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

Benner, Peter; Breiten, Tobias; Hartmann, Carsten; Schmidt, Burkhard

doi:10.3934/jcd.2020001

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

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Benner, Peter
Computational Methods in Systems and Control Theory, Max Planck Institute for Dynamics of Complex Technical Systems, Max Planck Society;

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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.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002E-73A7-B

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.