Consensus of edge dynamics on directed multi-agent systems

Consensus in multi-agent systems means that reach an agreement among states of the whole group. However, almost all the existed works on consensus have been in the description of the states of nodes, and fewer efforts have been devoted to the consensus taking place on the edges of multi-agent systems. In this paper, we focus on the dynamics proceed on the edges and establish a discrete-time and a continuous-time edge consensus protocols respectively for directed multi-agent systems. By mapping the edge topology to its line graph of the original nodal topology, we analyze the consensus of the edge protocols rigorously, and get that both the discrete-time protocol and the continuous-time protocol of directed multi-agent systems can guarantee that an edge consensus is asymptotically reached for all initial states when the original directed system is strongly connected. Numerical simulations are provided to show the effectiveness of both the discrete-time and the continuous-time models.