Decentralized estimation of Laplacian eigenvalues in multi-agent systems

Authors:
Mauro Franceschelli;Andrea Gasparri;Alessandro Giua;Carla Seatzu
Affiliations:
Department of Electrical and Electronic Engineering, University of Cagliari, Piazza D'Armi, 09123 Cagliari, Italy;Department of Engineering, University of Rome "Roma Tre", Via Vasca Navale 79, 00146 Roma, Italy;Department of Electrical and Electronic Engineering, University of Cagliari, Piazza D'Armi, 09123 Cagliari, Italy and LSIS, University of Aix-Marseille, Marseille, France;Department of Electrical and Electronic Engineering, University of Cagliari, Piazza D'Armi, 09123 Cagliari, Italy
Venue:
Automatica (Journal of IFAC)
Year:
2013

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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.