An anticipatory protocol to reach fast consensus in multi-agent systems.

We introduce a new consensus protocol with delays for networks where the agents are using past information to anticipate their neighbours’ states. We consider directed and undirected networks under the proposed algorithm, and study the necessary and sufficient conditions for consensus reaching. We show how to tune the delay parameter for the proposed consensus protocol to obtain fast convergence speed for all connected networks. We prove that for all networks we can always find a set of parameters for the proposed algorithm and guarantee a convergence speed corresponding to dominant root −1. Moreover, we argue that our algorithm can increase the convergence speed, especially in badly connected networks (networks with few connections). We also give some insights into the optimality of our choice of delay parameter and demonstrate that it represents an optimal choice.