A New Framework for $\mathcal{H}_2$-Optimal Model Reduction

TL;DR

This paper introduces a novel, efficient framework for H2-optimal model reduction of linear systems using tangential interpolation, significantly reducing computational costs while maintaining accuracy.

Contribution

It presents a decoupled approach that speeds up H2-optimal reduction and produces a useful surrogate model without extra cost, extending the applicability of interpolatory reduction methods.

Findings

Significant speedup in H2-optimal reduction process

Effective generation of surrogate models for error estimation

Demonstrated success on numerical examples

Abstract

In this contribution, a new framework for H2-optimal reduction of multiple-input, multiple- output linear dynamical systems by tangential interpolation is presented. The framework is motivated by the local nature of both tangential interpolation and H2-optimal approxi- mations. The main advantage is given by a decoupling of the cost of optimization from the cost of reduction, resulting in a significant speedup in H2-optimal reduction. In addition, a middle-sized surrogate model is produced at no additional cost and can be used e.g. for error estimation. Numerical examples illustrate the new framework, showing its effectiveness in producing H2-optimal reduced models at a far lower cost than conventional algorithms. The paper ends with a brief discussion on how the idea behind the framework can be extended to approximate further system classes, thus showing that this truly is a general framework for interpolatory H2 reduction rather than just an additional reduction algorithm.