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Comparison of Two Structure-Exploiting Optimization Algorithms for Integral Quadratic Constraints
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.
University of California, CA, USA.
2003 (English)In: Proceedings of the 4th IFAC symposium on Robust Control Design, 2003Conference 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.

Place, publisher, year, edition, pages
Keyword [en]
Interior-point algorithms, Semidefinite programs, Integral quadratic constraints
National Category
Engineering and Technology Control Engineering
URN: urn:nbn:se:liu:diva-90286ISBN: 9780080440125OAI: diva2:613768
4th IFAC symposium on Robust Control Design, Milan, Italy, June, 2003
Swedish Research Council, 271-2000-770
Available from: 2013-04-02 Created: 2013-03-24 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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