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A Decomposition Approach for Solving KYP-SDPs
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
University of Melbourne, Australia.
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
2005 (English)In: Proceedings of the 16th IFAC World Congress, 2005, 1021-1021 p.Conference paper (Refereed)
Abstract [en]

Semidefinite programs originating from the Kalman-Yakubovich-Popov lemma are convex optimization problems and there exist polynomial time algorithms that solve them. However, the number of variables is often very large making the computational time extremely long. Algorithms more efficient than general purpose solvers are thus needed. In this paper a generalized Benders decomposition algorithm is applied to the problem to improve efficiency.

Place, publisher, year, edition, pages
2005. 1021-1021 p.
Keyword [en]
Optimization, Decomposition methods, Robust control
National Category
Engineering and Technology Control Engineering
URN: urn:nbn:se:liu:diva-36970DOI: 10.3182/20050703-6-CZ-1902.01022Local ID: 33173ISBN: 978-3-902661-75-3OAI: diva2:257819
16th IFAC World Congress, Prague, Czech Republic, July, 2005
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-10-09
In thesis
1. Optimization Algorithms for System Analysis and Identification
Open this publication in new window or tab >>Optimization Algorithms for System Analysis and Identification
2004 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Optimization is a powerful and frequently used tool in many fields of research. In this thesis two relevant and important problems from robust control system analysis and system identification are solved using optimization algorithms.

Many of the most important examples of optimization in control and signal processing applications involve semidefinite programming with linear matrix inequality constraints derived from the Kalman-Yakubovich-Popov lemma. For realistic examples these semidefinite programs have a huge number of variables making them intractable for general purpose solvers. Three customized algorithms for this class of optimization problems are presented and compared to each other. Preprocessing of the semidefinite program that may improve numerical issues are discussed. This preprocessing also makes it possible to relax some assumptions usually made on the semidefinite program. Moreover, it is shown how to use the algorithms for other stability regions than the left half plane.

Even though missing data is quite common in many control and signal processing applications, most system identification algorithms do not address this phenomenon in a good way. This often results in parameter estimates with a large bias. In this thesis the maximum likelihood criterion for identication of Autoregressive models with an exogenous signal subject to missing data is investigated. Two algorithms for identifying the models are presented and are compared to the expectation maximization algorithm. From optimality conditions is computed estimates of the asymptotic variance of the parameter estimates. In addition, it is discussed how a criterion equivalent to the maximum likelihood criterion opens up the possibility to apply a wide range of other optimization algorithms to the estimation problem. It is also shown what property of the data it is that determines why one model is more likely to have produced the data than another. Finally, the multiple optima problem is addressed.

Place, publisher, year, edition, pages
Linköping: Linköping University, 2004. 190 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 919
National Category
Control Engineering
urn:nbn:se:liu:diva-98177 (URN)91-85297-19-4 (ISBN)
Public defence
2005-01-14, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Swedish Research Council
Available from: 2013-10-09 Created: 2013-09-30 Last updated: 2013-10-09Bibliographically approved

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