A Unified Software Framework for Empirical Gramians

A common approach in model reduction is balanced truncation, which is based on Gramian matrices classifying 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 als...

Verfasser: Himpe, Christian
Ohlberger, Mario
FB/Einrichtung:FB 10: Mathematik und Informatik
Dokumenttypen:Artikel
Medientypen:Text
Erscheinungsdatum:2013
Publikation in MIAMI:17.02.2014
Datum der letzten Änderung:16.06.2021
Angaben zur Ausgabe:[Electronic ed.]
Quelle:Himpe, Christian; Ohlberger, Mario: A Unified Software Framework for Empirical Gramians. Journal of Mathematics; 2013, Vol. 2013, 365909. http://dx.doi.org/doi:10.1155/2013/365909
Fachgebiet (DDC):510: Mathematik
Lizenz:CC BY 3.0
Sprache:English
Anmerkungen:Finanziert durch den Open-Access-Publikationsfonds 2013/2014 der Deutschen Forschungsgemeinschaft (DFG) und der Westfälischen Wilhelms-Universität Münster (WWU Münster).
Format:PDF-Dokument
URN:urn:nbn:de:hbz:6-64319528070
Permalink:https://nbn-resolving.de/urn:nbn:de:hbz:6-64319528070
Onlinezugriff:365909.pdf

A common approach in model reduction is balanced truncation, which is based on Gramian matrices classifying 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 provided 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 systems.