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Interpolatory model reduction of parameterized bilinear dynamical systems

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Abstract

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.

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Acknowledgments

Supported in part by the National Science Foundation under contract DMS–1522616 and the National Institute for Occupational Safety and Health under contract 200-2014-59669. The work of Gugercin was also supported in part by the Alexander von Humboldt Foundation.

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Authors and Affiliations

  1. Department of Mathematics, Virginia Tech, Blacksburg, VA, 24061-0123, USA

    Andrea Carracedo Rodriguez, Serkan Gugercin & Jeff Borggaard

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  1. Andrea Carracedo Rodriguez
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  2. Serkan Gugercin
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  3. Jeff Borggaard
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Correspondence to Andrea Carracedo Rodriguez.

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Communicated by: Peter Benner

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Carracedo Rodriguez, A., Gugercin, S. & Borggaard, J. Interpolatory model reduction of parameterized bilinear dynamical systems. Adv Comput Math 44, 1887–1916 (2018). https://doi.org/10.1007/s10444-018-9611-y

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  • DOI: https://doi.org/10.1007/s10444-018-9611-y

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