Journal of Guangxi Normal University(Natural Science Edition) ›› 2026, Vol. 44 ›› Issue (3): 128-138.doi: 10.16088/j.issn.1001-6600.2025070804

• Mathematics • Previous Articles     Next Articles

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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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

CLC Number:  O175.1; O231
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