Interpolatory Model Reduction of Parameterized Bilinear Dynamical Systems
For engineers and scientists simulating large-scale parametric bilinear dynamical systems, this provides a novel method to reduce model complexity while preserving parameter-dependent behavior.
This work extends interpolatory projection methods for model reduction from nonparametric bilinear systems to parametric bilinear systems, deriving conditions for matching transfer functions and their parameter sensitivities (Jacobian and Hessian) without explicitly computing them.
Interpolatory projection methods for model reduction of nonparametric linear dynamical systems have been successfully extended to nonparametric bilinear dynamical systems. However, this is not the case 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 is 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 extra 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.