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

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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.

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Acknowledgments

The first author gratefully acknowledges the support provided by the U.S. Air Force Research Laboratory (AFRL) Summer Faculty Fellowship Program (SFFP).

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Authors and Affiliations

  1. New Mexico State University, P.O. Box 30001, MSC 4230, Las Cruces, NM, 88003, USA

    Alla Kammerdiner

  2. Air Force Research Laboratory, Munitions Directorate, 101 West Eglin Boulevard, Eglin AFB, FL, 32542, USA

    Alexander Veremyev & Eduardo Pasiliao

Authors
  1. Alla Kammerdiner
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  2. Alexander Veremyev
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  3. Eduardo Pasiliao
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Correspondence to Alla Kammerdiner.

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Kammerdiner, A., Veremyev, A. & Pasiliao, E. On Laplacian spectra of parametric families of closely connected networks with application to cooperative control. J Glob Optim 67, 187–205 (2017). https://doi.org/10.1007/s10898-016-0406-8

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  • DOI: https://doi.org/10.1007/s10898-016-0406-8

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