Bipartite Consensus Control of Multiagent Systems on Coopetition Networks

Cooperation and competition are two typical interactional relationships in natural and engineering networked systems. Some complex behaviors can emerge through local interactions within the networked systems. This paper focuses on the coexistence of competition and cooperation (i.e., coopetition) at the network level and, simultaneously, the collective dynamics on such coopetition networks. The coopetition network is represented by a directed signed graph. The collective dynamics on the coopetition network is described by a multiagent system. We investigate two bipartite consensus strategies for multiagent systems such that all the agents converge to a final state characterized by identical modulus but opposite sign. Under a weak connectivity assumption that the coopetition network has a spanning tree, some sufficient conditions are derived for bipartite consensus of multiagent systems with the help of a structural balance theory. Finally, simulation results are provided to demonstrate the bipartite consensus formation.