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On predefined-time synchronisation of chaotic systems

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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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    1. 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.
    2. Assali, El Abed, 2021. "Predefined-time synchronization of chaotic systems with different dimensions and applications," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    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. 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).

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