Network Consensus Based On Edge Dynamics

In recent years,the consensus problem has become a hot topic in coordinated control of multi-agent systems.As the study on consensus of node dynamics becomes mature,people realize that many scenarios in real life,such as transportation networks,social networks,etc.are better described by edge dynamics,which would be more reasonable and accurate.Therefore,it is of great practical significance and theoretical value to study the consensus of edge dynamics which has gradually become a new research topic.Motivated by the above research background and by combining the graph theory,linear system theory and nonlinear system theory,the consensus problem of linear net-works and nonlinear networks based on edge dynamics are investigated systematically in this article.In this paper,two linear forms of the edge dynamics consensus protocols are proposed.We show that if the communication topology is a directed cyclic pursuit graph and the given node dynamics can reach a consensus,then a consensus can also be reached for the edge dynamics,and the final convergence value is the average of the initial state of all edges.Moreover,we investigate the implementation of the linear protocols with discrete-time communication.Some simulation examples are present-ed to show the effectiveness of the theoretical results.In addition,this paper designs the nonlinear form of edge dynamics consensus protocol.When the communication topology is an undirected cyclic pursuit graph,we consider two cases where the given node dynamics can or cannot achieve consensus and give the sufficient conditions for systems to achieve edge consensus respectively.