H$_2$ Optimal Model Order Reduction over a Finite Time Interval

TL;DR

This paper introduces a novel model order reduction technique that minimizes a time-limited H₂ norm by deriving gradient expressions and solving a nonlinear optimization problem, improving model efficiency over a finite time interval.

Contribution

It provides a closed-form gradient expression for the time-limited H₂ norm and formulates a new reduction method based on nonlinear optimization.

Findings

Gradient expressions enable efficient optimization

Reduced models minimize the time-limited H₂ norm

Method improves model accuracy over finite intervals

Abstract

For a time-limited version of the H$_2$ norm defined over a fixed time interval, we obtain a closed form expression of the gradients. After that, we use the gradients to propose a time-limited model order reduction method. The method involves obtaining a reduced model which minimizes the time-limited H$_2$ norm, formulated as a nonlinear optimization problem. The optimization problem is solved using standard optimization software.