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Robust synchronization of drive–response chaotic systems via adaptive sliding mode control

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  • Li, Wang-Long
  • Chang, Kuo-Ming

Abstract

A robust adaptive sliding control scheme is developed in this study to achieve synchronization for two identical chaotic systems in the presence of uncertain system parameters, external disturbances and nonlinear control inputs. An adaptation algorithm is given based on the Lyapunov stability theory. Using this adaptation technique to estimate the upper-bounds of parameter variation and external disturbance uncertainties, an adaptive sliding mode controller is then constructed without requiring the bounds of parameter and disturbance uncertainties to be known in advance. It is proven that the proposed adaptive sliding mode controller can maintain the existence of sliding mode in finite time in uncertain chaotic systems. Finally, numerical simulations are presented to show the effectiveness of the proposed control scheme.

Suggested Citation

  • Li, Wang-Long & Chang, Kuo-Ming, 2009. "Robust synchronization of drive–response chaotic systems via adaptive sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2086-2092.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2086-2092
    DOI: 10.1016/j.chaos.2007.06.067
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    References listed on IDEAS

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    1. Park, Ju H., 2006. "Synchronization of a class of chaotic dynamic systems with controller gain variations," Chaos, Solitons & Fractals, Elsevier, vol. 27(5), pages 1279-1284.
    2. Zhang, Qing & Chen, Shihua & Hu, Yuanming & Wang, Changping, 2006. "Synchronizing the noise-perturbed unified chaotic system by sliding mode control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 317-324.
    3. 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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    3. 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).
    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. Alsaade, Fawaz W. & Yao, Qijia & Bekiros, Stelios & Al-zahrani, Mohammed S. & Alzahrani, Ali S. & Jahanshahi, Hadi, 2022. "Chaotic attitude synchronization and anti-synchronization of master-slave satellites using a robust fixed-time adaptive controller," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    6. Yao, Qijia & Alsaade, Fawaz W. & Al-zahrani, Mohammed S. & Jahanshahi, Hadi, 2023. "Fixed-time neural control for output-constrained synchronization of second-order chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).

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