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Chaos synchronization in noisy environment using nonlinear filtering and sliding mode control

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  • Behzad, Mehdi
  • Salarieh, Hassan
  • Alasty, Aria

Abstract

This paper presents an algorithm for synchronizing two different chaotic systems, using a combination of the extended Kalman filter and the sliding mode controller. It is assumed that the drive chaotic system has a random excitation with a stochastically chaotic behavior. Two different cases are considered in this study. At first it is assumed that all state variables of the drive system are available, i.e. complete state measurement, and a sliding mode controller is designed for synchronization. For the second case, it is assumed that the output of the drive system does not contain the whole state variables of the drive system, and it is also affected by some random noise. By combination of extended Kalman filter and the sliding mode control, a synchronizing control law is proposed. As a case study, the presented algorithm is applied to the Lur’e-Genesio chaotic systems as the drive-response dynamic systems. Simulation results show the good performance of the algorithm in synchronizing the chaotic systems in presence of noisy environment.

Suggested Citation

  • Behzad, Mehdi & Salarieh, Hassan & Alasty, Aria, 2008. "Chaos synchronization in noisy environment using nonlinear filtering and sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 36(5), pages 1295-1304.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:5:p:1295-1304
    DOI: 10.1016/j.chaos.2006.07.058
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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.
    2. Feng, Jianwen & Chen, Shihua & Wang, Changping, 2005. "Adaptive synchronization of uncertain hyperchaotic systems based on parameter identification," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1163-1169.
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    4. Park, Ju H., 2005. "Adaptive synchronization of hyperchaotic Chen system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 959-964.
    5. Park, Ju H., 2006. "Synchronization of Genesio chaotic system via backstepping approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1369-1375.
    6. Park, Ju H., 2005. "Adaptive synchronization of Rossler system with uncertain parameters," Chaos, Solitons & Fractals, Elsevier, vol. 25(2), pages 333-338.
    7. Millerioux, G. & Anstett, F. & Bloch, G., 2005. "Considering the attractor structure of chaotic maps for observer-based synchronization problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 68(1), pages 67-85.
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    Cited by:

    1. Asheghan, Mohammad Mostafa & Beheshti, Mohammad T.H., 2009. "An LMI approach to robust synchronization of a class of chaotic systems with gain variations," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1106-1111.
    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. González, Graciela Adriana & Nielsen, Christopher & Bortoff, Zachary, 2022. "Attractivity of unstable equilibria for a controlled Chen system via small output feedback," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    4. Ayati, Moosa & Khaloozadeh, Hamid, 2009. "A stable adaptive synchronization scheme for uncertain chaotic systems via observer," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2473-2483.
    5. Salarieh, Hassan & Alasty, Aria, 2008. "Adaptive control of chaotic systems with stochastic time varying unknown parameters," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 168-177.
    6. Santos Coelho, Leandro dos & de Andrade Bernert, Diego Luis, 2009. "An improved harmony search algorithm for synchronization of discrete-time chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2526-2532.

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