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On predefined-time synchronisation of chaotic systems

Author

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  • Anguiano-Gijón, Carlos Alberto
  • Muñoz-Vázquez, Aldo Jonathan
  • Sánchez-Torres, Juan Diego
  • Romero-Galván, Gerardo
  • Martínez-Reyes, Fernando

Abstract

An active control Lyapunov-function design for predefined-time synchronisation of chaotic systems, based on the Lorenz attractor, is proposed in this paper. The proposed controller guarantees that before a known time, which is predefined during the control design, two chaotic systems are synchronised, enforcing a predefined-time sliding mode synchronisation. Numerical simulations are presented in order to show the reliability of the proposed method. Firstly, an application to secure communication is addressed, showing that, after the synchronisation is achieved, the exact message reconstruction is performed through a two-channel communication protocol, one channel for transmitting the message, and the other one for maintaining the synchronisation. An additional simulation case, about the synchronisation of two Rössler systems, is presented to show the applicability of the proposed scheme in a different chaotic system.

Suggested Citation

  • Anguiano-Gijón, Carlos Alberto & Muñoz-Vázquez, Aldo Jonathan & Sánchez-Torres, Juan Diego & Romero-Galván, Gerardo & Martínez-Reyes, Fernando, 2019. "On predefined-time synchronisation of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 172-178.
    • Handle: RePEc:eee:chsofr:v:122:y:2019:i:c:p:172-178
    DOI: 10.1016/j.chaos.2019.03.015
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    References listed on IDEAS

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    1. Mukherjee, Somenath & Ray, Rajdeep & Samanta, Rajkumar & Khondekar, Mofazzal H. & Sanyal, Goutam, 2017. "Nonlinearity and chaos in wireless network traffic," Chaos, Solitons & Fractals, Elsevier, vol. 96(C), pages 23-29.
    2. Xu, Fei & Lai, Yongzeng & Shu, Xiao-Bao, 2018. "Chaos in integer order and fractional order financial systems and their synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 117(C), pages 125-136.
    3. Mitra, Vramori & Solomon, Infant & Prakash, N. Hari & Sarma, Arun & Sarma, Bornali, 2017. "Complexity and onset of chaos control in a DC glow discharge magnetized plasma using all pass filter," Chaos, Solitons & Fractals, Elsevier, vol. 103(C), pages 613-621.
    4. 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.
    5. Kocamaz, Uğur Erkin & Cevher, Barış & Uyaroğlu, Yılmaz, 2017. "Control and synchronization of chaos with sliding mode control based on cubic reaching rule," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 92-98.
    6. Mahmoud, Gamal M. & Arafa, Ayman A. & Abed-Elhameed, Tarek M. & Mahmoud, Emad E., 2017. "Chaos control of integer and fractional orders of chaotic Burke–Shaw system using time delayed feedback control," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 680-692.
    7. Shao, Hua & Shi, Yuming & Zhu, Hao, 2018. "On distributional chaos in non-autonomous discrete systems," Chaos, Solitons & Fractals, Elsevier, vol. 107(C), pages 234-243.
    8. Ouannas, Adel & Odibat, Zaid & Hayat, Tasawar, 2017. "Fractional analysis of co-existence of some types of chaos synchronization," Chaos, Solitons & Fractals, Elsevier, vol. 105(C), pages 215-223.
    9. Messadi, M. & Mellit, A., 2017. "Control of chaos in an induction motor system with LMI predictive control and experimental circuit validation," Chaos, Solitons & Fractals, Elsevier, vol. 97(C), pages 51-58.
    10. Lahmiri, Salim & Bekiros, Stelios, 2018. "Chaos, randomness and multi-fractality in Bitcoin market," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 28-34.
    11. 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, Mengjiao & Zang, Hongyan & Bai, Luyuan, 2022. "A new predefined-time sliding mode control scheme for synchronizing chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    2. Yacine, Zedjiga & Hamiche, Hamid & Djennoune, Saïd & Mammar, Saïd, 2022. "Finite-time impulsive observers for nonlinear systems represented by Takagi–Sugeno models: Application to a chaotic system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 321-352.
    3. Luo, Runzi & Song, Zijun & Liu, Shuai, 2023. "Fixed-time observed synchronization of chaotic system with all state variables unavailable in some periods," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. Assali, El Abed, 2021. "Predefined-time synchronization of chaotic systems with different dimensions and applications," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).

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