Fast Consensus in Multi-Agent Systems With Star Topology Using High Gain Observers

This letter addresses the consensus problem of multi-agent systems for a static undirected communication topology. It is known that for a static undirected graph, the convergence rate of the consensus protocol depends on the second smallest eigenvalue of the graph Laplacian. The fastest convergence rate can be achieved when the communication topology is given by a complete graph which is costly in terms of the required number of communication links. On the other hand the star topology is ubiquitous in nature and widely used in practical applications due to its robustness property but the convergence rate of the consensus protocol with the star topology is slower than the complete graph. In this letter, we show that the convergence rate of the star topology can be increased by adding observers to each agent except the root agent. The complete graph is chosen as a reference target system and we show that the convergence rate of the consensus protocol with the star topology approaches the convergence rate of the consensus protocol with the complete graph for sufficiently small ϵ, which is a high-gain observer parameter. Furthermore, we show that for sufficiently small ϵ, the trajectories of the agents with the star topology approach the trajectories of the agents with the virtual complete graph. Simulations are provided that show the effectiveness of our theoretical results.