neural Networks. In The 2012 Iberoamerican Conference on Electronics Engineering and Computer Science.         [ Links ]

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