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Since 2009 DISC organizes a Winter Course, lectured by an international guest lecturer on a particular topic or research field relevant for systems and control. The course is typically scheduled in February and can be organized in one or more university locations. In 2009 Prof. Roberto Tempo lectured on "Probabilistic and Randomization Methods for Control of Uncertain Systems". This year Prof. Thanos Antoulas (Rice University) will teach a DISC winter course on Model reduction. Please make a reservation in your calendar for the week of February 22, 2010.
Abstract
At first, we will present an overview of the model reduction area stressing both the theoretical and the application sides. The main reduction methodologies will be classified in four categories: (i) SVD, (ii) Krylov, (iii) iterative and (iv) reduction from measurements.
The detailed technical part starts with an overview of linear dynamical systems, and the associated convolution and Hankel operators. The singular values of the latter turn out to be of central importance. The solution of the closely related Lyapunov matrix equation will be discussed in detail. This sets the stage for the introduction of balanced truncation, a reduction method in the SVD category. The related, and in some fields very popular, POD (Proper Orthogonal Decomposition) method will also be briefly explored. Next, we will focus attention on Krylov reduction methods, including the Lanczos and Arnoldi procedures. It will be shown that as far as the reduction problem is concerned, their main property is the matching of moments of the original system at various points in the complex plain. In general, these are rational Krylov methods and are equivalent to rational interpolation. Optimal reduction in the H2 sense for instance, falls under this category. The next chapter will explore iterative methods, which seek to combine the best attributes of the SVD and the Krylov reduction approaches.
Finally, we will investigate non-intrusive reduction methods, that is, methods of constructing (models and) reduced models without detailed knowledge of the inner workings of the process under investigation. We will assume instead, that input/output measurements are available. The main tool in this case is the Loewner-shifed Loewner matrix pencil.
Throughout, the various concepts encountered will be illustrated with examples and followed by homework assignments designed to enhance their understanding.
Date and Location
February 22-24, 2010 at the University of Groningen, The Netherlands. The course will be taught in 3 days of 4 hours lecturing and 3 hours assignment. Starting time first day will be at 9.30.
Registration and fee
Registration fee for taking or auditing a full course is € 450. This fee is waived for DISC members. The registration form is available on the DISC website.
Credits
For attending the DISC Winter Course you can obtain 1 credit.
Suggestion for hotels (not included)
University Guest House
Asgard Hotel
Eden City Hotel
Martini Hotel
Further information
Contact the organizer Jacquelien Scherpen (
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) or the DISC secretariat (
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).
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