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Inhalt des Dokuments

Absolventen-Seminar • Numerische Mathematik

Dieses Semester wird das Seminar online auf Zoom stattfinden.

Absolventen-Seminar
Verantwortliche Dozenten:
Prof. Dr. Tobias BreitenProf. Dr. Christian MehlProf. Dr. Volker Mehrmann
Koordination:
Ines Ahrens
Termine:
Do 10:00-12:00
Inhalt:
Vorträge von Bachelor- und Masterstudenten, Doktoranden, Postdocs und manchmal auch Gästen zu aktuellen Forschungsthemen
Wintersemester 2020/2021 Vorläufige Terminplanung
Datum
Zeit
Vortragende(r)
Titel
Do 05.11.
10:15 Uhr
Vorbesprechung
Tim Moser
A Riemannian Framework for Ecient H2-Optimal Model
Reduction of Port-Hamiltonian Systems

Do 12.11.
10:15 Uhr
Do 19.11.
10:15 Uhr
Volker Mehrmann
Do 26.11.
10:15 Uhr
Do 03.12.
10:15 Uhr
Felix Black
Do 10.12.
10:15 Uhr
Amon Lahr
Do 17.12.
10:15 Uhr
Florian Stelzer
Do 07.01.
10:15 Uhr
Tobias Breiten
Do 14.01.
10:15 Uhr
Ines Ahrens
Do 21.01.
10:15 Uhr
Riccardo Morandin
Ruili Zhang
Do 28.01.
10:15 Uhr
Onkar Jadhav
Philipp Krah
Do 04.02.
10:15 Uhr
Paul Schwerdtner
Simon Bäse
Do 11.02.
10:15 Uhr
Marine Froidevaux
Do 18.02.
10:15 Uhr
Philipp Schulze
Do 25.02.
10:15 Uhr
Christoph Zimmer

Tim Moser (TU München)

Donnerstag, 05. November 2020

A Riemannian Framework for Ecient H2-Optimal Model Reduction of Port-Hamiltonian Systems

The port-Hamiltonian systems paradigm provides a powerful framework for the network modeling of multi-physics systems. By exploiting inherent system characteristics such as passivity, the modeling in port-Hamiltonian form also facilitates the subsequent controller design. Therefore it is advantageous to preserve the port-Hamiltonian structure in the model reduction process for which different approaches have been proposed (see e.g. [1], [2]).

In [1], a modified version of the iterative rational Krylov algorithm (IRKA-PH) was proposed for the H2-optimal model reduction of port-Hamilonian systems. Since IRKA-PH is based on Petrov-Galerkin projections, certain degrees of freedom must be given up in order to preserve the port-Hamiltonian structure. This inevitably leads to the fact that it is generally not possible to satisfy all necessary H2- optimality conditions in this projective framework.

We address this issue and propose a novel Riemannian framework for the H2-optimal reduction of port-Hamiltonian systems. We incorporate geometric constraints using the Riemannian problem formulation of [3] and exploit the computationally efficient pole-residue formulation of the H2-error proposed in [4]. By this means, preservation of the port-Hamiltonian structure and H2-optimality upon convergence are guaranteed and the framework is also accessible for the reduction of large-scale systems.

References
[1] S. Gugercin, R. V. Polyuga, C. Beattie, and A. van der Schaft, "Structure-preserving tangential interpolation for model reduction of port-Hamiltonian systems," Automatica, vol. 48, no. 9, pp. 1963-1974, 2012.
[2] R. V. Polyuga and A. J. van der Schaft, "Effort- and flow-constraint reduction methods for structure preserving model reduction of port-Hamiltonian systems," Systems & Control Letters, vol. 61, no. 3, pp. 412-421, 2012.
[3] K. Sato, "Riemannian optimal model reduction of linear port-Hamiltonian systems," Automatica, vol. 93, pp. 428-434, 2018.
[4] L. Meier and D. Luenberger, "Approximation of linear constant systems," IEEE Transactions on Automatic Control, vol. 12, no. 5, pp. 585-588, 1967.

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