The model reduction of multi-agent system depended on the spanning tree of directed graph

This work explores the model reduction problem based on the edge agreement dynamics of multi-agent system. To begin with, the general concepts of weighted edge Laplacian of directed graph are proposed and its algebraic properties are further explored. From the systematic and structural view of the edge agreement dynamics, we note that multi-agent system can be then translated into a output feedback interconnection of the spanning tree subsystem and the co-spanning tree subsystem. In addition, based on the essential edge Laplacian, we derive a model reduction representation of the closed-loop multi-agent system based on the spanning tree subgraph.