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Adaptive synchronization of two different chaotic systems with time varying unknown parameters

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  • Salarieh, Hassan
  • Shahrokhi, Mohammad

Abstract

In this paper a nonlinear control method based on Lyapunov stability theorem is proposed to design an adaptive controller for synchronizing two different chaotic systems. It is assumed that the unknown parameters of the drive and the response chaotic systems are time varying. It is shown that the proposed scheme can identify the system parameters if the system parameters are time invariant and the richness conditions is satisfied. To demonstrate the effectiveness of the proposed technique it has been applied to Lorenz–Chen dynamic systems, as drive–response systems. Simulation results indicate that the proposed adaptive controller has a high performance in synchronizing two chaotic systems.

Suggested Citation

  • Salarieh, Hassan & Shahrokhi, Mohammad, 2008. "Adaptive synchronization of two different chaotic systems with time varying unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 125-136.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:1:p:125-136
    DOI: 10.1016/j.chaos.2006.08.038
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    References listed on IDEAS

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    1. Park, Ju H., 2006. "Chaos synchronization between two different chaotic dynamical systems," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 549-554.
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    5. Fotsin, Hilaire & Bowong, Samuel, 2006. "Adaptive control and synchronization of chaotic systems consisting of Van der Pol oscillators coupled to linear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 822-835.
    6. Park, Ju H., 2005. "Adaptive synchronization of hyperchaotic Chen system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 959-964.
    7. Park, Ju H., 2006. "Synchronization of Genesio chaotic system via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1369-1375.
    8. Fotsin, Hilaire & Bowong, Samuel & Daafouz, Jamal, 2005. "Adaptive synchronization of two chaotic systems consisting of modified Van der Pol–Duffing and Chua oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 26(1), pages 215-229.
    9. Park, Ju H., 2005. "Adaptive synchronization of Rossler system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 333-338.
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    Cited by:

    1. Zhang, Xingpeng & Li, Dong & Zhang, Xiaohong, 2017. "Adaptive fuzzy impulsive synchronization of chaotic systems with random parameters," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 77-83.
    2. Heydari, Mahdi & Salarieh, Hassan & Behzad, Mehdi, 2011. "Stochastic chaos synchronization using Unscented Kalman–Bucy Filter and sliding mode control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1770-1784.
    3. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive chaos synchronization in Chua's systems with noisy parameters," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(3), pages 233-241.
    4. Dadras, Sara & Momeni, Hamid Reza, 2010. "Adaptive sliding mode control of chaotic dynamical systems with application to synchronization," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2245-2257.
    5. Shahverdiev, E.M. & Bayramov, P.A. & Shore, K.A., 2009. "Cascaded and adaptive chaos synchronization in multiple time-delay laser systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 180-186.
    6. Xiao, Jiang-Wen & Gao, Jiexuan & Huang, Yuehua & Wang, Yan-Wu, 2009. "Reduced-order adaptive control design for the stabilization and synchronization of a class of nonlinear chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1156-1162.

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