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Contraction theory based adaptive synchronization of chaotic systems

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  • Sharma, B.B.
  • Kar, I.N.

Abstract

Contraction theory based stability analysis exploits the incremental behavior of trajectories of a system with respect to each other. Application of contraction theory provides an alternative way for stability analysis of nonlinear systems. This paper considers the design of a control law for synchronization of certain class of chaotic systems based on backstepping technique. The controller is selected so as to make the error dynamics between the two systems contracting. Synchronization problem with and without uncertainty in system parameters is discussed and necessary stability proofs are worked out using contraction theory. Suitable adaptation laws for unknown parameters are proposed based on the contraction principle. The numerical simulations verify the synchronization of the chaotic systems. Also parameter estimates converge to their true values with the proposed adaptation laws.

Suggested Citation

  • Sharma, B.B. & Kar, I.N., 2009. "Contraction theory based adaptive synchronization of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2437-2447.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2437-2447
    DOI: 10.1016/j.chaos.2008.09.031
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    References listed on IDEAS

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    1. Yassen, M.T., 2005. "Controlling chaos and synchronization for new chaotic system using linear feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 913-920.
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    Cited by:

    1. Handa, Himesh & Sharma, B.B., 2016. "Novel adaptive feedback synchronization scheme for a class of chaotic systems with and without parametric uncertainty," Chaos, Solitons & Fractals, Elsevier, vol. 86(C), pages 50-63.

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