A quadratic programming approach for solving the ℓ1 multiblock problem

Nicola Elia, Munther A. Dahleh

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


The authors present a new method to compute solutions to the general multiblock ℓ1 control problem. The method is based on solving a standard H2 problem and a finite-dimensional semidefinite quadratic programming problem of appropriate dimension. The new method has most of the properties that separately characterize many existing approaches, in particular, as the dimension of the quadratic programming problem increases, this method provides converging upper and lower bounds on the optimal ℓ1 norm and, for well posed multiblock problems, ensures the convergence in norm of the suboptimal solutions to an optimal ℓ1 solution. The new method does not require the computation of the interpolation conditions, and it allows the direct computation of the suboptimal controller.

Original languageEnglish (US)
Pages (from-to)1242-1252
Number of pages11
JournalIEEE Transactions on Automatic Control
Issue number9
StatePublished - 1998
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received March 20, 1996; revised November 11, 1997. Recommended by Associate Editor, J. Shamma. This work was supported by the NSF under Grant 9157306-ECS, Draper Laboratory under Grant DL-H-441636, and AFOSR under Grant F49620-95-0219.


  • Computational methods
  • Optimal control
  • Quadratic programming
  • ℓ control


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