Interpolatory model reduction for quadratic-bilinear systems using error estimators

Abstract

Purpose

The purpose of this paper is to propose an interpolation-based projection framework for model reduction of quadratic-bilinear systems. The approach constructs projection matrices from the bilinear part of the original quadratic-bilinear descriptor system and uses these matrices to project the original system.

Design/methodology/approach

The projection matrices are constructed by viewing the bilinear system as a linear parametric system, where the input associated with the bilinear part is treated as a parameter. The advantage of this approach is that the projection matrices can be constructed reliably by using an a posteriori error bound for linear parametric systems. The use of the error bound allows us to select a good choice of interpolation points and parameter samples for the construction of the projection matrices by using a greedy-type framework.

Findings

The results are compared with the standard quadratic-bilinear projection methods and it is observed that the approximations through the proposed method are comparable to the standard method but at a lower computational cost (offline time).

Originality/value

In addition to the proposed model order reduction framework, the authors extend the one-sided moment matching parametric model order reduction (PMOR) method to a two-sided method that doubles the number of moments matched in the PMOR method.

Citation

Ahmad, M.I., Benner, P. and Feng, L. (2019), "Interpolatory model reduction for quadratic-bilinear systems using error estimators", Engineering Computations, Vol. 36 No. 1, pp. 25-44. https://doi.org/10.1108/EC-04-2018-0162