Coordination of multi-agent systems on interacting physical and communication topologies

A new framework is given for coordination of multi-agent systems that are interconnected by a physical coupling digraph. The edges of this graph represent physical couplings between agents that are fixed due to dynamical interactions. On top of the physical graph, distributed control protocols are designed where the allowed communications between agents for control purposes are prescribed by a second fixed communication digraph. The physical and communication digraphs are generally different and the combination of these two graphs forms a cyber-physical system. The interactions between physical and communication graphs are the focus of this paper. We consider different interactions between two graphs, including the case when their pinned Laplacian commutes, the case of the communication graph with diagonalizable pinned Laplacian, and the case of two general graphs. Moreover, within each graph, the relations between the agents can be either collaborative or antagonistic. To capture this, the theory of bipartite consensus is used. Coordination protocols for different cases are designed that are distributed with respect to the communication graph, and overcome the detrimental effects of the signed physical graph. The proposed control methods are illustrated by simulation examples.