Consensus protocols for networked multiagent systems with relative position and neighboring velocity information

The consensus problem appears frequently in the coordination of multiagent systems in science and engineering and involves the agreement of networked agents upon certain quantities of interest. In this paper, we focus on a new consensus protocol for networked multiagent systems. The proposed control protocol consists of a standard term capturing relative position information and a new term capturing neighboring velocity information. In particular, the addition of the latter term results in an increase of the rate of system convergence while maintaining a fixed graph structure and without increasing the maximum eigenvalue of the graph Laplacian. Furthermore, in certain cases, it is shown that the maximum singular value of the graph Laplacian is not increased. This departs from the traditional view that the Fiedler eigenvalue, a function of graph structure, governors the system´s rate of convergence. In addition, it is shown that a connected and undirected graph topology acts as a weighted complete graph topology with the addition of this latter term to a standard consensus protocol. A comparative numerical example is provided to demonstrate the advantages of this new consensus protocol.