Adaptive bipartite tracking control for coopetition networks

Cooperation and competition are two typical interactional relationships in natural and engineering networked systems. Some interesting collective behaviors can emerge through local interactions within the networked systems. This paper considers a bipartite consensus for a group of agents interacting both cooperatively and competitively. Meanwhile, the intrinsic nonlinear dynamics of all the agents are unknown for the neighboring agents. Thus, the interaction network, which we call a coopetition network, is firstly represented by a signed graph. Then, some adaptive estimate laws are proposed for the unknown dynamics. Finally, an adaptive tracking control is designed for each agent to reach a bipartite consensus on the state of the leader. Some sufficient conditions are derived for bipartite consensus of multi-agent systems with the help of a structural balance theory. Simulation results are provided to demonstrate the bipartite consensus formation.