Distributed Finite Time Termination of Ratio Consensus for Averaging in the presence of Delays

TL;DR

This paper introduces a distributed finite-time stopping criterion for ratio consensus algorithms that enables agents in a network to detect when they have approximated the average within a specified tolerance, even with communication delays.

Contribution

It proposes a novel finite-time termination method for ratio consensus in networks with delays, enhancing practical implementation of distributed averaging.

Findings

Algorithm successfully detects convergence within finite time.

Simulations demonstrate effectiveness under communication delays.

Abstract

Distributed averaging of agent initial conditions is a well-studied problem in context of networked systems where coordination amongst the agents is of paramount importance. The asymptotic nature of convergence of distributed averaging protocols and presence of communication delays, however, makes it challenging to implement in practical settings. It is important that agents develop the ability to detect on their own when average of the initial conditions of the agents is achieved within some pre-specified tolerance and stop further computations to avoid overhead expenses in the presence of delays. This article presents a distributed finite time stopping criterion for distributed averaging using ratio consensus on a fixed interconnection topology. The practical utility of the algorithm has been illustrated through simulations.