IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v646y2024ics0378437124004175.html
   My bibliography  Save this article

Non-chattering finite-time and fixed-time flocking of Cucker–Smale systems

Author

Listed:
  • Wang, Huimin
  • Li, Shihan
  • Yang, Hailan
  • Cai, Yuchen
  • Sun, Yongzheng

Abstract

In this paper, the non-chattering finite/fixed-time flocking problems of Cucker–Smale (C–S) systems are investigated. To address the chattering issue, two novel chattering-free protocols are proposed to achieve the flocking of C–S systems within a finite/fixed time. Using the stability theory of differential equations, sufficient conditions for achieving the flocking are established, and the upper bounds of convergence time are given. The connection between the chattering-free flocking protocols and the classic finite/fixed-time control schemes involving the signum function is shown for the first time. Moreover, we discover a correlation between the settling time and the group size. Finally, the effectiveness of the presented protocols is validated via several simulations.

Suggested Citation

  • Wang, Huimin & Li, Shihan & Yang, Hailan & Cai, Yuchen & Sun, Yongzheng, 2024. "Non-chattering finite-time and fixed-time flocking of Cucker–Smale systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 646(C).
    • Handle: RePEc:eee:phsmap:v:646:y:2024:i:c:s0378437124004175
    DOI: 10.1016/j.physa.2024.129908
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437124004175
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2024.129908?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Qizhen Xiao & Hongliang Liu & Zhenghua Xu & Zigen Ouyang, 2020. "On Collision Avoiding Fixed-Time Flocking with Measurable Diameter to a Cucker–Smale-Type Self-Propelled Particle Model," Complexity, Hindawi, vol. 2020, pages 1-12, May.
    2. Wu, Jun & Liu, Yicheng, 2021. "Flocking behaviours of a delayed collective model with local rule and critical neighbourhood situation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 179(C), pages 238-252.
    3. Zhang, Wanli & Yang, Xinsong & Yang, Shiju & Alsaedi, Ahmed, 2021. "Finite-time and fixed-time bipartite synchronization of complex networks with signed graphs," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 319-329.
    4. Sun, Yongzheng & Wang, Yajun & Zhao, Donghua, 2015. "Flocking of multi-agent systems with multiplicative and independent measurement noises," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 440(C), pages 81-89.
    5. Pu, Hao & Li, Fengjun, 2023. "Fixed/predefined-time synchronization of complex-valued discontinuous delayed neural networks via non-chattering and saturation control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).
    6. Zhang, Wanli & Li, Chuandong & Huang, Tingwen & Huang, Junjian, 2018. "Fixed-time synchronization of complex networks with nonidentical nodes and stochastic noise perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 1531-1542.
    7. Ghommam, Jawhar & Saad, Maarouf & Mnif, Faisal, 2021. "Finite-time circular formation around a moving target with multiple underactuated ODIN vehicles," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 180(C), pages 230-250.
    8. Hongliang Liu & Xiao Wang & Xiang Li & Yicheng Liu, 2020. "Finite-time flocking and collision avoidance for second-order multi-agent systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(1), pages 102-115, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sun, Ruyi & Chang, Jiaqi & Wang, Hongmei & Li, Miaomiao & Sun, Yongzheng, 2024. "Time and energy costs for synchronization of multi-layer networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 440-455.
    2. Cai, Shuiming & Zhou, Feilong & He, Qinbin, 2019. "Fixed-time cluster lag synchronization in directed heterogeneous community networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 128-142.
    3. Suo, JingJing & Hu, Hongxiao & Xu, Liguang, 2023. "Delay-dependent impulsive control for lag quasi-synchronization of stochastic complex dynamical networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 134-153.
    4. Hu, Jingting & Sui, Guixia & Li, Xiaodi, 2020. "Fixed-time synchronization of complex networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    5. Wang, Shasha & Jian, Jigui, 2023. "Predefined-time synchronization of incommensurate fractional-order competitive neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    6. Yiping Luo & Yuejie Yao, 2019. "Finite-Time Synchronization of Uncertain Complex Dynamic Networks with Nonlinear Coupling," Complexity, Hindawi, vol. 2019, pages 1-14, December.
    7. Beregov, R.Y. & Melkikh, A.V., 2021. "Auto-oscillations and chaos at collective motion of agents," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    8. Rezaei, Vahid & Khanmirza, Esmaeel, 2024. "Continuous-time min-max consensus protocol: A unified approach," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 292-310.
    9. Liu, Xinmiao & Xia, Jianwei & Huang, Xia & Shen, Hao, 2020. "Generalized synchronization for coupled Markovian neural networks subject to randomly occurring parameter uncertainties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    10. 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).
    11. Yang, Shiju & Li, Chuandong & He, Xiping & Zhang, Wanli, 2022. "Variable-time impulsive control for bipartite synchronization of coupled complex networks with signed graphs," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    12. Huafei Chen & Jia Chen & Dan Qu & Kelin Li & Fei Luo, 2022. "An Uncertain Sandwich Impulsive Control System with Impulsive Time Windows," Mathematics, MDPI, vol. 10(24), pages 1-14, December.
    13. Zhu, Jian & Xi, Jingke & Li, Shihan & Shi, Hongjun & Sun, Yongzheng, 2024. "Time cost estimation for flocking of Cucker–Smale type models with switching protocol," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 636(C).
    14. Jianying Xiao & Yongtao Li, 2022. "Novel Synchronization Conditions for the Unified System of Multi-Dimension-Valued Neural Networks," Mathematics, MDPI, vol. 10(17), pages 1-24, August.
    15. Xu, Yao & Liu, Xinzhi & Zhang, Lu & Li, Wenxue & Wu, Yongbao & Liu, Yang, 2024. "Fixed-time bipartite synchronization of nonlinear impulsive time-varying signed networks with delays," Applied Mathematics and Computation, Elsevier, vol. 480(C).
    16. Chao Li & Qiming Yang & Bowen Pang & Tiance Chen & Qian Cheng & Jiaomin Liu, 2021. "A Mixed Strategy of Higher-Order Structure for Link Prediction Problem on Bipartite Graphs," Mathematics, MDPI, vol. 9(24), pages 1-13, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:646:y:2024:i:c:s0378437124004175. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.