Trajectory tracking error using fractional order time-delay recurrent neural networks using Krasovskii-Lur’e functional for Chua’s circuit via inverse optimal control

Authors

  • J. Perez Padrón Universidad Autonoma de Nuevo Leon
  • J.P. Pérez Padrón Universidad Autonoma de Nuevo Leon, Facultad de Ciencias Fisico-Matematicas, Dept. Sistemas Dinamicos San Nicolas de los Garza, Nuevo Leon, Mexico.
  • C.F. Mendez-Barrios Centro de Investigacion y Estudios de Posgrado, Facultad de Ingenieria, Dr. Manuel Nava # 8, Zona Universitaria, 78290, San Luis Potosi, S.L.P., Mexico,
  • E.J. Gonzalez-Galvan Centro de Investigacion y Estudios de Posgrado, Facultad de Ingenieria, Dr. Manuel Nava # 8, Zona Universitaria,78290, San Luis Potosi, S.L.P., Mexico,

DOI:

https://doi.org/10.31349/RevMexFis.66.98

Keywords:

Trajectory Tracking, Fractional Order Time-Delay Recurrent Neural Network, Fractional Order Lyapunov-Krasovskii-Lur’e Analysis

Abstract

This paper presents an application of a Fractional Order Time Delay Neural Networks to chaos synchronization. The two main methodologies, on which the approach is based, are fractional order time-delay recurrent neural networks and the fractional order  inverse optimal control for nonlinear systems. The problem of trajectory tracking is studied, based on the fractional order Lyapunov-Krasovskii and Lur’e theory, that achieves the global asymptotic stability of the tracking error between a delayed recurrent neural network and a reference function is obtained. The method is illustrated for the synchronization, the analytic results we present a trajectory tracking simulation of a fractional order time-delay dynamical network and the Fractional Order Chua’s circuits

Author Biography

J. Perez Padrón, Universidad Autonoma de Nuevo Leon

Joel Perez Padron obtained his B.Sc. degree in Mathematics in 1991, from the Faculty of Physical and Mathematical Sciences, a Master’s degree in Electrical Engineering with specialization in Control in 2001, from the Faculty of Mechanical and Electrical Engineering, and a Ph.D. in Industrial Physics Engineering with specialization in Control in 2008, from the Faculty of Physical and Mathematical Sciences of Nuevo Leon Autonomous University.

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Published

2019-12-28

How to Cite

[1]
J. Perez Padrón, J. Pérez Padrón, C. Mendez-Barrios, and E. Gonzalez-Galvan, “Trajectory tracking error using fractional order time-delay recurrent neural networks using Krasovskii-Lur’e functional for Chua’s circuit via inverse optimal control”, Rev. Mex. Fís., vol. 66, no. 1 Jan-Feb, pp. 98–104, Dec. 2019.

Issue

Vol. 66 No. 1 Jan-Feb (2020): Revista Mexicana de Física

Section

14 Other areas in Physics

License

Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.