Design of optimal sparse feedback gains via the alternating direction method of multipliers

Fu Lin, Makan Fardad, Mihailo R. Jovanovic

Research output: Contribution to journalArticlepeer-review

359 Scopus citations


We design sparse and block sparse feedback gains that minimize the variance amplification (i.e., the {\cal H}2 norm) of distributed systems. Our approach consists of two steps. First, we identify sparsity patterns of feedback gains by incorporating sparsity-promoting penalty functions into the optimal control 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, the sparsity structure of feedback gains is identified using the alternating direction method of multipliers, which is a powerful algorithm well-suited to large optimization problems. This method alternates between promoting the sparsity of the controller and optimizing the closed-loop performance, which allows us to exploit the structure of the corresponding objective functions. In particular, we take advantage of the separability of the sparsity-promoting penalty functions to decompose the minimization problem into sub-problems that can be solved analytically. Several examples are provided to illustrate the effectiveness of the developed approach.

Original languageEnglish (US)
Article number6497509
Pages (from-to)2426-2431
Number of pages6
JournalIEEE Transactions on Automatic Control
Issue number9
StatePublished - 2013


  • Alternating direction method of multipliers (ADMM)
  • \ell minimization
  • communication architectures
  • continuation methods
  • optimization
  • separable penalty functions
  • sparsity-promoting optimal control
  • structured distributed design

ASJC Scopus subject areas

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


Dive into the research topics of 'Design of optimal sparse feedback gains via the alternating direction method of multipliers'. Together they form a unique fingerprint.

Cite this