Sparse quadratic regulator

Mihailo R. Jovanovic, Fu Lin

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

9 Scopus citations


We consider a control design problem aimed at balancing quadratic performance of linear systems with additional requirements on the control signal. These are introduced in order to obtain controls that are either sparse or infrequently changing in time. To achieve this objective, we augment a standard quadratic performance index with an additional term that penalizes either the ℓ1 norm or the total variation of the control signal. We show that the minimizer of this convex optimization problem can be found by solving a two point boundary value problem (TPBVP) with non-differentiable nonlinearities. Furthermore, we employ alternating direction method of multipliers to determine the optimal controller iteratively from a sequence of linear TPBVPs. Examples are provided to illustrate the developed method.

Original languageEnglish (US)
Title of host publication2013 European Control Conference, ECC 2013
PublisherIEEE Computer Society
Number of pages6
ISBN (Print)9783033039629
StatePublished - Jan 1 2013
Event2013 12th European Control Conference, ECC 2013 - Zurich, Switzerland
Duration: Jul 17 2013Jul 19 2013

Publication series

Name2013 European Control Conference, ECC 2013


Other2013 12th European Control Conference, ECC 2013


  • Alternating direction method of multipliers
  • convex optimization
  • linear time-invariant systems
  • quadratic performance
  • sparsity
  • total variation

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