On recovering the parametric model of the Chua system via a gradient algorithm
C. Aguilar–Ibáñez ª *, E. Hernández–Rubio b and M.S. Suárez–Castañón b
ª Centro de Investigación en Computación, Instituto Politécnico Nacional, Av. Juan de Dios Batiz s/n Esq. Miguel Othón de M., Unidad Profesional Adolfo López Mateos, Col. Nueva Industrial Vallejo, Apartado postal 75476, México, D.F. 07738, México, FAX: +(52) 55 5586–2936.
b Escuela Superior de Cómputo, Instituto Politécnico Nacional, Av. Juan de Dios Batiz s/n Esq. Miguel Othón de M., Unidad Profesional Adolfo López Mateos, Col. Nueva Industrial Vallejo, México, D.F. 07738, México.
* Corresponding author ]]> e–mail: caguilar@cic.ipn.mx
Recibido el 22 de enero de 2007
Aceptado el 25 de septiembre de 2007
Abstract
The Chua circuit parameter estimation problem is addressed in this paper. This circuit is algebraically observable and identifiable with respect to its two measurable voltages. This fact allows us to straightforwardly propose two linear estimators for recovering the unknown parameters, where the estimator gains are continuously adjusted by means of a gradient algorithm, until the estimated parameters converge to the actual values. The convergence of this method is demonstrated by using the Lyapunov method.
Keywords: Chua's circuit; chaos; reconstruction and observers; Lyapunov's approach.
Resumen
]]> En este trabajo se trata el problema de estimación de los parámetros del circuito de Chua. Este circuito es algebraicamente observable e identificable con respecto a sus dos voltajes disponibles. Este hecho nos permite proponer directamente dos estimadores lineales para la recuperación de los parámetros desconocidos, donde las ganancias de los estimadores son ajustadas continuamente mediante un algoritmo de gradiente, hasta que los parámetros estimados convergen con los valores reales. La convergencia de este método es demostrada empleando el método de Lyapunov.Descriptores: Circuito de Chua; caos; reconstrucción y observadores; enfoque de Lyapunov.
PACS: 07.05.Dz , 45.80.+ r, 45.20.J0j
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Acknowledgments
M.S. Suarez–Castañón wishes to thank the Instituto Politécnico Nacional and the Fideicomiso para el Desarrollo de Recursos Humanos del Banco de México for making possible his postdoctoral stay at the University of Houston. Part of this work was prepared during this postdoctoral visit.
This research was supported under research grants 20071088 and 20071109.
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