On Laplacian spectra of parametric families of closely connected networks with application to cooperative control

Alla Kammerdiner (), Alexander Veremyev and Eduardo Pasiliao
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Alla Kammerdiner: New Mexico State University
Alexander Veremyev: Munitions Directorate
Eduardo Pasiliao: Munitions Directorate

Journal of Global Optimization, 2017, vol. 67, issue 1, No 9, 187-205

Abstract: Abstract In this paper, we introduce mathematical models for studying a supernetwork that is comprised of closely connected groups of subnetworks. For several related classes of such supernetworks, we explicitly derive an analytical representation of their Laplacian spectra. This work is motivated by an application of spectral graph theory in cooperative control of multi-agent networked systems. Specifically, we apply our graph-theoretic results to establish bounds on the speed of convergence and the communication time-delay for solving the average-consensus problem by a supernetwork of clusters of integrator agents.

Keywords: Supernetworks; Parametric families of graphs; Laplacian spectra; Average-consensus problem (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10898-016-0406-8

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