Decentralized Estimation of Laplacian Eigenvalues in Multi-Agent Systems

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.