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arXiv · 1206.4509

Decentralized Estimation of Laplacian Eigenvalues in Multi-Agent Systems

Mauro Franceschelli·Andrea Gasparri·Alessandro Giua·Carla Seatzu
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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.

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Mauro Franceschelli, Andrea Gasparri, Alessandro Giua, Carla Seatzu. 2012-06-20. Decentralized Estimation of Laplacian Eigenvalues in Multi-Agent Systems. https://arxiv.org/abs/1206.4509

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