Sparse feedback synthesis via the alternating direction method of multipliers

Fu Lin, Makan Fardad, Mihailo R. Jovanovic

Research output: Chapter in Book/Entry/PoemConference contribution

46 Scopus citations


We study the design of feedback gains that strike a balance between the H2 performance of distributed systems and the sparsity of controller. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsity-promoting penalty functions into the H2 problem, where the added terms penalize the number of communication links in the distributed controller. Second, we optimize feedback gains subject to structural constraints determined by the identified sparsity patterns. In the first step, we identify sparsity structure of feedback gains using the alternating direction method of multipliers, which is a powerful algorithm well-suited to large optimization problems. This method alternates between optimizing the sparsity and optimizing the closed-loop H2 norm, which allows us to exploit the structure of the corresponding objective functions. In particular, we take advantage of the separability of sparsity-promoting penalty functions to decompose the minimization problem into sub-problems that can be solved analytically. An example is provided to illustrate the effectiveness of the developed approach.

Original languageEnglish (US)
Title of host publication2012 American Control Conference, ACC 2012
Number of pages6
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


Other2012 American Control Conference, ACC 2012
CityMontreal, QC


  • Alternating direction method of multipliers
  • cardinality minimization
  • communication architectures
  • distributed systems
  • homotopy
  • l minimization
  • sparsity-promoting optimal control
  • sum-of-logs penalty

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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