Interval Coordination of Multiagent Networks With Antagonistic Interactions

This paper studies interval coordination problems for multiagent systems with antagonistic interactions. For strongly connected signed networks, it is shown that when the intersection of intervals imposed by agents is nonempty: (1) the multiagent system achieves bipartite consensus with structurally balanced network; (2) all agents’ states must converge to 0, if the signed network is structurally unbalanced. We establish the consensus conditions for bipartite consensus and zero-value consensus by employing the Gauge Transformation and robust analysis of signed networks. When the signed networks are strongly connected and the intersection of intervals is empty, the system reaches an asymptotically stable and unique equilibrium. Moreover, the equilibrium states are only decided by the network structure and interval constraints, and are not related to initial agents’ states. Associating the equilibrium of dynamics with the solution of a system of nonlinear equations, we obtain the uniqueness, stability and continuity of equilibria. Finally, numerical simulations are presented to illustrate the theoretical results.