Scaling laws for consensus protocols subject to noise

TL;DR

This paper analyzes how additive noise affects discrete-time consensus protocols, providing exact formulas for steady-state disagreement and linking noise robustness to graph properties like the Kemeny constant.

Contribution

It introduces a precise characterization of noise impact on consensus protocols using Markov chain theory and graph metrics, advancing understanding of robustness in formation control.

Findings

Exact expression for steady-state disagreement in reversible Markov chain-based protocols.

Connection between noise robustness and the Kemeny constant of the underlying graph.

Framework for analyzing formation control protocols under noise.

Abstract

We study the performance of discrete-time consensus protocols in the presence of additive noise. When the consensus dynamic corresponds to a reversible Markov chain, we give an exact expression for a weighted version of steady-state disagreement in terms of the stationary distribution and hitting times in an underlying graph. We then show how this result can be used to characterize the noise robustness of a class of protocols for formation control in terms of the Kemeny constant of an underlying graph.