Publikation: Balanced realizations of finite dimensional time invariant dynamical systems
Dateien
Datum
Autor:innen
Herausgeber:innen
ISSN der Zeitschrift
Electronic ISSN
ISBN
Bibliografische Daten
Verlag
Schriftenreihe
Auflagebezeichnung
URI (zitierfähiger Link)
Internationale Patentnummer
Link zur Lizenz
Angaben zur Forschungsförderung
Projekt
Open Access-Veröffentlichung
Sammlungen
Core Facility der Universität Konstanz
Titel in einer weiteren Sprache
Publikationstyp
Publikationsstatus
Erschienen in
Zusammenfassung
In this thesis we demonstrate, how to receive a balanced realization of a finite dimensional linear time invariant (FDLTI) dynamical system. For that purpose we use the discretized heat equation as an application. We get such a balanced realization by following the algorithms in Robust and Optimal Control. So first we make the system observable, by applying one such algorithm and afterwards we make it controllable with a dual one. Then we have a minimal realization. From this point on we can apply a balancing algorithm to get a balanced realization. An important role in these algorithms plays the Lyapunov equation. In the controllability as well as the observability algorithm, we start by solving a Lyapunov equation. For these equations, we implemented the Lyapunov solver presented in Krylov subspace methods for large Lyapunov equations. This Lyapunov solver is based on a low rank block Krylov approximation. The way to a balanced realization connects this Lyapunov solver with the well known control theory of FDLTI dynamical systems.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
Schlagwörter
Konferenz
Rezension
Zitieren
ISO 690
THIELE, Michael, 2021. Balanced realizations of finite dimensional time invariant dynamical systems [Bachelor thesis]. Konstanz: Universität KonstanzBibTex
@mastersthesis{Thiele2021Balan-54846,
year={2021},
title={Balanced realizations of finite dimensional time invariant dynamical systems},
address={Konstanz},
school={Universität Konstanz},
author={Thiele, Michael}
}RDF
<rdf:RDF
xmlns:dcterms="http://purl.org/dc/terms/"
xmlns:dc="http://purl.org/dc/elements/1.1/"
xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
xmlns:bibo="http://purl.org/ontology/bibo/"
xmlns:dspace="http://digital-repositories.org/ontologies/dspace/0.1.0#"
xmlns:foaf="http://xmlns.com/foaf/0.1/"
xmlns:void="http://rdfs.org/ns/void#"
xmlns:xsd="http://www.w3.org/2001/XMLSchema#" >
<rdf:Description rdf:about="https://kops.uni-konstanz.de/server/rdf/resource/123456789/54846">
<dc:creator>Thiele, Michael</dc:creator>
<dc:contributor>Thiele, Michael</dc:contributor>
<void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/>
<dcterms:abstract xml:lang="eng">In this thesis we demonstrate, how to receive a balanced realization of a finite dimensional linear time invariant (FDLTI) dynamical system. For that purpose we use the discretized heat equation as an application. We get such a balanced realization by following the algorithms in Robust and Optimal Control. So first we make the system observable, by applying one such algorithm and afterwards we make it controllable with a dual one. Then we have a minimal realization. From this point on we can apply a balancing algorithm to get a balanced realization. An important role in these algorithms plays the Lyapunov equation. In the controllability as well as the observability algorithm, we start by solving a Lyapunov equation. For these equations, we implemented the Lyapunov solver presented in Krylov subspace methods for large Lyapunov equations. This Lyapunov solver is based on a low rank block Krylov approximation. The way to a balanced realization connects this Lyapunov solver with the well known control theory of FDLTI dynamical systems.</dcterms:abstract>
<bibo:uri rdf:resource="https://kops.uni-konstanz.de/handle/123456789/54846"/>
<dcterms:title>Balanced realizations of finite dimensional time invariant dynamical systems</dcterms:title>
<dcterms:hasPart rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/54846/3/Thiele_2-gcf6ni62133i3.pdf"/>
<dc:language>eng</dc:language>
<dcterms:rights rdf:resource="http://creativecommons.org/licenses/by/4.0/"/>
<foaf:homepage rdf:resource="http://localhost:8080/"/>
<dc:rights>Attribution 4.0 International</dc:rights>
<dspace:isPartOfCollection rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
<dspace:hasBitstream rdf:resource="https://kops.uni-konstanz.de/bitstream/123456789/54846/3/Thiele_2-gcf6ni62133i3.pdf"/>
<dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-09-10T07:53:10Z</dc:date>
<dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2021-09-10T07:53:10Z</dcterms:available>
<dcterms:issued>2021</dcterms:issued>
<dcterms:isPartOf rdf:resource="https://kops.uni-konstanz.de/server/rdf/resource/123456789/39"/>
</rdf:Description>
</rdf:RDF>
