On the optimality of sparse long-range links in circulant consensus networks

Research output: Chapter in Book/Entry/PoemConference contribution

5 Scopus citations


We consider spatially invariant consensus networks in which the link weights, the directed graph describing the interconnection topology, and the temporal dynamics, are all characterized by circulant matrices. We seek the best new links, subject to budget constraints, whose addition to the network maximally improves its rate of convergence to consensus. We show that the optimal circulant link creation problem is convex and can be written as a semidefinite program. Motivated by small-world networks, we apply the link creation problem to circulant networks which possess only local communication links. We observe that the optimal new links are always sparse and long-range, and have an increasingly pronounced effect on the convergence rate of the network as its size grows. To further investigate the properties of optimal links, we restrict attention to the creation of links with small strengths, which we refer to as weak links. We employ perturbation methods to reformulate the optimal weak link creation problem, and uncover conditions on the network architecture which guarantee sparse and long-range solutions to this optimization problem.

Original languageEnglish (US)
Title of host publicationACC 2015 - 2015 American Control Conference
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9781479986842
StatePublished - Jul 28 2015
Event2015 American Control Conference, ACC 2015 - Chicago, United States
Duration: Jul 1 2015Jul 3 2015

Publication series

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


Other2015 American Control Conference, ACC 2015
Country/TerritoryUnited States


  • Circulant matrices
  • consensus facilitation
  • convex optimization
  • link creation
  • long-range links
  • small-world networks
  • social networks
  • sparse interconnection topology
  • weak communication links

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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