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Optimization Algorithms for System Analysis and Identification
Linköping University, Department of Electrical Engineering, Automatic Control. Linköping University, The Institute of Technology.
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.
Series
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 919
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:liu:diva-98177ISBN: 91-85297-19-4 (print)OAI: oai:DiVA.org:liu-98177DiVA: diva2:652393
Public defence
2005-01-14, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (English)
Supervisors
Funder
Swedish Research Council
Available from: 2013-10-09 Created: 2013-09-30 Last updated: 2013-10-09Bibliographically approved
List of papers
1. Comparison of Two Structure-Exploiting Optimization Algorithms for Integral Quadratic Constraints
Open this publication in new window or tab >>Comparison of Two Structure-Exploiting Optimization Algorithms for Integral Quadratic Constraints
2003 (English)In: Proceedings of the 4th IFAC symposium on Robust Control Design, 2003Conference paper, Published paper (Refereed)
Abstract [en]

As the semidefinite programs that result from integral quadratic contstraints are usually large it is important to implement efficient algorithms. The interior-point algorithms in this paper are primal-dual potential reduction methods and handle multiple constraints. Two approaches are made. For the first approach the computational cost is dominated by a least-squares problem that has to be solved in each iteration. The least squares problem is solved using an iterative method, namely the conjugate gradient method. The computational effort for the second approach is dominated by forming a linear system of equations. This systems of equations is used to compute the search direction in each iteration. If the number of variables are reduced by solving a smaller subproblem the resulting system has a very nice structure and can be solved efficiently. The first approach is more efficient for larger problems but is not as numerically stable.

Keyword
Interior-point algorithms, Semidefinite programs, Integral quadratic constraints
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-90286 (URN)9780080440125 (ISBN)
Conference
4th IFAC symposium on Robust Control Design, Milan, Italy, June, 2003
Funder
Swedish Research Council, 271-2000-770
Available from: 2013-04-02 Created: 2013-03-24 Last updated: 2013-10-09
2. KYPD: A Solver for Semidefinite Programs Derived from the Kalman-Yakubovich-Popov Lemma
Open this publication in new window or tab >>KYPD: A Solver for Semidefinite Programs Derived from the Kalman-Yakubovich-Popov Lemma
2004 (English)In: Proceedings of the 2004 IEEE International Symposium on Computer Aided Control System Design, 2004, 1-6 p.Conference paper, Published paper (Refereed)
Abstract [en]

Semidenite programs derived from the Kalman-Yakubovich-Popov lemma are quite common in control and signal processing applications. The programs are often of high dimension making them hard or impossible to solve with general-purpose solvers. KYPD is a customized solver for KYP-SDPs that utilizes the inherent structure of the optimization problem thus improving efficiency signicantly.

Keyword
Semidefinite programming, Kalman-Yakubovich-Popov lemma
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-24089 (URN)10.1109/CACSD.2004.1393841 (DOI)3655 (Local ID)0-7803-8636-1 (ISBN)3655 (Archive number)3655 (OAI)
Conference
2004 IEEE International Symposium on Computer Aided Control System Design, Taipei, Taiwan, September, 2004
Available from: 2009-10-07 Created: 2009-10-07 Last updated: 2013-10-09
3. A Decomposition Approach for Solving KYP-SDPs
Open this publication in new window or tab >>A Decomposition Approach for Solving KYP-SDPs
2005 (English)In: Proceedings of the 16th IFAC World Congress, 2005, 1021-1021 p.Conference paper, Published 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.

Keyword
Optimization, Decomposition methods, Robust control
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-36970 (URN)10.3182/20050703-6-CZ-1902.01022 (DOI)33173 (Local ID)978-3-902661-75-3 (ISBN)33173 (Archive number)33173 (OAI)
Conference
16th IFAC World Congress, Prague, Czech Republic, July, 2005
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2013-10-09
4. An Iterative Method for Identification of ARX Models from Incomplete Data
Open this publication in new window or tab >>An Iterative Method for Identification of ARX Models from Incomplete Data
2000 (English)In: Proceedings of the 39th IEEE Conference on Decision and Control, IEEE , 2000, 203-208 vol.1 p.Conference paper, Published paper (Refereed)
Abstract [en]

This paper describes a very simple and intuitive algorithm to estimate parameters of ARX models from incomplete data sets. An iterative scheme involving two least squares steps and a bias correction is all that is needed.

Place, publisher, year, edition, pages
IEEE, 2000
Keyword
Autoregressive processes, Iterative methods, Least squares approximations, Parameter estimation
National Category
Engineering and Technology Control Engineering
Identifiers
urn:nbn:se:liu:diva-90788 (URN)10.1109/CDC.2000.912759 (DOI)0-7803-6638-7 (ISBN)
Conference
39th IEEE Conference on Decision and Control, Sydney, Australia, 12-15 December, 2000
Available from: 2013-04-16 Created: 2013-04-07 Last updated: 2014-12-15

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