When to stop iterating in digraphs of unknown size? An application to finite-time average consensus

Abstract

In multi-agent systems, existing distributed algorithms for finite-time average consensus allow the agents to calculate the exact average in finite time, but typically require the agents to continue the iterative process indefinitely. The problem is that it is impossible for one agent to be certain that all other agents have also computed the average (at least not without a priori bounds on the network size or diameter). In this paper, we enhance an existing finite-time distributed algorithm with a distributed termination mechanism that allows the nodes to agree on terminating their iterations when they have all computed the exact average. This is accomplished by exploiting the fact that the distributed algorithm allows each node to compute, in a finite number of steps, an upper bound of its eccentricity in the network. The proposed distributed termination mechanism also facilitates the computation, in a finite number of steps, of an upper bound on the diameter of the network, which can be used by several algorithms that require such global information. Illustrative examples demonstrate the validity and performance of the proposed algorithm.