Group synchronisation for multi-agent systems with compound noises over Markovian switching cooperative–competitive topologies

2026-04-17

PRE

Yingxue Du

Qiuyu Jia

Ruizhe Geng *

Dandan Li

Zhi Liu *

Ancai Zhang *

DOI：10.1080/00207721.2026.2657311

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Abstract

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This article focuses on the group synchronisation problem of multi-agent systems (MASs) subject to multiplicative and additive noises under Markovian switching cooperative–competitive networks, where the intensity of multiplicative noise can be described by the relative distance among neighbouring agents rather than a general bounded function. By designing a time-varying control gain, a stochastic approximation group synchronisation control protocol is proposed under multiplicative and additive noises interference, and the convergence of MASs in the mean square and almost sure senses is achieved if the topology contains a directed spanning tree and the time-varying control gain θ(t) satisfies ∫t0∞θ(t)dt=∞ and ∫t0∞θ2(t)dt<∞. Furthermore, the connection between the convergence rate and the time-varying control gain θ(t)=ϖ(t+ϱ)ς is involved, that is, the convergence rates of mean square errors satisfy E(Y(t))2=O(t−ς). Finally, simulation examples of MASs with seven agents over Markovian switching cooperative–competitive topologies show that the state trajectories of three agents converge to one consistent state, while the remaining agents converge to another. Moreover, the smaller noise intensities of multiplicative and additive noises, and the control gain θ(t)=ϖ(t+ϱ)ς with larger parameter ς lead to a faster convergence rate.

Keywords:

Group synchronisation

Markovian switching topologies

compound noises

cooperative–competitive network

Group synchronisation for multi-agent systems with compound noises over Markovian switching cooperative–competitive topologies

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