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

Author

Listed:
  • Alla Kammerdiner

    (New Mexico State University)

  • Alexander Veremyev

    (Munitions Directorate)

  • Eduardo Pasiliao

    (Munitions Directorate)

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.

Suggested Citation

  • Alla Kammerdiner & Alexander Veremyev & Eduardo Pasiliao, 2017. "On Laplacian spectra of parametric families of closely connected networks with application to cooperative control," Journal of Global Optimization, Springer, vol. 67(1), pages 187-205, January.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:1:d:10.1007_s10898-016-0406-8
    DOI: 10.1007/s10898-016-0406-8
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    References listed on IDEAS

    as
    1. Shenglong Hu & Liqun Qi, 2015. "The Laplacian of a uniform hypergraph," Journal of Combinatorial Optimization, Springer, vol. 29(2), pages 331-366, February.
    2. Alexander Veremyev & Vladimir Boginski & Eduardo Pasiliao, 2015. "Analytical characterizations of some classes of optimal strongly attack-tolerant networks and their Laplacian spectra," Journal of Global Optimization, Springer, vol. 61(1), pages 109-138, January.
    Full references (including those not matched with items on IDEAS)

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