Approximation, Analysis and Control of Large-Scale Systems

300 Pages·2016·4.47 MB·English

Approximation, Analysis and Control
of
Large-Scale Systems
Theory and Applications
by
Giordano Scarciotti
A Thesis submitted in fulfillment of requirements for the degree of
Doctor of Philosophy
Control and Power Research Group
Department of Electrical and Electronic Engineering
Imperial College London
2016
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Abstract
This work presents some contributions to the fields of approximation, analysis and control
of large-scale systems. Consequently the Thesis consists of three parts. The first part cov-
ersapproximationtopicsandincludesseveralcontributionstotheareaofmodelreduction.
Firstly, modelreductionbymomentmatchingforlinearandnonlineartime-delaysystems,
including neutral differential time-delay systems with discrete-delays and distributed de-
lays, is considered. Secondly, a theoretical framework and a collection of techniques to
obtainreducedordermodelsbymomentmatchingfrominput/outputdataforlinear(time-
delay) systems and nonlinear (time-delay) systems is presented. The theory developed is
then validated with the introduction and use of a low complexity algorithm for the fast
estimation of the moments of the NETS-NYPS benchmark interconnected power system.
Then, the model reduction problem is solved when the class of input signals generated by
alinearexogenoussystemwhichdoesnothaveanimplicit(differential)formisconsidered.
The work regarding the topic of approximation is concluded with a chapter covering the
problem of model reduction for linear singular systems. The second part of the Thesis,
which concerns the area of analysis, consists of two very different contributions. The first
proposes a new “discontinuous phasor transform” which allows to analyze in closed-form
the steady-state behavior of discontinuous power electronic devices. The second presents
in a unified framework a class of theorems inspired by the Krasovskii-LaSalle invariance
principle for the study of “liminf” convergence properties of solutions of dynamical sys-
tems. Finally, in the last part of the Thesis the problem of finite-horizon optimal control
with input constraints is studied and a methodology to compute approximate solutions of
the resulting partial differential equation is proposed.
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Declaration of Originality
I hereby declare that the work presented in this thesis is my own unless otherwise stated.
To the best of my knowledge the work is original and ideas developed in collaboration
with others have been appropriately referenced.
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Copyright Declaration
The copyright of this thesis rests with the author and is made available under a Creative
Commons Attribution Non-Commercial No Derivatives licence. Researchers are free to
copy, distribute or transmit the thesis on the condition that they attribute it, that they
do not use it for commercial purposes and that they do not alter, transform or build upon
it. For any reuse or redistribution, researchers must make clear to others the licence terms
of this work.
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Acknowledgments
ThedifficultyofaPhDisnotinthestudyorworkthatitrequires,butinthepsychological
burden created by the continuous uncertainty of the research investigation. Fortunately,
duringmyPhDIhadtheluckofhavingaroundexceptionalpeople,whosupportedmeand
alleviated the burden of this experience. My deepest gratitude goes to Alessandro Astolfi
for an uncountable number of reasons. For sure being supervised by someone who is an
exceptionally clever and talented researcher helped my PhD. But Alessandro, in addition
tothis, isalsoanextraordinaryhumanbeing. ItisthislatterqualitythatmademyPhDa
veryenjoyableexperience(whichisaquiterareoccurrence). IowemygratitudetoLaurent
Praly, first for accepting to work with me and then for the week I spent in Fontainebleau
where he crashed my ego in less than 10 minutes, and to Zhong-Ping Jiang, for the time
spent at New York University. Although I am still waiting for the final decision, I wish
to thank all the persons who believed in me and directly contributed to my preparation
for the JRF: Alessandro Astolfi, Paul Mitcheson, Thomas Parisini, Richard Syms, Oleksiy
Sydoruk, Eric Yeatman, Laurent Praly, Ron Hui, Hubregt Visser, Thulasi Mylvaganam
and Alberto Padoan. I wish to thank my two examiners, David Angeli and Malcolm
Smith, for the time spent reading my thesis and for the interesting discussions during my
viva voce. I wish to express my gratitude to all the persons who loved me and supported
me during these years. Although things did not work out, I owe my gratitude to Valeria
who followed me to UK where she has been an invaluable support for me. I wish to thank
the group of PhD students and researchers that I met when I started my PhD and that
readily accepted me: Adriano, Andrea, Antonio, Inma, Jaehwa, Jose, Michele, Thulasi;
and the people who joined along the way: Alberto and Paolo. Among these, I want to
make a special mention to a few people. I wish to thank Michele and his “cover” Emma,
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my perfect flatmate, for their friendship and help in difficult times. Thanks to Tessa who
welcomedmeinherhouseandmademefeelhome. IwishtothankmyoldfriendsDaniela,
Emanuele,Francesco,Giacomo,LucaandMartinaforbeingalwaysthere. ThankstoMax,
first as my GTA coordinator, then as an extremely witty friend. Thanks to Alberto for
our climbing adventures. A special thanks goes to Thulasi for the mind-blowing year we
had together and for her irreplaceable help and contagious energy. I owe sincere gratitude
to my family for their support and love even though they are still quite puzzled regarding
what their grumpy son is doing.