Design of optimal sparse interconnection graphs for synchronization of oscillator networks

Makan Fardad, Fu Lin, Mihailo R. Jovanovic

Research output: Contribution to journalArticlepeer-review

72 Scopus citations


We study the optimal design of a conductance network as a means for synchronizing a given set of oscillators. Synchronization is achieved when all oscillator voltages reach consensus, and performance is quantified by the mean-square deviation from the consensus value. We formulate optimization problems that address the tradeoff between synchronization performance and the number and strength of oscillator couplings. We promote the sparsity of the coupling network by penalizing the number of interconnection links. For identical oscillators, we establish convexity of the optimization problem and demonstrate that the design problem can be formulated as a semidefinite program. Finally, for special classes of oscillator networks we derive explicit analytical expressions for the optimal conductance values.

Original languageEnglish (US)
Article number6716960
Pages (from-to)2457-2462
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number9
StatePublished - Sep 2014


  • Consensus
  • convex relaxation
  • optimization
  • oscillator synchronization
  • semidefinite programming
  • sparse graph

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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