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Synchronizing different chaotic systems using active sliding mode control

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  • Haeri, Mohammad
  • Emadzadeh, Amir Abbas

Abstract

An active sliding mode controller is designed to synchronize three pairs of different chaotic systems (Lorenz–Chen, Chen–Lü, and Lü–Lorenz) in drive–response structure. It is assumed that the system parameters are known. The closed loop error dynamics depend on the linear part of the response systems and parameters of the controller. Therefore, the synchronization rate can be adjusted through these parameters. Analysis of the stability for the proposed method is derived based on the Lyapunov stability theorem. Finally, numerical results are presented to show the effectiveness of the proposed control technique.

Suggested Citation

  • Haeri, Mohammad & Emadzadeh, Amir Abbas, 2007. "Synchronizing different chaotic systems using active sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 119-129.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:1:p:119-129
    DOI: 10.1016/j.chaos.2005.09.037
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    References listed on IDEAS

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    1. Lin, Jui-Sheng & Yan, Jun-Juh & Liao, Teh-Lu, 2005. "Chaotic synchronization via adaptive sliding mode observers subject to input nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 371-381.
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    Cited by:

    1. Zhao, Yang & Wang, Wei, 2009. "Chaos synchronization in a Josephson junction system via active sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 60-66.
    2. Ahmadi, Ali Akbar & Majd, Vahid Johari, 2009. "GCS of a class of chaotic dynamic systems with controller gain variations," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1238-1245.
    3. Tavazoei, Mohammad Saleh & Haeri, Mohammad, 2008. "Synchronization of chaotic fractional-order systems via active sliding mode controller," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 57-70.
    4. Ahmadi, Ali Akbar & Majd, Vahid Johari, 2009. "Robust synchronization of a class of uncertain chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1092-1096.
    5. Zhang, Yinping & Sun, Jitao, 2009. "Impulsive robust fault-tolerant feedback control for chaotic Lur’e systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1440-1446.
    6. Naseh, Majid Reza & Haeri, Mohammad, 2009. "Robustness and robust stability of the active sliding mode synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 196-203.
    7. Yao, Qijia, 2021. "Synchronization of second-order chaotic systems with uncertainties and disturbances using fixed-time adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Wang, Bo & Wen, Guangjun, 2009. "On the synchronization of uncertain master–slave chaotic systems with disturbance," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 145-151.
    9. Zhao, Yang, 2009. "Synchronization of two coupled systems of J-J type using active sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3035-3041.
    10. Farivar, Faezeh & Aliyari Shoorehdeli, Mahdi & Nekoui, Mohammad Ali & Teshnehlab, Mohammad, 2012. "Chaos control and generalized projective synchronization of heavy symmetric chaotic gyroscope systems via Gaussian radial basis adaptive variable structure control," Chaos, Solitons & Fractals, Elsevier, vol. 45(1), pages 80-97.
    11. Shirkavand, Mehrdad & Pourgholi, Mahdi & Yazdizadeh, Alireza, 2022. "Robust global fixed-time synchronization of different dimensions fractional-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).

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