Multivariate moment matching for model order reduction of quadratic-bilinear systems using error bounds

TL;DR

This paper introduces an adaptive moment-matching approach for quadratic-bilinear system model reduction, utilizing error bounds to intelligently select interpolation points, resulting in more accurate reduced models.

Contribution

It extends error bounds to quadratic-bilinear systems and develops a greedy algorithm for optimal shift frequency selection in model reduction.

Findings

Proposed method achieves higher accuracy than standard approaches.

Error bounds effectively guide the selection of interpolation points.

Method demonstrates improved approximation quality in numerical experiments.

Abstract

We propose an adaptive moment-matching framework for model order reduction of quadratic-bilinear descriptor systems. In this framework, an important issue is the selection of those shift frequencies where moment-matching is to be achieved. Often, the choice is random or linked to the linear part of the nonlinear system. In this paper, we extend the use of an existing a posteriori error bound for general linear time invariant systems to quadratic-bilinear systems and develop a greedy-type framework to select a good choice of interpolation points for the construction of the projection matrices. The results are compared with standard quadratic-bilinear projection methods and we observe that the approximations obtained by the proposed method yield high accuracy.