Exponential Consensus Formation in Time-Varying Multiagent Systems via Compactification Methods

TL;DR

This paper proves exponential convergence in multiagent systems with time-varying interactions using compactification techniques, under mild conditions on interaction graph properties.

Contribution

It introduces a novel approach employing compactification methods to establish exponential contraction results in multiagent systems.

Findings

Exponential contraction of diameter and variance is achieved.

Results hold under mild assumptions on interaction graph properties.

Applicable to systems with time-varying interaction graphs.

Abstract

In this article, we establish exponential contraction results for the diameter and variance of general first-order multiagent systems. Our approach is based on compactification techniques, and works under rather mild assumptions. Namely, we posit that either the scrambling coefficient, or the algebraic connectivity of the averaged interaction graphs of the system over all time windows of a given length are uniformly positive.