Bipartite consensus for multi-agent systems with noises over Markovian switching topologies

Abstract In this paper, we investigate the distributed control problem for multi-agent systems (MASs) subject to multiplicative and additive noises over switching networks, where both cooperative and antagonistic interactions coexist. The communication topology is governed by a continuous-time Markovian chain. A stochastic approximation technique is utilized to handle stochastic bipartite consensus with communication noises. The major challenge, due to the fact that the intensity of the multiplicative noise is nonlinearly coupled with the distance between agents, is that the coexistence of antagonistic information and multiplicative noise makes the multiplicative noise term impossible to be converted into an error form. This leads to the inapplicability of the Lyapunov-based method. To cope with this, we first show the boundedness of agents’ states where the second moment approach is employed. Based on it, the mean square and almost surely bipartite consensus are achieved under some mild requirements. The efficiency of the proposed method is supported by an example.