On the Optimal Control of
Mechanical Systems
–
Hybrid Control Strategies and
Hybrid Dynamics
Von der Fakult¨at f¨ur Elektrotechnik, Informatik und
Mathematik der Universit¨at Paderborn zur Erlangung des
akademischen Grades Doktor der Naturwissenschaften
(Dr. rer. nat.) genehmigte Dissertation von
Kathrin Flaßkamp
Paderborn 2013
Gutachter: Jun.-Prof. Dr. Sina Ober-Bl¨obaum
Prof. Dr. Michael Dellnitz
Prof. Dr. Todd D. Murphey
Tag der m¨undlichen Pr¨ufung: 20. Dezember 2013
I regarded as quite useless the reading of large treatises of pure analysis:
too large a number of methods pass at once before the eyes. It is in the
works of application that one must study them; one judges their utility
there and appraises the manner of making use of them.
Joseph Louis Lagrange (1736–1813), Italian-French astronomer and mathematician.
Quotation as reported by J. F. Maurice in Moniteur Universel (1814). In W. F.
Bynum, Roy Porter (Eds.): Oxford Dictionary of Scientific Quotations, Oxford Uni-
versity Press, 2012
Acknowledgements
First of all, I would like to express my deepest gratitude to Jun.-Prof. Dr. Sina Ober-
Bl¨obaum for her constant support and advice, for introducing me to the interesting
field of optimal control and geometric mechanics, to many exciting open questions
therein and to its vivid, international research community. I also thank her for
giving me the freedom to follow my own ideas, for the numerous extensive and
helpful discussions, also late in the evening or over long distances, and finally and
foremost, for supervising this thesis.
I am grateful to Prof. Dr. Michael Dellnitz who has risen my interest in dynamical
systems and related topics already during my studies and who later gave me the
opportunity to work at the Chair of Applied Mathematics. I deeply appreciate
his impressive enthusiasm, the motivation he passes on and the rousing manner of
thinking about mathematics as well as his participation in my development in the
last years.
Then, I would like to thank Prof. Dr. Ansgar Tr¨achtler for getting me enthusiastic
about control theory as an interdisciplinary field of research at first, during my
studies, and, in particular, for his interest in novel mathematical methods for control
engineering, which raised my wish for balancing “theory” and “application” in my
own work.
Special thanks also to Prof. Dr. Todd Murphey from the Northwestern University
(Evanston, Illinois) who even intensified my interest in optimal control and geometric
mechanics throughout our collaboration and especially during my visit at his lab in
June 2012. I appreciated the stimulating discussions with himself and his group and
the friendly atmosphere in his lab.
I gratefully acknowledge the financial support I have received within the Collabora-
tive Research Center SFB 614, “Self-optimizing concepts and structures in mechan-
ical engineering” and highly appreciated the interdisciplinary research within this
project. Especially, I would like to thank my colleagues Christian Heinzemann, Mar-
tin Kr¨uger, Tobias Meyer, Dr. Claudia Priesterjahn, Peter Reinold, Dr. Ing. Christoph
Romaus, Tobias Schneider, Christoph Schulte, Albert Seifried, Dominik Steenken,
and Julia Timmermann for the productive and enjoyable collaboration.
Many thanks go to my – partly former – colleagues at the University of Paderborn
for many enlightening and fruitful discussions, their helpful advices and valuable
support, distracting moments once in a while, and their kindness; all of which con-
tributed a lot in making the last years an experience I would not have wanted to
miss. Namely, I would like to thank Dr. Alessandro Dell’Aere, Dr. Mirko Hessel-von
Molo, Dr. Stefan Klus, Dr. Anna-Lena Meyer, Sebastian Peitz, Dr. Marcus Post,
Dr. Robert Preis, Maik Ringkamp, Stefan Sertl, Bianca Thiere and Dr. Katrin Wit-
ting from the Chair of Applied Mathematics and Dr. Alexander Schmeding and
Beate Kossak, formerly at the Institute of Mathematics. In particular, I am grateful
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