Consensus Filters on Small World Networks

In recent years, the broad applications of multi-agent systems in many areas have stimulated a great deal of interests in studying consensus or agreement problems. In this paper we investigate consensus update schemes motivated by the Kalman filter, which take into account the communication noise and the reliability of information states from each agent in the group. We study the consensus update schemes on a small-world network model, which describes a transition from a completely regular lattice to a completely random graph as the rewiring probability increases from zero to one. We found that the convergence speed of the consensus algorithm on a completely regular lattice can be greatly enhanced by just randomly rewiring a very small number of links in the network. We further analyze the relationship between the convergence speed of the consensus algorithm and the second smallest eigenvalue of the graph Laplacian