339 research outputs found
Model reduction of controlled Fokker--Planck and Liouville-von Neumann equations
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
A unifying framework for tangential interpolation of structured bilinear control systems
In this paper, we consider the structure-preserving model order reduction
problem for multi-input/multi-output bilinear control systems by tangential
interpolation. We propose a new type of tangential interpolation problem for
structured bilinear systems, for which we develop a new structure-preserving
interpolation framework. This new framework extends and generalizes different
formulations of tangential interpolation for bilinear systems from the
literature and also provides a unifying framework. We then derive explicit
conditions on the projection spaces to enforce tangential interpolation in
different settings, including conditions for tangential Hermite interpolation.
The analysis is illustrated by means of three numerical examples.Comment: 33 pages, 9 figure
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