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Uniform synchronization for chaotic dynamical systems via event-triggered impulsive control

Author

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  • Liu, Bin
  • Sun, Zhijie
  • Luo, Yihao
  • Zhong, Yuxuan

Abstract

This article studies the issue of uniform synchronization for chaotic dynamical systems via event-triggered impulsive control (ETIC). The synchronization scheme is executed by designing ETIC with three levels of event-triggering conditions. Under the designed ETIC, the uniform exponential synchronization is achieved for master–slave chaotic systems. It shows the uniform synchronization via ETIC is robust with respect to time delays in ETIC. Moreover, the notions including rate of control and cost of control are proposed for comparisons with uniform synchronization via classic impulsive control (CIC) which is time-triggered impulsive control. The chaotic Lorenz system is used to test the performances of uniform synchronization via ETIC and CIC. The specific ETIC and CIC for uniform synchronization of master–slave Lorenz systems are designed and the numerical simulations of synchronizations via ETIC and CIC are given. It is shown that from the number of control, the rate of control, and the cost of control, ETIC has obvious advantages than CIC for uniform synchronization of master–slave Lorenz systems.

Suggested Citation

  • Liu, Bin & Sun, Zhijie & Luo, Yihao & Zhong, Yuxuan, 2019. "Uniform synchronization for chaotic dynamical systems via event-triggered impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 531(C).
    • Handle: RePEc:eee:phsmap:v:531:y:2019:i:c:s0378437119309823
    DOI: 10.1016/j.physa.2019.121725
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    Citations

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    Cited by:

    1. Shoreh, A.A.-H. & Kuznetsov, N.V. & Mokaev, T.N., 2022. "New adaptive synchronization algorithm for a general class of complex hyperchaotic systems with unknown parameters and its application to secure communication," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    2. Bin Liu & Bo Xu & Guohua Zhang & Lisheng Tong, 2019. "Review of Some Control Theory Results on Uniform Stability of Impulsive Systems," Mathematics, MDPI, vol. 7(12), pages 1-28, December.
    3. Li, Mingyue & Wang, Mingzhu & Liu, Wenlu & Wu, Shuchen & Li, Xiaodi, 2023. "Exponential stability of nonlinear systems via event-triggered impulsive control based on partial states," Applied Mathematics and Computation, Elsevier, vol. 459(C).
    4. Man-Wen Tian & Shu-Rong Yan & Jinping Liu & Khalid A. Alattas & Ardashir Mohammadzadeh & Mai The Vu, 2022. "A New Type-3 Fuzzy Logic Approach for Chaotic Systems: Robust Learning Algorithm," Mathematics, MDPI, vol. 10(15), pages 1-20, July.
    5. Tan, Hailian & Wu, Jianwei & Bao, Haibo, 2022. "Event-triggered impulsive synchronization of fractional-order coupled neural networks," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    6. Yu, Nanxiang & Zhu, Wei, 2021. "Event-triggered impulsive chaotic synchronization of fractional-order differential systems," Applied Mathematics and Computation, Elsevier, vol. 388(C).
    7. Can Zhao & Jinde Cao & Kaibo Shi & Yiqian Tang & Shouming Zhong & Fawaz E. Alsaadi, 2022. "Improved Nonfragile Sampled-Data Event-Triggered Control for the Exponential Synchronization of Delayed Complex Dynamical Networks," Mathematics, MDPI, vol. 10(19), pages 1-24, September.
    8. Zhao, Can & Liu, Xinzhi & Zhong, Shouming & Shi, Kaibo & Liao, Daixi & Zhong, Qishui, 2021. "Leader-following consensus of multi-agent systems via novel sampled-data event-triggered control," Applied Mathematics and Computation, Elsevier, vol. 395(C).

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