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A Decomposition Algorithm for KYP-SDPs
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2009 (English)In: Proceedings of the 10th European Control Conference (ECC), 2009, 3202-3207 p.Conference paper (Refereed)
Abstract [en]

In this paper, a structure exploiting algorithm for semidefinite programs derived from the Kalman-Yakubovich-Popov lemma, where some of the constraints appear as complicating constraints is presented. A decomposition algorithm is proposed, where the structure of the problem can be utilized. In a numerical example, where a controller that minimizes the sum of the H2-norm and the H-norm is designed, the algorithm is shown to be faster than SeDuMi and the special purpose solver KYPD.

Place, publisher, year, edition, pages
2009. 3202-3207 p.
Keyword [en]
Optimization, Optimization Algorithms
National Category
Computational Mathematics Engineering and Technology Control Engineering
URN: urn:nbn:se:liu:diva-21937DOI: 10.3166/EJC.18.249-256OAI: diva2:242267
10th European Control Conference (ECC), Budapest, Hungary, August, 2009
Available from: 2009-10-07 Created: 2009-10-06 Last updated: 2013-10-09
In thesis
1. Structure Exploitation in Semidefinite Programming for Control
Open this publication in new window or tab >>Structure Exploitation in Semidefinite Programming for Control
2010 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Many control problems can be cast as semidefinite programs. However, since the size of these problems grow quite quickly, the computational time to solve them can be quite substantial. In order to reduce the computational time, many proposals of how to tailormake algorithms to various types of control problems can be found in the literature. In this thesis, two papers with similar ambitions are presented.

The first paper deals with the case where the constraints of the optimization problem are of the type that stems from the Kalman-Yakubovic-Popov lemma, and where some of these constraints are so called complicating constraints. This means the optimization problem will be greatly simplified if these constraints were not present. By the use of Lagrangian relaxation, the optimization problem is decomposed into smaller ones, which can be solved independently of each other. Computational results show that for some classes of problems, this algorithm can reduce the computational time compared to using a solver which does not take into account the nature of the complicating constraints.

In the second paper, the fact that many control-related semidefinite programs have matrix-valued variables is utilized to speed up computations. This implies that the corresponding basis matrices have a certain low-rank structure which can be exploited when formulating the equations for the search directions, something that was discovered in the 90s and is implemented in LMI Lab. However, much has happened in the area of semidefinite programming since the release of LMI Lab, and new, faster algorithms have been developed. However, the idea of using the lowrank structure in the basis matrices can still be used. We implement this, using the publicly available solver SDPT3 in combination with our code for formulating the system of equations for the search directions. In order to facilitate for potential users, we also describe how the modeling language YALMIP is changed so that this lowrank structure can be tracked, and how the code can be easily interfaced. Computational results show that the computational time is decreased.

Place, publisher, year, edition, pages
Linköping: Linköping University, 2010. 58 p.
Linköping Studies in Science and Technology. Thesis, ISSN 0280-7971 ; 1430
National Category
Control Engineering
urn:nbn:se:liu:diva-98178 (URN)LiU-TEK-LIC-2010:1 (Local ID)978-91-7393-441-1 (ISBN)LiU-TEK-LIC-2010:1 (Archive number)LiU-TEK-LIC-2010:1 (OAI)
Available from: 2013-10-09 Created: 2013-09-30 Last updated: 2013-10-09Bibliographically approved

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