Dynamics of Generic Linear Agents Over Signed Networks Without Structural Constraints

Abstract

Signed networks have been widely used to describe cooperative and competitive interactions in multiagent systems (MASs) so far. Most of the existing dynamics results of MASs on signed networks have a certain constraint on the network topology, that is, the network topology is required to have sufficient connectivity for realizing consensus or bipartite consensus. The highlight of this article is to extend the existing dynamics of MASs to a more general signed network, in which there are no any structural constraints on the topology. This general setting of the network topology unifies most existing models, such as consensus, bipartite consensus, and bipartite containment, which are usually analyzed separately in the same framework using different methods. Relying on a method of constructing cooperative auxiliary digraphs, it is theoretically proved that the agents in closed strong connected components with balanced structure and unbalanced structure gradually reach separately bipartite consensus and consensus, and the agents outside the closed strong connected components gradually enter the convex hull formed by the agents in the closed strong connected components, that is, achieving bipartite containment. Finally, a computer simulation is presented to verify the theoretical discovery.