Group-Bipartite Consensus in the Networks With Cooperative-Competitive Interactions

This brief addresses the group-bipartite consensus problem of multi-agent systems with cooperative-competitive interactions. By combining the characteristics of group consensus and bipartite consensus, the concept of group-bipartite consensus is introduced to specify multiple bipartite consensus behavior. A distributed control protocol is then proposed for the topology graphs with acyclic partition and sign-balanced couples. The network topology studied in this brief eliminates the constraint that negative links can only exist between different groups, and thus the weights between agents in the same group can be either positive or negative. Some necessary and sufficient conditions for solving group-bipartite consensus problems are established by constructing a new form of the Laplacian matrix associated with the directed communication graphs. A simulation example is given to validate the theoretical results.