A Unified Software Framework for Empirical Gramians

TL;DR

This paper presents a unified software framework that computes six types of empirical gramians, facilitating model reduction for nonlinear MIMO systems through a consistent computational approach.

Contribution

It introduces a comprehensive software framework that unifies the computation of various empirical gramians for nonlinear systems, extending balanced truncation methods.

Findings

Framework supports six types of empirical gramians.

Enables model reduction for nonlinear MIMO systems.

Provides a uniform computational approach.

Abstract

A common approach in model reduction is balanced truncation, which is based on gramian matrices classifiying certain attributes of states or parameters of a given dynamic system. Initially restricted to linear systems, the empirical gramians not only extended this concept to nonlinear systems, but also provide a uniform computational method. This work introduces a unified software framework supplying routines for six types of empirical gramians. The gramian types will be discussed and applied in a model reduction framework for multiple-input-multiple-output (MIMO) systems.