On the optimal synchronization of oscillator networks via sparse interconnection graphs

Makan Fardad, Fu Lin, Mihailo R. Jovanovic

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

We study the optimal design of a conductance network as a means for synchronizing a given set of oscillators. By considering the conductance that connects two oscillators as the measure of the amount of communication between them, we formulate an optimal control problem that addresses the trade-off between synchronization performance and communication. Additionally, we promote the sparsity of the network by penalizing the number of interconnection links. For identical oscillators, we establish convexity and show that the design problem can be formulated as a semidefinite program. For non-identical oscillators, that can be considered as perturbations around a central (average) oscillator, we show that it is meaningful to design an optimal conductance network by assuming that all oscillators are identical to the central oscillator. Finally, for special classes of oscillator networks we derive explicit formulas for the optimal conductance values.

Original languageEnglish (US)
Title of host publication2012 American Control Conference, ACC 2012
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages4777-4782
Number of pages6
ISBN (Print)9781457710957
DOIs
StatePublished - 2012
Event2012 American Control Conference, ACC 2012 - Montreal, QC, Canada
Duration: Jun 27 2012Jun 29 2012

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2012 American Control Conference, ACC 2012
CountryCanada
CityMontreal, QC
Period6/27/126/29/12

Keywords

  • Convex relaxation
  • optimization
  • oscillator synchronization
  • semidefinite programming
  • sparse communication architecture

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    Fardad, M., Lin, F., & Jovanovic, M. R. (2012). On the optimal synchronization of oscillator networks via sparse interconnection graphs. In 2012 American Control Conference, ACC 2012 (pp. 4777-4782). [6315116] (Proceedings of the American Control Conference). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/acc.2012.6315116