广西师范大学学报（自然科学版） ›› 2026, Vol. 44 ›› Issue (3): 128-138.doi: 10.16088/j.issn.1001-6600.2025070804

• 数学 • 上一篇    下一篇

分数Brown运动干扰下非线性多智能体系统的聚类均方一致性

陈律1, 陈文平1*, 丁倚婷1, 李友亮1, 周霞1,2,3*   

  1. 1.桂林电子科技大学 数学与计算科学学院,广西 桂林 541004;
    2.广西应用数学中心(桂林电子科技大学),广西 桂林 541004;
    3.广西高校数据分析与计算重点实验室(桂林电子科技大学),广西 桂林 541004
  • 收稿日期:2025-07-08 修回日期:2025-08-09 出版日期:2026-05-05 发布日期:2026-05-13
  • 通讯作者: 陈文平(1977—),男,桂林电子科技大学讲师,博士。E-mail: wpchen@guet.edu.cn;周霞(1981—),女,桂林电子科技大学教授,博士。E-mail: xiazhou201612@guet.edu.cn
  • 基金资助:
    国家自然科学基金(12161024);广西自然科学基金(2025GXNSFAA069197);广西研究生教育创新计划项目(YCSW2025363)

Cluster Mean Square Consensus of Nonlinear Multi-agent Systems with Fractional Brownian Motion

CHEN LÜ1, CHEN Wenping1*, DING Yiting1, LI Youliang1, ZHOU Xia1,2,3*   

  1. 1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin Guangxi 541004, China;
    2. Center for Applied Mathematics of Guangxi (Guilin University of Electronic Technology), Guilin Guangxi 541004, China;
    3. Guangxi Colleges and Universities Key Laboratory of Data Analysis and Computation (Guilin University of Electronic Technology), Guilin Guangxi 541004, China
  • Received:2025-07-08 Revised:2025-08-09 Online:2026-05-05 Published:2026-05-13

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摘要： 多智能体之间的通信和协作可能受到随机噪声的影响,因此,本文研究在分数Brown运动干扰下非线性多智能体系统的聚类均方一致性问题。首先,将随机噪声建模为分数Brown运动,而不是标准Brown运动。其次,本文研究的非线性多智能体系统的聚类均方一致性,当只有一个聚类时聚类均方一致性退化为均方恒同一致性。基于分布式控制理论、随机分析理论、图论等,构建一个无穷小算子,构造一种新颖的带双积分形式的Lyapunov泛函,设计带有时变控制增益的控制器,获得系统聚类均方一致的充分条件,并给出数值实例验证结论的正确性和方法的有效性。

关键词: 分数Brown运动, 非线性, 多智能体系统, 聚类均方一致性, 牵制控制

Abstract: The communication and collaboration among multiple agents may be affected by random noise. Therefore, this paper investigates the problem of cluster mean square consensus for nonlinear multi-agent systems under fractional Brownian motion disturbances. Firstly, the stochastic noise in the study is modeled as fractional Brownian motion rather than standard Brownian motion. Secondly, the cluster mean square consensus of the nonlinear multi-agent system is examined, where the case of a single cluster reduces to mean square consensus. Based on distributed control theory, stochastic analysis theory, graph theory, and other frameworks, an infinitesimal operator is constructed, and a novel Lyapunov functional with a double-integral form is designed. A controller with time-varying control gains is developed, and sufficient conditions for achieving cluster mean square consensus of the system are derived. A numerical example is provided to validate the correctness of the conclusions and the effectiveness of the proposed method.

Key words: fractional Brownian motion, nonlinear, multi-agent systems, cluster mean square consensus, pinning control

中图分类号:  O175.1; O231

[1] MINSKY M. The society of mind[M].New York: Simon & Schuster, 1988.
[2] ZHOU X, HUANG C Y, LI P, et al. Leader-following identical consensus for Markov jump nonlinear multi-agent systems subjected to attacks with impulse[J]. Nonlinear Analysis: Modelling and Control, 2023, 28: 1-25. DOI: 10.15388/namc.2023.28.33003.
[3] YU C B, QIN J H, GAO H J. Cluster synchronization in directed networks of partial-state coupled linear systems under pinning control[J]. Automatica, 2014, 50(9): 2341-2349. DOI: 10.1016/j.automatica.2014.07.013.
[4] LIN X, ZHENG Y S, WANG L. Consensus of switched multi-agent systems with random networks[J]. International Journal of Control, 2017, 90(5): 1113-1122. DOI: 10.1080/00207179.2016.1201865.
[5] LI M L, DENG F Q. Cluster consensus of nonlinear multi-agent systems with Markovian switching topologies and communication noises[J]. ISA Transactions, 2021, 116: 113-120. DOI: 10.1016/j.isatra.2021.01.034.
[6] MANDELBROT B B, van NESS J W. Fractional Brownian motions, fractional noises and applications[J]. SIAM Review, 1968, 10(4): 422-437. DOI: 10.2307/2027184.
[7] CHEN W P, LÜ S J, CHEN H, et al. Analysis of two Legendre spectral approximations for the variable-coefficient fractional diffusion-wave equation[J]. Advances in Difference Equations, 2019, 2019(1): 418. DOI: 10.1186/s13662-019-2347-2.
[8] ZHOU X, ZHOU D P, LIU X, et al. Delayed impulsive SDEs driven by multiplicative fBm noise and additive fBm noise[J]. Mathematical Methods in the Applied Sciences, 2021:1-16. DOI: 10.1002/mma.7721.
[9] ZHANG W G, LI Z, LIU Y J, et al. Pricing European option under fuzzy mixed fractional Brownian motion model with jumps[J]. Computational Economics, 2021, 58(2): 483-515. DOI: 10.1007/s10614-020-10043-z.
[10] MO L P, YUAN X L, YU Y G. Containment control for multi-agent systems with fractional Brownian motion[J]. Applied Mathematics and Computation, 2021, 398: 125814. DOI: 10.1016/j.amc.2020.125814.
[11] ZHOU X, ZHOU X, CHENG J, et al. Integral sliding mode control and stability for Markov jump systems with structured perturbations and time-varying delay driven by fractional Brownian motion[J]. ISA Transactions, 2024, 151: 62-72. DOI: 10.1016/j.isatra.2024.05.025.
[12] 高钰博, 叶钊显, 黄帅, 等. 网络攻击下具有Markov切换拓扑的多智能体系统的一致性[J]. 广西师范大学学报(自然科学版), 2025, 43(2): 168-178. DOI: 10.16088/j.issn.1001-6600.2024040204.
[13] ZHOU X, XI M X, LIU W B, et al. Delayed consensus in mean-square of mass under Markov switching topologies and brown noise[J]. Journal of Applied Analysis & Computation, 2024, 14(1): 543-559. DOI: 10.11948/20230307.
[14] 呼文军, 马忠军, 马梅. 领导-跟随多智能体系统在分布式自适应控制下的滞后一致性[J]. 广西师范大学学报(自然科学版), 2018, 36(1): 70-75. DOI: 10.16088/j.issn.1001-6600.2018.01.009.
[15] 隆紫庭, 马忠军, 李科赞. 多智能体系统的实用-分量一致性[J]. 广西师范大学学报(自然科学版), 2024, 42(1): 139-146. DOI: 10.16088/j.issn.1001-6600.2023041202.
[16] 于俊生, 马忠军, 李科赞. 事件触发控制下多智能体系统的部分分量一致性[J]. 广西师范大学学报(自然科学版), 2023, 41(4): 149-157. DOI: 10.16088/j.issn.1001-6600.2022090401.
[17] LI F B, MA Z J, DUAN Q C. Clustering component synchronization in a class of unconnected networks via pinning control[J]. Physica A: Statistical Mechanics and Its Applications, 2019, 525: 394-401. DOI: 10.1016/j.physa.2019.03.080.
[18] MA Z J, WANG Y, LI X M. Cluster-delay consensus in first-order multi-agent systems with nonlinear dynamics[J]. Nonlinear Dynamics, 2016, 83(3): 1303-1310. DOI: 10.1007/s11071-015-2403-8.
[19] WANG Q F, WANG Z S, MA L. Adaptive finite-time bipartite consensus of multi-agent systems with communication link uncertainty under signed digraph[J]. Neurocomputing, 2024, 598: 128012. DOI: 10.1016/j.neucom.2024.128012.
[20] 姚瑶, 张捷, 王健安, 等. 基于状态反馈和输出反馈的离散线性多智能体系统的二分一致性研究[J]. 控制与决策, 2025, 40(2): 537-545. DOI: 10.13195/j.kzyjc.2023.1496.
[21] WANG Y, MA Z J, CAO J D, et al. Adaptive cluster synchronization in directed networks with nonidentical nonlinear dynamics[J]. Complexity, 2016, 21(S2): 380-387. DOI: 10.1002/cplx.21816.
[22] ZHOU X, LIU W B, LI F B, et al. Partial component consensus in mean-square for delayed nonlinear multi-agent systems with uncertain nonhomogeneous Markov switching topologies and aperiodic denial-of-service cyber-attacks[J]. Mathematical Methods in the Applied Sciences, 2024, 47(11): 9207-9221. DOI: 10.1002/mma.10068.
[23] GAO R, YANG G H. Resilient cluster consensus for discrete-time high-order multi-agent systems against malicious adversaries[J]. Automatica, 2024, 159: 111382. DOI: 10.1016/j.automatica.2023.111382.
[24] QIN J H, YU C B. Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition[J]. Automatica, 2013, 49(9): 2898-2905. DOI: 10.1016/j.automatica.2013.06.017.
[25] YAGHOUBI Z, ALI TALEBI H. Cluster consensus of fractional-order non-linear multi-agent systems with switching topology and time-delays via impulsive control[J]. International Journal of Systems Science, 2020, 51(10): 1685-1698. DOI: 10.1080/00207721.2020.1772404.
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