Sparse estimation of Laplacian eigenvalues in multiagent networks

TL;DR

This paper introduces a scalable method to estimate observable Laplacian eigenvalues in unknown multiagent networks using limited measurements, applicable to various dynamics and verified through simulations.

Contribution

It presents a novel, scalable algorithm for exactly recovering observable Laplacian eigenvalues from agent measurements without prior network knowledge.

Findings

Algorithm accurately estimates observable eigenvalues

Applicable to continuous and discrete-time systems

Validated through numerical simulations

Abstract

We propose a method to efficiently estimate the Laplacian eigenvalues of an arbitrary, unknown network of interacting dynamical agents. The inputs to our estimation algorithm are measurements about the evolution of a collection of agents (potentially one) during a finite time horizon; notably, we do not require knowledge of which agents are contributing to our measurements. We propose a scalable algorithm to exactly recover a subset of the Laplacian eigenvalues from these measurements. These eigenvalues correspond directly to those Laplacian modes that are observable from our measurements. We show how our technique can be applied to networks of multiagent systems with arbitrary dynamics in both continuous- and discrete-time. Finally, we illustrate our results with numerical simulations.