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Adaptive approximation method for joint parameter estimation and identical synchronization of chaotic systems

Inés P. Mariño1 and Joaquín Míguez2

  • 1Nonlinear Dynamics and Chaos Group, Departamento de Matemáticas y Física Aplicadas y Ciencias de la Naturaleza, Universidad Rey Juan Carlos, C/ Tulipán s/n, 28933 Móstoles, Madrid, Spain
  • 2Departamento de Teoría de la Señal y Comunicaciones, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain

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Phys. Rev. E 72, 057202 – Published 17 November, 2005

DOI: https://doi.org/10.1103/PhysRevE.72.057202

Abstract

We introduce a numerical approximation method for estimating an unknown parameter of a (primary) chaotic system which is partially observed through a scalar time series. Specifically, we show that the recursive minimization of a suitably designed cost function that involves the dynamic state of a fully observed (secondary) system and the observed time series can lead to the identical synchronization of the two systems and the accurate estimation of the unknown parameter. The salient feature of the proposed technique is that the only external input to the secondary system is the unknown parameter which needs to be adjusted. We present numerical examples for the Lorenz system which show how our algorithm can be considerably faster than some previously proposed methods.

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  19. We note that if xi is the actual observable, it is straightforward to obtain ẋi with either analog or digital circuitry.

  20. We have found that for lesser values of the variance, and Ts=40, the algorithm gets easily stuck in local minima of the cost function ∫0Ts∣x1(τ)−y1(τ)∣2dτ.

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Phys. Rev. E 72, 057202– Published 17 November, 2005
  • Received 27 May 2005

© 2005 American Physical Society

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