Interpolatory model reduction of parameterized bilinear dynamical systems

Interpolatory projection methods for model reduction of nonparametric linear dynamical systems have been successfully extended to nonparametric bilinear dynamical systems. However, this has not yet occurred for parametric bilinear systems. In this work, we aim to close this gap by providing a natura...

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Bibliographic Details
Published in:Advances in computational mathematics 2018-12, Vol.44 (6), p.1887-1916
Main Authors: Carracedo Rodriguez, Andrea, Gugercin, Serkan, Borggaard, Jeff
Format: Article
Language:English
Subjects:
Computational mathematics
Computational Mathematics and Numerical Analysis
Computational Science and Engineering
Dynamical systems
Interpolation
Mathematical and Computational Biology
Mathematical Modeling and Industrial Mathematics
Mathematical models
Mathematics
Mathematics and Statistics
Model reduction
Parameter sensitivity
Projection
Reduced order models
Subspaces
Transfer functions
Visualization
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Summary:Interpolatory projection methods for model reduction of nonparametric linear dynamical systems have been successfully extended to nonparametric bilinear dynamical systems. However, this has not yet occurred for parametric bilinear systems. In this work, we aim to close this gap by providing a natural extension of interpolatory projections to model reduction of parametric bilinear dynamical systems. We introduce necessary conditions that the projection subspaces must satisfy to obtain parametric tangential interpolation of each subsystem transfer function. These conditions also guarantee that the parameter sensitivities (Jacobian) of each subsystem transfer function are matched tangentially by those of the corresponding reduced-order model transfer function. Similarly, we obtain conditions for interpolating the parameter Hessian of the transfer function by including additional vectors in the projection subspaces. As in the parametric linear case, the basis construction for two-sided projections does not require computing the Jacobian or the Hessian.
ISSN:1019-7168
1572-9044
DOI:10.1007/s10444-018-9611-y