An ADMM algorithm for matrix completion of partially known state covariances

Fu Lin, Mihailo R. Jovanović, Tryphon T. Georgiou

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Scopus citations


We study the inverse problem of reproducing partially known second-order statistics of a linear time invariant system by the least number of possible input disturbance channels. This can be formulated as a rank minimization problem, and for its solution, we employ a convex relaxation based on the nuclear norm. The resulting optimization problem can be cast as a semi-definite program and solved efficiently using generalpurpose solvers for small- And medium-size problems. In this paper, we focus on issues and techniques that are pertinent to large-scale systems. We bring in a re-parameterization which transforms the problem into a form suitable for the alternating direction method of multipliers. Furthermore, we show that each iteration of this algorithm amounts to solving a system of linear equations, an eigenvalue decomposition, and a singular value thresholding. An illustrative example is provided to demonstrate the effectiveness of the developed approach.

Original languageEnglish (US)
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Print)9781467357173
StatePublished - 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: Dec 10 2013Dec 13 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0743-1546
ISSN (Electronic)2576-2370


Other52nd IEEE Conference on Decision and Control, CDC 2013


  • Alternating direction method of multipliers
  • Convex optimization
  • Low-rank approximation
  • Nuclear norm regularization
  • Singular value thresholding
  • State covariances
  • Structured matrix completion problems


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