A quadratic programming approach for solving the ℓ1 multiblock problem

Nicola Elia; Munther A. Dahleh

doi:10.1109/9.718608

A quadratic programming approach for solving the ℓ₁ multiblock problem

Nicola Elia, Munther A. Dahleh

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	1242-1252
Number of pages	11
Journal	IEEE Transactions on Automatic Control
Volume	43
Issue number	9
DOIs	https://doi.org/10.1109/9.718608
State	Published - 1998
Externally published	Yes

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.

Keywords

Computational methods
Optimal control
Quadratic programming
ℓ control

Publisher link

10.1109/9.718608

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Cite this

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title = "A quadratic programming approach for solving the ℓ1 multiblock problem",

abstract = "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.",

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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.",

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N2 - 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.

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