Solving the N-Consensus Problem: Combining Clustering and Synchronization

This article presents a state synchronization method within multi-agent systems upon multiple states. Based on their formation in state space, the agents decide on a clustering and synchronize their states within these clusters. The solution steps for this N-consensus problem, clustering and synchronization, may both be solved entirely in a decentral manner. This is achieved by means of a distributed Variational Bayes to describe the distribution of the agents' positions as a mixture of densities. The entire N-consensus problem is illustrated with graphical probabilistic models whose underlying potential is shown to be maximized when reaching the final N-consensus. An improvement of the overall convergence speed is achieved by a dynamical adaption of the distributed Variational Bayes, which leads to an intertwining of clustering and synchronization.