The Multi-agent Rendezvous using Consensus and Gossip Algorithm

Abstract

The multi-agent system is a hot topic in control systems theory. Consensus algorithm and gossip algorithm are two main examples of multi-agent systems control. Consensus algorithm converges from different initial states of agents to a certain convergence value in a given fixed graph. Gossip algorithm is similar to the consensus algorithm but the graph is randomly selected each time. These algorithms are used in the multi-agent formation control or network system. In this thesis, we propose a new concept of a cluster graph where it is composed of three parts: one set of agents with fixed connections, another set of agents with randomly selected connections, and lastly fixed edges connecting the two former mentioned sets. We used a bipartite graph from graph theory to analyze this system easily. Furthermore, we prove asymptotic stability of this system by basic consensus and gossip algorithm proof method and gershgorin’s disk theorem. Along with this, we can find the convergence values of five cases of last connection edges with simple mathematic methods. In this thesis, we show the system stability simulation which is coded in Matlab. So the result gives the five different system is stable and there is some convergence value. Finally, this thesis concludes the simple system application simulation. First one is y position convergence in 2 dimension multi-agent formation control. Next is agent XY-coordinate synchronization in system.