Decentralised minimum-time average consensus in digraphs

Distributed algorithms for average consensus in directed graphs are typically asymptotic in the literature. In this work, we propose a protocol to distributively reach average consensus in a finite number of steps on interconnection topologies that form strongly connected directed graphs (digraphs). The average consensus value can be computed, based exclusively on local observations at each component, by running a protocol that requires each component to observe and store its own value over a finite and minimal number of steps, and to have knowledge of the number of its out-going links (i.e., the number of components to which it sends information). The proposed algorithm is demonstrated via illustrative examples.