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Robust Synchronization of Fractional-Order Chaotic Systems at a Pre-Specified Time Using Sliding Mode Controller with Time-Varying Switching Surfaces

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  • Khanzadeh, Alireza
  • Pourgholi, Mahdi

Abstract

A main problem associated with the synchronization of two chaotic systems is that the time in which complete synchronization will occur is not specified. Synchronization time is either infinitely large or is finite but only its upper bound is known and this bound depends on the systems' initial conditions. In this paper we propose a method for synchronizing of two chaotic systems precisely at a time which we want. To this end, time-varying switching surfaces sliding mode control is used and the control law based on Lyapunov stability theorem is derived which is able to synchronize two fractional-order chaotic systems precisely at a pre specified time without concerning about their initial conditions. Moreover, by eliminating the reaching phase in the proposed synchronization scheme, robustness against existence of uncertainties and exogenous disturbances is obtained. Because of the existence of fractional integral of the sign function instead of the sign function in the control equation, the necessity for infinitely fast switching be obviated in this method. To show the effectiveness of the proposed method the illustrative examples under different situations are provided and the simulation results are reported.

Suggested Citation

  • Khanzadeh, Alireza & Pourgholi, Mahdi, 2016. "Robust Synchronization of Fractional-Order Chaotic Systems at a Pre-Specified Time Using Sliding Mode Controller with Time-Varying Switching Surfaces," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 69-77.
    • Handle: RePEc:eee:chsofr:v:91:y:2016:i:c:p:69-77
    DOI: 10.1016/j.chaos.2016.05.007
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    References listed on IDEAS

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    6. 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.
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    Cited by:

    1. Durdu, Ali & Uyaroğlu, Yılmaz, 2017. "The Shortest Synchronization Time with Optimal Fractional Order Value Using a Novel Chaotic Attractor Based on Secure Communication," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 98-106.
    2. Chen, Yun & Xu, Yanyi & Lin, Qian & Zhang, Xiyong, 2020. "Model and criteria on the global finite-time synchronization of the chaotic gyrostat systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 515-533.

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