Cluster Consensus in Networks of Agents With Weighted Cooperative–Competitive Interactions

This brief concerns a general cooperative-competitive network with weighted interactions, based on which the cluster consensus problem is addressed. A directed network with the weighted cooperative-competitive interactions is classified into three categories: 1) interactively balanced; 2) sub-balanced; and 3) unbalanced digraphs. In interactively balanced or sub-balanced networks, cluster consensus can be achieved, while in interactively unbalanced networks, cluster consensus can be reached in need of additional control inputs exerted on specific pinned agents. Simulations are finally presented to verify the theoretical results.