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A fixed-time robust controller based on zeroing neural network for generalized projective synchronization of chaotic systems

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  • Xiao, Lin
  • Li, Linju
  • Cao, Penglin
  • He, Yongjun

Abstract

Generalized projective synchronization (GPS) as a deeply influential chaos synchronization has always attracted lots of attention. However, plenty of traditional control methods do not predict its synchronization time or have no regard for the interference of noise in practical applications. Inspired by the fact that zeroing neural network (ZNN) can solve the time-varying problems well, this paper adopts the design method of the ZNN to construct a fixed-time robust controller (FXTRC), realizing the GPS of a class of chaotic systems. The fixed-time synchronization and robustness of chaotic systems under the FXTRC are clearly demonstrated by detailed theoretical analyses. Moreover, the upper bound of the synchronization time can be calculated by introducing the Beta function when the FXTRC is applied to control the GPS of chaotic systems. Numerical simulations prove the correctness of the theoretical analyses and the superiority of the FXTRC over the previous control methods.

Suggested Citation

  • Xiao, Lin & Li, Linju & Cao, Penglin & He, Yongjun, 2023. "A fixed-time robust controller based on zeroing neural network for generalized projective synchronization of chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    • Handle: RePEc:eee:chsofr:v:169:y:2023:i:c:s0960077923001807
    DOI: 10.1016/j.chaos.2023.113279
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    References listed on IDEAS

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    1. Dutta, Maitreyee & Roy, Binoy Krishna, 2021. "A new memductance-based fractional-order chaotic system and its fixed-time synchronisation," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    2. Chen, Chuan & Li, Lixiang & Peng, Haipeng & Yang, Yixian & Mi, Ling & Qiu, Baolin, 2019. "Fixed-time projective synchronization of memristive neural networks with discrete delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    3. Wang, Leimin & Dong, Tiandu & Ge, Ming-Feng, 2019. "Finite-time synchronization of memristor chaotic systems and its application in image encryption," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 293-305.
    4. Zhang, Hai & Cheng, Jingshun & Zhang, Hongmei & Zhang, Weiwei & Cao, Jinde, 2021. "Quasi-uniform synchronization of Caputo type fractional neural networks with leakage and discrete delays★," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    5. Zhang, Hai & Cheng, Yuhong & Zhang, Hongmei & Zhang, Weiwei & Cao, Jinde, 2022. "Hybrid control design for Mittag-Leffler projective synchronization on FOQVNNs with multiple mixed delays and impulsive effects," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 341-357.
    6. Yan, Jianping & Li, Changpin, 2005. "Generalized projective synchronization of a unified chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 26(4), pages 1119-1124.
    7. Li, Changpin & Yan, Jianping, 2006. "Generalized projective synchronization of chaos: The cascade synchronization approach," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 140-146.
    8. Wang, Cong & Zhang, Hong-li & Fan, Wen-hui & Ma, Ping, 2020. "Finite-time function projective synchronization control method for chaotic wind power systems," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
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    1. Guo, Pengteng & Shi, Qiqing & Jian, Zeng & Zhang, Jing & Ding, Qun & Yan, Wenhao, 2024. "An intelligent controller of homo-structured chaotic systems under noisy conditions and applications in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    2. Zheng, Boyu & Han, Zhiyong & Li, Chunquan & Zhang, Zhijun & Yu, Junzhi & Liu, Peter X., 2024. "A flexible-predefined-time convergence and noise-suppression ZNN for solving time-variant Sylvester equation and its application to robotic arm," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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