The Multi-agent Rendezvous using Gossip and Consensus Algorithms: Directed Bipartite Connection

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 values of agents to a certain value in a given graph. Gossip algorithm is similar to consensus but the graph is randomly selected each time. In this paper, 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. The Laplacian matrix and randomly averaging matrix are key points of the system equation. There are three cases of connections between two groups. We use lemmas to solve asymptotic stable convergence of the system. This simulation shows the asymptotic stable of 3 bipartite graph connections in a few seconds.