Distributed finite-time termination for consensus algorithm in switching topologies

TL;DR

This paper introduces a finite-time stopping criterion for consensus algorithms in networks with changing topologies, enabling agents to determine convergence within finite time rather than asymptotically.

Contribution

The paper proposes a Maximum-Minimum protocol that allows distributed detection of convergence in finite time for consensus algorithms under dynamic network topologies.

Findings

Global maximum and minimum values are strictly monotonic even with changing topology.

Each node can access global max and min values using the proposed protocol.

The method is validated through experiments with NodeJS socket.io servers.

Abstract

In this article, we present a finite time stopping criterion for consensus algorithms in networks with dynamic communication topology. Recent results provide asymptotic convergence to the consensus algorithm. However, the asymptotic convergence of these algorithms pose a challenge in the practical settings where the response from agents is required in finite time. To this end, we propose a Maximum-Minimum protocol which propagates the global maximum and minimum values of agent states (while running consensus algorithm) in the network. We establish that global maximum and minimum values are strictly monotonic even for a dynamic topology and can be utilized to distributively ascertain the closeness to convergence in finite time. We show that each node can have access to the global maximum and minimum by running the proposed Maximum-Minimum protocol and use it as a finite time stopping criterion for the otherwise asymptotic consensus algorithm. The practical utility of the algorithm is illustrated through experiments where each agent is instantiated by a NodeJS socket.io server.