Optimization-based parametric model order reduction via $\mathcal{H}_2\otimes\mathcal{L}_2$ first-order necessary conditions

TL;DR

This paper develops a new optimization-based method for parametric model order reduction that guarantees stability and achieves lower approximation errors by leveraging $\

Contribution

It introduces first-order optimality conditions for structured reduced models and proposes a stability-preserving optimization approach for $\

Findings

Produces stable reduced models with lower errors

Outperforms existing methods in numerical experiments

Offers a theoretical comparison to prior approaches

Abstract

In this paper, we generalize existing frameworks for $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal model order reduction to a broad class of parametric linear time-invariant systems. To this end, we derive first-order necessary ptimality conditions for a class of structured reduced-order models, and then building on those, propose a stability-preserving optimization-based method for computing locally $\mathcal{H}_2\otimes\mathcal{L}_2$-optimal reduced-order models. We also make a theoretical comparison to existing approaches in the literature, and in numerical experiments, show how our new method, with reasonable computational effort, produces stable optimized reduced-order models with significantly lower approximation errors.