Large-scale and infinite dimensional dynamical model approximation

208 Pages·2017·6.55 MB·English

Large-scale and infinite dimensional dynamical model
approximation
Igor Pontes Duff Pereira
To cite this version:
Igor Pontes Duff Pereira. Large-scale and infinite dimensional dynamical model approximation. Mod-
eling and Simulation. UNIVERSITÉ DE TOULOUSE, 2017. English. ￿NNT: ￿. ￿tel-01699233￿
HAL Id: tel-01699233
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TTHHÈÈSSEE
En vue de l’obtention du
DOCTORAT DE L’UNIVERSITÉ DE TOULOUSE
Délivré par : l’Institut Supérieur de l’Aéronautique et de l’Espace (ISAE)
Présentée et soutenue le 11/01/2017 par :
Igor Pontes Duff Pereira
Large-scale and infinite dimensional dynamical
model approximation
JURY
M. Olivi Chargée de recherche INRIA Rapporteur
W. Michiels Professeur KU Leuven Rapporteur
A. C. Antoulas Professeur Rice University Examinateur
S. Gugercin Professeur Virginia Tech Examinateur
J. Daafouz Professeur Université de Lorraine Examinateur
A. Seuret Chargé de recherche LAAS CNRS Examinateur
C. Poussot-Vassal Ingénieur de recherche ONERA Directeur de thèse
C. Seren Ingénieur de recherche ONERA Co-directeur de thèse
École doctorale et spécialité :
EDSYS : Automatique 4200046
Unité de Recherche :
ONERA - The French Aerospace Lab
Centre de Toulouse
Département de Commande des Systèmes et Dynamique du Vol
Directeurs de Thèse :
C. Poussot-Vassal (directeur de thèse)
C. Seren (co-directeur de thèse)
Rapporteurs :
Martine Olivi et Wim Michiels

-This Page Intentionally Left Blank-

Aos meus pais,
Ana Maria (in memoriam) e Carlos Eduardo,
por tudo que fizeram por mim
ao longo de minha vida

Acknowledgements
I am very grateful for all of the support and encouragement I have received from many people
in the course of completing this work. First of all, many thanks go to my advisers Dr. Charles
Poussot-Vassal and Dr. Cedric Seren for giving me the opportunity to achieve this Ph.D. thesis.
I am also thankful for their guidance, constructive criticism and advice which have enabled me
to complete this project successfully.
I would also like to thank Dr. Martine Olivi and Prof. Wim Michiels for accepting to review
this manuscript. Their constructive comments have given me keys to improving this work and
lead to extend it. Likewise, I would like to thank Prof. Athanasios C. Antoulas, Prof. Serkan
Gugercin, Prof. Jamal Daafouz and Dr. Alexandre Seuret for accepting to be part of my jury.
IwouldliketothankaswellProf. ChristopherBeattieandonceagainProf. SerkanGugercin
forhavingmeasaguestintheDepartmentofMathematicsatVirginiaTech. Thisstaywasvery
enjoyable and crucial for my training as a researcher. Also, I would like to thanks the Doctoral
School EDSYS for making this stay possible through the international mobility scholarship.
I would also like to thanks my fellow Ph.D. students of the CSDV, who have helped to make
these three years a very enjoyable and agreeable period through the numerous coffee breaks
and other activities. Special thanks to Alvaro Perez, Flávio Ribeiro, Raquel Stella da Silva
de Aguiar and Leandro Lustosa for the enormous support, great conversations and pleasant
companionships.
Iwishtoexpressmygratitudetomygirlfriend,JoanaEichenberger,forallthelove,support,
and comprehension.
Finally, I could not forget to thank in a special way all my family, who always supported me
unconditionally in every possible way during my life. For this reason, I would like to express my
kind wishes to everyone, especially to my father Carlos Eduardo, my mother-in-law Claudia and
my brother Pedro.
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Abstract
In the engineering area (e.g. aerospace, automotive, biology, circuits), dynamical systems are
the basic framework used for modeling, controlling and analyzing a large variety of systems and
phenomena. Due to the increasing use of dedicated computer-based modeling design software,
numerical simulation turns to be more and more used to simulate a complex system or phe-
nomenonandshortenbothdevelopmenttimeandcost. However,theneedofanenhancedmodel
accuracy inevitably leads to an increasing number of variables and resources to manage at the
price of a high numerical cost. This counterpart is the justification for model reduction.
For linear time-invariant systems, several model reduction approaches have been effectively
developed since the 60’s. Among these, interpolation-based methods stand out due to their
flexibility and low computational cost, making them a predestined candidate in the reduction of
truly large-scale systems. Recent advances demonstrate ways to find reduction parameters that
locally minimize the H2 norm of the mismatch error.
Ingeneral,areduced-orderapproximationisconsideredtobeafinitedimensionalmodel. This
representation is quite general and a wide range of linear dynamical systems can be converted
in this form, at least in principle. However, in some cases, it may be more relevant to find
reduced-order models having some more complex structures. As an example, some transport
phenomenasystemshavetheirHankelsingularvalueswhichdecayveryslowlyandarenoteasily
approximated by a finite dimensional model. In addition, for some applications, it is valuable to
haveastructuredreduced-ordermodelwhichreproducesthephysicalbehaviors. Thatiswhy, in
thisthesis,reduced-ordermodelshavingdelaystructureshavebeenmorespecificallyconsidered.
This work has focused, on the one hand, in developing new model reduction techniques for
reducedordermodelshavingdelaystructures,and,ontheotherhand,infindingnewapplications
of model approximation. The major contribution of this thesis covers approximation topics and
includes several contributions to the area of model reduction. A special attention was given to
the H2 optimal model approximation problem for delayed structured models. For this purpose,
some new theoretical and methodological results were derived and successfully applied to both
academic and industrial benchmarks.
In addition, the last part of this manuscript is dedicated to the analysis of time-delayed
systemsstabilityusinginterpolatorymethods. Sometheoreticalstatementsaswellasanheuristic
aredevelopedenablingtoestimateinafastandaccuratewaythestabilitychartsofthosesystems.
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