Journal of Global Optimization

, Volume 67, Issue 1–2, pp 187–205 | Cite as

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

  • Alla Kammerdiner
  • Alexander Veremyev
  • Eduardo Pasiliao
Article

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 

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Alla Kammerdiner
    • 1
  • Alexander Veremyev
    • 2
  • Eduardo Pasiliao
    • 2
  1. 1.New Mexico State UniversityLas CrucesUSA
  2. 2.Air Force Research LaboratoryMunitions DirectorateEglin AFBUSA

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