Algorithms for leader selection in stochastically forced consensus networks

Fu Lin, Makan Fardad, Mihailo R. Jovanovic

Research output: Contribution to journalArticlepeer-review

110 Scopus citations


We are interested in assigning a pre-specified number of nodes as leaders in order to minimize the mean-square deviation from consensus in stochastically forced networks. This problem arises in several applications including control of vehicular formations and localization in sensor networks. For networks with leaders subject to noise, we show that the Boolean constraints (which indicate whether a node is a leader) are the only source of nonconvexity. By relaxing these constraints to their convex hull we obtain a lower bound on the global optimal value. We also use a simple but efficient greedy algorithm to identify leaders and to compute an upper bound. For networks with leaders that perfectly follow their desired trajectories, we identify an additional source of nonconvexity in the form of a rank constraint. Removal of the rank constraint and relaxation of the Boolean constraints yields a semidefinite program for which we develop a customized algorithm well-suited for large networks. Several examples ranging from regular lattices to random graphs are provided to illustrate the effectiveness of the developed algorithms.

Original languageEnglish (US)
Article number6780618
Pages (from-to)1789-1802
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number7
StatePublished - Jul 2014


  • Alternating direction method of multipliers (ADMMs)
  • consensus networks
  • convex optimization
  • convex relaxations
  • greedy algorithm
  • leader selection
  • performance bounds
  • semidefinite programming (SDP)
  • sensor selection
  • variance amplification

ASJC Scopus subject areas

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


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