SciELO - Scientific Electronic Library Online

 
vol.19 issue2Identification of Harmonic Sources in Electrical Power Systems Using State Estimation with Measurement ErrorA Counting Logic for Trees author indexsubject indexsearch form
Home Pagealphabetic serial listing  

Services on Demand

Journal

Article

Indicators

Related links

  • Have no similar articlesSimilars in SciELO

Share


Computación y Sistemas

On-line version ISSN 2007-9737Print version ISSN 1405-5546

Comp. y Sist. vol.19 n.2 Ciudad de México Apr./Jun. 2015

https://doi.org/10.13053/CyS-19-2-1908 

Artículos

 

PID Control Law for Trajectory Tracking Error Using Time-Delay Adaptive Neural Networks for Chaos Synchronization

 

Joel Pérez P. y José P. Pérez

 

Universidad Autónoma de Nuevo León (UANL), Facultad de Ciencias Físico Matemáticas, Monterrey, México. joelperezp@yahoo.com, josepazp@gmail.com

Corresponding author is Joel Pérez P.

 

Article received on 12/11/2013.
Accepted on 01/09/2014.

 

Abstract

This paper presents an application of Time-Delay adaptive neural networks based on a dynamic neural network for trajectory tracking of unknown nonlinear plants. Our approach is based on two main methodologies: the first one employs Time-Delay neural networks and Lyapunov-Krasovskii functions and the second one is Proportional-Integral-Derivative (PID) control for nonlinear systems. The proposed controller structure is composed of a neural identifier and a control law defined by using the PID 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 the tracking of the nonlinear system.

Keywords: Lyapunov-Krasovskii function stability, chaos synchronization, trajectory tracking, time-delay adaptive neural networks, PID control.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Acknowledgements

The authors appreciate the support from CONACYT and the Dynamical Systems Group of the Faculty of Physical and Mathematical Sciences of the Autonomous University of Nuevo León, México.

 

References

1. Baldi, P. & Atiya, A. F. (1994). How delays affect neural dynamics and learning. IEEE Trans. on Neural Networks, Vol. 5, pp. 612-621.         [ Links ]

2. Forti, M. (1994). Necessary and suffiient conditions for absolute stability of neural networks. IEEE Trans. on Circuits and Systems, Vol. 41, pp. 491-494.         [ Links ]

3. Hale, J. K. & V.Lunel, S. M. (1991). Introduction to the Theory of Functional Differential Equations. Springer Verlag, New York, USA.         [ Links ]

4. Ioannou, P. A. & Sun, J. (2003). Robust Adaptive Control. Prentice Hall, Upper Saddle River, New Jersey, USA.         [ Links ]

5. Kelly, R., Guerra, R. H., & Reyes, F. (1999). Lya-punov stable control of robot manipulators: a fuzzy self-tuning procedure. Intelligent Automation and Soft Computing, Vol. 5, pp. 313-326.         [ Links ]

6. Khalil, H. (1996). Nonlinear System Analysis. Prentice Hall, Upper Saddle River, New Jersey, USA, 2 edition.         [ Links ]

7. Liao, X., Chen, G., & Sánchez, E. N. (2002). Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach. Neural Networks, Vol. 15, pp. 855-866.         [ Links ]

8. Liao, X., Chen, G., & Sánchez, E. N. (2002). Lmi-based approach for asymptotically stability analysis of delayed neural networks. IEEE Trans. on Circuits and Systems, Vol. 49, pp. 1033-1039.         [ Links ]

9. Pérez, J., Pérez, J. P., Rdz, F., & Flores, A. (2013). Trajectory tracking for the chaotic pendulum using pi control law. Revista Mexicana de Fisica, Vol. 59, pp. 471-477.         [ Links ]

10. Sánchez, E., Pérez, J., Ricalde, L., & Chen, G. (2001 ). Chaos production and synchronization via adaptive neural control. Proceeding of IEEE Conference on Decision and Control, Orlando, USA.         [ Links ]

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

12. Yazdizadeh, A. & Khorasani, K. (2002). Adaptive time delay neural network structures for nonlinear system identification. Elsevier Science.         [ Links ]

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