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Optimization Algorithms for System Analysis and Identification
Linköpings universitet, Institutionen för systemteknik, Reglerteknik. Linköpings universitet, Tekniska högskolan.
2004 (Engelska)Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
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.

Ort, förlag, år, upplaga, sidor
Linköping: Linköping University , 2004. , s. 190
Serie
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 919
Nationell ämneskategori
Reglerteknik
Identifikatorer
URN: urn:nbn:se:liu:diva-98177ISBN: 91-85297-19-4 (tryckt)OAI: oai:DiVA.org:liu-98177DiVA, id: diva2:652393
Disputation
2005-01-14, Visionen, Hus B, Campus Valla, Linköpings universitet, Linköping, 10:15 (Engelska)
Handledare
Forskningsfinansiär
VetenskapsrådetTillgänglig från: 2013-10-09 Skapad: 2013-09-30 Senast uppdaterad: 2013-10-09Bibliografiskt granskad
Delarbeten
1. Comparison of Two Structure-Exploiting Optimization Algorithms for Integral Quadratic Constraints
Öppna denna publikation i ny flik eller fönster >>Comparison of Two Structure-Exploiting Optimization Algorithms for Integral Quadratic Constraints
2003 (Engelska)Ingår i: Proceedings of the 4th IFAC symposium on Robust Control Design, 2003Konferensbidrag, Publicerat paper (Refereegranskat)
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.

Nyckelord
Interior-point algorithms, Semidefinite programs, Integral quadratic constraints
Nationell ämneskategori
Teknik och teknologier Reglerteknik
Identifikatorer
urn:nbn:se:liu:diva-90286 (URN)9780080440125 (ISBN)
Konferens
4th IFAC symposium on Robust Control Design, Milan, Italy, June, 2003
Forskningsfinansiär
Vetenskapsrådet, 271-2000-770
Tillgänglig från: 2013-04-02 Skapad: 2013-03-24 Senast uppdaterad: 2013-10-09
2. KYPD: A Solver for Semidefinite Programs Derived from the Kalman-Yakubovich-Popov Lemma
Öppna denna publikation i ny flik eller fönster >>KYPD: A Solver for Semidefinite Programs Derived from the Kalman-Yakubovich-Popov Lemma
2004 (Engelska)Ingår i: Proceedings of the 2004 IEEE International Symposium on Computer Aided Control System Design, 2004, s. 1-6Konferensbidrag, Publicerat paper (Refereegranskat)
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.

Nyckelord
Semidefinite programming, Kalman-Yakubovich-Popov lemma
Nationell ämneskategori
Teknik och teknologier Reglerteknik
Identifikatorer
urn:nbn:se:liu:diva-24089 (URN)10.1109/CACSD.2004.1393841 (DOI)3655 (Lokalt ID)0-7803-8636-1 (ISBN)3655 (Arkivnummer)3655 (OAI)
Konferens
2004 IEEE International Symposium on Computer Aided Control System Design, Taipei, Taiwan, September, 2004
Tillgänglig från: 2009-10-07 Skapad: 2009-10-07 Senast uppdaterad: 2013-10-09
3. A Decomposition Approach for Solving KYP-SDPs
Öppna denna publikation i ny flik eller fönster >>A Decomposition Approach for Solving KYP-SDPs
2005 (Engelska)Ingår i: Proceedings of the 16th IFAC World Congress, 2005, s. 1021-1021Konferensbidrag, Publicerat paper (Refereegranskat)
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.

Nyckelord
Optimization, Decomposition methods, Robust control
Nationell ämneskategori
Teknik och teknologier Reglerteknik
Identifikatorer
urn:nbn:se:liu:diva-36970 (URN)10.3182/20050703-6-CZ-1902.01022 (DOI)33173 (Lokalt ID)978-3-902661-75-3 (ISBN)33173 (Arkivnummer)33173 (OAI)
Konferens
16th IFAC World Congress, Prague, Czech Republic, July, 2005
Tillgänglig från: 2009-10-10 Skapad: 2009-10-10 Senast uppdaterad: 2013-10-09
4. An Iterative Method for Identification of ARX Models from Incomplete Data
Öppna denna publikation i ny flik eller fönster >>An Iterative Method for Identification of ARX Models from Incomplete Data
2000 (Engelska)Ingår i: Proceedings of the 39th IEEE Conference on Decision and Control, IEEE , 2000, s. 203-208 vol.1Konferensbidrag, Publicerat paper (Refereegranskat)
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.

Ort, förlag, år, upplaga, sidor
IEEE, 2000
Nyckelord
Autoregressive processes, Iterative methods, Least squares approximations, Parameter estimation
Nationell ämneskategori
Teknik och teknologier Reglerteknik
Identifikatorer
urn:nbn:se:liu:diva-90788 (URN)10.1109/CDC.2000.912759 (DOI)0-7803-6638-7 (ISBN)
Konferens
39th IEEE Conference on Decision and Control, Sydney, Australia, 12-15 December, 2000
Tillgänglig från: 2013-04-16 Skapad: 2013-04-07 Senast uppdaterad: 2014-12-15

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