A Distributed Solution to the Network Reconstruction Problem

Fabio Morbidi 1 Alain Y. Kibangou 1
1 NECS - Networked Controlled Systems
Inria Grenoble - Rhône-Alpes, GIPSA-DA - Département Automatique
Abstract : It has been recently shown in Ren et al. (2010) that by collecting noise-contaminated time series generated by a coupled-oscillator system at each node of a network, it is possible to robustly reconstruct its topology, i.e. determine the graph Laplacian. Restricting ourselves to linear consensus dynamics over undirected communication networks, in this paper we introduce a new dynamic average consensus least-squares algorithm to locally estimate these time series at each node, thus making the reconstruction process fully distributed and more easily applicable in the real world. We also propose a novel efficient method for separating the off-diagonal entries of the reconstructed Laplacian, and examine several concepts related to the trace of the dynamic correlation matrix of the coupled single integrators, which is a distinctive element of our network reconstruction method. The theory is illustrated with examples from computer, power and transportation systems.
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Fabio Morbidi, Alain Y. Kibangou. A Distributed Solution to the Network Reconstruction Problem. Systems and Control Letters, Elsevier, 2014, 70, pp.85-91. ⟨10.1016/j.sysconle.2014.05.008⟩. ⟨hal-01001828⟩

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