| Zeit: | 7. Februar 2023 |
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Prof. Kanat Camlibel
Bernoulli Institute for Mathematics, Computer Science, and Artificial Intelligence
University of Groningen
Groningen, Netherlands
Tuesday 2023-02-07 4 p.m.
IST Seminar Room 2.255 - Pfaffenwaldring 9 - Campus Stuttgart-Vaihingen
Abstract
This talk focuses on a data-driven model reduction approach on the basis of noisy data. Firstly, the concept of data reduction is introduced. In particular, we show that the set of reduced-order models obtained by applying a Petrov-Galerkin projection to all systems explaining the data characterized in a large-dimensional quadratic matrix inequality (QMI) can again be characterized in a lower-dimensional QMI. Next, we develop a data-driven generalized balanced truncation method that relies on two steps. First, we provide necessary and sufficient conditions such that systems explaining the data have common generalized Gramians. Second, these common generalized Gramians are used to construct projection matrices that allow to characterize a class of reduced-order models via generalized balanced truncation in terms of a lower-dimensional QMI by applying the data reduction concept. Additionally, we present alternative procedures to compute a priori and a posteriori upper bounds with respect to the true system generating the data.
Biographical Information
Kanat Camlibel received the Ph.D. degree in mathematical theory of systems and control from Tilburg University in 2001. From 2001 to 2005, he held post-doctoral positions at the University of Groningen and Tilburg University. Between 2005 and 2007, he was an assistant professor at Eindhoven University of Technology. In 2007, he joined the University of Groningen where he is currently a full professor at the Bernoulli Institute for Mathematics, Computer Science, and Artificial Intelligence. His research interests include differential variational inequalities, complementarity problems, optimization, piecewise affine dynamical systems, switched linear systems, constrained linear systems, multi-agent systems, model reduction, geometric theory of linear systems, and data-driven control. Dr. Camlibel is an associate editor of the IEEE Transactions on Automatic Control, and is the past associate editor of International Journal of Robust and Nonlinear Control, SIAM Journal on Control and Optimization, and Systems and Control Letters.