Decentralized Estimation of Laplacian Eigenvalues in Multi-Agent Systems

TL;DR

This paper introduces a decentralized algorithm enabling multi-agent systems to estimate the Laplacian eigenvalues of their network topology through local interactions, transforming the problem into a signal processing task.

Contribution

It proposes a novel local interaction rule that allows agents to estimate Laplacian eigenvalues without centralized coordination.

Findings

Algorithm accurately estimates eigenvalues in simulations

Method works for undirected graph topologies

Estimates are obtained through local agent interactions

Abstract

In this paper we present a decentralized algorithm to estimate the eigenvalues of the Laplacian matrix that encodes the network topology of a multi-agent system. We consider network topologies modeled by undirected graphs. The basic idea is to provide a local interaction rule among agents so that their state trajectory is a linear combination of sinusoids oscillating only at frequencies function of the eigenvalues of the Laplacian matrix. In this way, the problem of decentralized estimation of the eigenvalues is mapped into a standard signal processing problem in which the unknowns are the finite number of frequencies at which the signal oscillates.