Decentralized Laplacian eigenvalues estimation for networked multi-agent systems

Abstract

In this paper we present a novel decentralized algorithm to estimate the eigenvalues of the Laplacian of the network topology of a multi-agent system. The basic idea is to provide a local interaction rule among agents so that their state oscillates only at frequencies corresponding to eigenvalues of the network topology. In this way, the problem of decentralized eigenvalue estimation is mapped into a problem of signal processing, solvable by applying the fast Fourier transform (FFT).