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  Model Reduction of Controlled Fokker-Planck and Liouville-von Neumann Equations

Benner, P., Breiten, T., Hartmann, C., & Schmidt, B. (2020). Model Reduction of Controlled Fokker-Planck and Liouville-von Neumann Equations. Journal of Computational Dynamics, 7(1), 1-33. doi:10.3934/jcd.2020001.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-002E-73A7-B Version Permalink: https://hdl.handle.net/21.11116/0000-0006-E7B1-D
Genre: Journal Article

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 Creators:
Benner, Peter1, Author           
Breiten, Tobias2, Author
Hartmann, Carsten3, Author
Schmidt, Burkhard4, Author
Affiliations:
1Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society, ou_1738141              
2Institut für Mathematik, Karl-Franzens-Universität, Graz, Austria, ou_persistent22              
3Institut für Mathematik, Brandenburgische Technische Universität, Cottbus, Germany, ou_persistent22              
4Institut für Mathematik, Freie Universität Berlin, Berlin, Germany, ou_persistent22              

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Free keywords: Mathematics, Numerical Analysis, math.NA
 Abstract: Model reduction methods for bilinear control systems are compared by means of
practical examples of Liouville-von Neumann and Fokker--Planck type. Methods
based on balancing generalized system Gramians and on minimizing an H2-type
cost functional are considered. The focus is on the numerical implementation
and a thorough comparison of the methods. Structure and stability preservation
are investigated, and the competitiveness of the approaches is shown for
practically relevant, large-scale examples.

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 Dates: 2020
 Publication Status: Issued
 Pages: -
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 Rev. Type: Peer
 Identifiers: DOI: 10.3934/jcd.2020001
URI: http://arxiv.org/abs/1706.09882
arXiv: 1706.09882
Other: pubdata_escidoc:2473904
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Title: Journal of Computational Dynamics
Source Genre: Journal
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Pages: - Volume / Issue: 7 (1) Sequence Number: - Start / End Page: 1 - 33 Identifier: -