Numerical solution of optimal control problems with implicitly defined discontinuities with applications in engineering [Elektronische Ressource] / vorgelegt von Ulrich Brandt-Pollmann

English
170 Pages
Read an excerpt
Gain access to the library to view online
Learn more

Description

INAUGURAL - DISSERTATIONzurErlangung der DoktorwurdederNaturwissenschaftlich-Mathematischen Gesamtfakult atderRuprecht - Karls - Universit atHeidelbergvorgelegt vonDiplom-Physiker Ulrich Brandt-Pollmannaus Lahn-Gie enTag der mundlic hen Prufung: 21.09.2004Numerical solution of optimal control problemswith implicitly de ned discontinuities withapplications in engineeringGutachter: Prof. Dr. Dr. h.c. Hans Georg BockGutachter: Prof. Dr. Dr. h.c. Jurgen WarnatzAbstractIn the thesis on hand we treat optimal control problems for implicitly discontinuousdynamical processes.We give a general model formulation which includes implicitly given state depen-dent discontinuities in the right hand sides of the DAE system. The formulation isadapted to real-world applications from chemical and biotechnological engineering.The resulting problems are large scale constrained problems of optimal control withimplicitly given discontinuities of a priori unknown chronology and number.Our solution approach builds on the direct multiple shooting approach which allowsthe combination of appropriate DAE solvers with modern simultaneous optimizationstrategies. To solve the underlying optimization problem we apply SQP methods.We explain our strategy to provide sensitivity information at the presence of implic-itly given discontinuities for large scale models.

Subjects

Informations

Published by
Published 01 January 2004
Reads 18
Language English
Document size 3 MB
Report a problem

INAUGURAL - DISSERTATION
zur
Erlangung der Doktorwurde
der
Naturwissenschaftlich-Mathematischen Gesamtfakult at
der
Ruprecht - Karls - Universit at
Heidelberg
vorgelegt von
Diplom-Physiker Ulrich Brandt-Pollmann
aus Lahn-Gie en
Tag der mundlic hen Prufung: 21.09.2004Numerical solution of optimal control problems
with implicitly de ned discontinuities with
applications in engineering
Gutachter: Prof. Dr. Dr. h.c. Hans Georg Bock
Gutachter: Prof. Dr. Dr. h.c. Jurgen WarnatzAbstract
In the thesis on hand we treat optimal control problems for implicitly discontinuous
dynamical processes.
We give a general model formulation which includes implicitly given state depen-
dent discontinuities in the right hand sides of the DAE system. The formulation is
adapted to real-world applications from chemical and biotechnological engineering.
The resulting problems are large scale constrained problems of optimal control with
implicitly given discontinuities of a priori unknown chronology and number.
Our solution approach builds on the direct multiple shooting approach which allows
the combination of appropriate DAE solvers with modern simultaneous optimization
strategies. To solve the underlying optimization problem we apply SQP methods.
We explain our strategy to provide sensitivity information at the presence of implic-
itly given discontinuities for large scale models. E cien t techniques for the derivative
generation of the right hand sides particularly adapted to structural sparsity pattern
changes of the adjacent Jacobians are presented.
We formulate an algorithm to treat the optimization problem which depends on
the chronology and number of discontinuities occuring in a digraph given by the
successive trajectories of the SQP steps.
We explain our modeling of a complex rack-in process of a distillation column and
present the models of two biotechnological processes. Each of the models is equipped
with characteristical implicit state dependent discontinuities of a priori unknown
chronology.
In numerical experiments we show the e cien t applicability of our algorithms to
the presented chemical process and to the two biotechnological applications. We
apply our approach to optimal feedback control of a biotechnological application
with implicit discontinuities.Zusammenfassung
In dieser Arbeit werden implizit zustandsabh angig unstetige dynamische Prozesse
behandelt.
Es wird eine allgemeine mathematische Modellformulierung angegeben, die implizit
gegebene zustandsabh angige Unstetigkeiten in den rechten Seiten des DAE-Systems
einschlie t. Anschlie end wird die Formulierung an konkrete chemische und biotech-
nologische Prozesse angepa t, woraus gro e nicht-lineare optimale Kontrollprob-
leme mit implizit gegebenen Unstetigkeiten von a priori unbekannter Anzahl und
Chronologie resultieren.
Unser L osungsansatz basiert auf dem direkten Mehrzielverfahren, welches die Kom-
bination eine problemangepa ten DAE L osers mit modernen simultanen Verfahren
der Optimierung erm oglicht. Zur L osung des Optimierungsproblems verwenden wir
SQP Verfahren.
Wir erkl aren unsere Strategie zur Bereitstellung von Sensitivit atsinformation bei im-
plizit gegebenen Unstetigkeiten fur large scale Modelle. E zien te Techniken fur die
Ableitungsgenerierung der rechten Seiten, die speziell an Dunnb esetztheitsmuster-
wechsel der entsprechenden Jacobi-Matrizen angepa t sind, werden pr asentiert.
Wir formulieren einen Algorithmus zur Behandlung des Optimierungsproblems, das
von der Chronologie sowie der Anzahl der Unstetigkeiten abh angt, die im durch
die Trajektorien in den einzelnen SQP Schritten gegebenen gerichteten Graphen
auftreten.
Unsere Modellierung eines komplexen Anfahrprozesses einer Destillationskolonne wir
eingehend erl autert. Au erdem gehen wir auf die Modelle zweier biotechnologischer
Prozesse detaillierter ein. Alle diese Modelle weisen charakteristische implizit zus-
tandsabh angige Unstetigkeiten a priori unbekannter Chronologie auf.
In numerischen Experimenten zeigen wir die e zien te Anwendbarkeit unserer Al-
gorithmen auf die pr asentierten chemischen und biotechnologischen Anwendungen.Wir wenden unseren Ansatz zur Feedback Steuerung biotechnologischen Anwendung
mit impliziten Unstetigkeiten an.Acknowledgements
Above all, I owe thanks to my advisors Prof. Dr. Dr. h.c. Hans Georg Bock and
Dr. Johannes P. Schl oder for their excellent support during the last years. It is
a pleasure to acknowledge the immense bene t of their deep knowledge and their
impressive overview for my work. I thank them just as much for the cordial and
productive atmosphere they create in our research group.
Further, I heartily thank my o ce mate Dr. Katja Mombaur for discussions, numer-
ous joint scienti c activities and her positive attitude toward whatever comes.
Let me extend my thanks to my colleague Andreas Alexis Sigurt Sch afer for his
patience concerning uncounted MUSCOD-II questions and for his highly structured
style of implementation. I am obliged to Dr. Moritz Diehl, especially for helping me
to get into contact with NMPC, and to Christian Kraus for valuable mathematical
and nonmathematical conversations.
Thomas Kl opfer always had an open ear for all kinds of questions and trouble
concerning our computers, even on weekends and holidays.
Throughout the time of my thesis research, I have been accompanied and supported
in many ways by members of ourh group and by other people at the IWR. I
would like to address thanks to all of them, especially to Dr. Stefan K orkel, Dr. Eka-
terina Kostina, and Sebastian Sager.
I am indebted to Dr. Dirk Lebiedz for several interesting joint projects and publi-
cations, and for private volleyball lessons.
Let me also thankfully mention my industrial project partner Dr. Jens K ohler
(BASF) who contributed to this work by posing the right questions, and who was
always available for a scienti c discussion.
I am deeply grateful to Margret Rothfuss for her patience, her clarity, and her ability
to get things o the ground.
I leave a special note to Ted for o ering encouragement and consolation whenever
needed.
Finally, I want to thank my anc ee Dr. Julia Hartmann for her love and for her
uncon ned support.
iThe nancial support by the Bundesministerium fur Bildung und Forschung within
the context of the project Nicht-Standard Probleme der Optimalen Steuerung is
gratefully acknowledged.
ii