Control of multiconsensus in multi-agent systems based on eigenvector centrality

In multiconsensus (or group consensus) the units of a multi-agent system split into clusters, with the agents of the same group converging towards the same consensus value, which, in general, is different from cluster to cluster. In this brief paper, we develop a new technique to achieve multiconsensus among agents described by second-order dynamics. To do this, we introduce a communication protocol where interactions between agents are directed and weighted. Our approach consists of two steps. First, the weights of the interaction network are assigned so that the network adjacency matrix has a given leading eigenvector. This allows the formation of clusters of nodes that have the same value of eigenvector centrality. Second, the gains of the communication protocols are selected to guarantee the stability of the error dynamics. We study both the cases of leaderless and leader-follower multiconsensus, providing analytical conditions for multiconsensus, and discuss a few numerical examples to illustrate our theoretical results. (c) 2024 Elsevier Ltd. All rights reserved.