Controllability, Identification, and Randomness in Distributed Systems

155 Pages·2014·4.274 MB·English

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Marzieh Nabi-Abdolyousefi
Controllability,
Identification, and
Randomness in Distributed
Systems
Doctoral Thesis Accepted by the University
of Washington, Washington, USA
123
Author Supervisor
Dr. MarziehNabi-Abdolyousefi Prof.MehranMesbahi
PaloAlto Research Center Universityof Washington
PaloAlto, CA Seattle,WA
USA USA
ISSN 2190-5053 ISSN 2190-5061 (electronic)
ISBN 978-3-319-02428-8 ISBN 978-3-319-02429-5 (eBook)
DOI 10.1007/978-3-319-02429-5
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Parts of this thesis have been published in the following journal articles:
• M. Nabi-Abdolyousefi and M. Mesbahi, Network Identification via Node
Knock-out, IEEE Transactions on Automatic Control, Vol. 57, Issue 12,
pp. 3214–3219, 2012.
• M. Nabi-Abdolyousefi and M. Mesbahi, A Sieve Method for Consensus-type
Network Tomography, IET Control Theory & Applications, Vol. 6, Issue 12,
pp. 1926–1932, 2012.
• M. Nabi-Abdolyousefi, M. Fazel, and M. Mesbahi, A Graph Realization
Approach to Network Identification, 51th IEEE Conference on Decision and
Control, Maui, USA, pp. 4642–4647, 2012.
• M.Nabi-AbdolyousefiandM.Mesbahi,Networkidentificationvianodeknock-
out (Can one hear the shape of the coordination?), 49th IEEE conference on
Decision and Control, Atlanta, USA, 2010.
• M. Nabi-Abdolyousefi and M. Mesbahi, On the Controllability Properties of
Circulant Networks, IEEE Transactions on Automatic Control (To appear),
2013.
• M. Nabi-Abdolyousefi and M. Mesbahi, System Theory over Random Net-
works: Controllability and Optimality Properties, 50th IEEE Conference on
Decision and Control, Orlando, USA, pp. 2323–2328, 2011.
• M. Nabi-Abdolyousefi and M. Mesbahi, Coordinated Decentralized Estimation
Over Random Networks, American Control Conference, San Francisco, USA,
2011.
I would like to dedicate this body of work
to my family members, who have supported
me throughout my life
Supervisor’s Foreword
Marzieh’s dissertation is comprised of four distinct, yet well-integrated facets.
The first facet involves the problem of network identification from input–output
data, based on the assumption that the nodes in the network are diffusively
coupled. In a sequence of original works, Marzieh blends ideas from a traditional
areainsystemtheory,namely,systemidentification,withthetheoryofnetworked
dynamic systems, to propose algorithmic means of identifying how the nodes in
thenetworkareinternallywiredbasedonavailablenetwork-leveldata.Tothebest
ofmyknowledge,Marziehisamongthefirstfewresearcherswhohaveexamined
this problem by combining algebraic graph theory and system identification.
Thisworkhasrelevancetoanumberofimportantareasincludingidentificationof
gene networks as well as fault detection in distributed networked systems.
ThesecondfacetofMarzieh’sresearchdetailedinherdissertationinvolvesthe
basicproblemofwhenonecancontrola(potentially,large-scale)networkbybeing
abletoinjectappropriatelychosensignalsintoonlyasubsetofnodesinthenetwork
and relate this ability to the structural features of the network. Marzieh’s disser-
tation addresses this important problem in three different settings for diffusively
coupled networks: (a) controllability and observability of path and circulant net-
works,(b)controllabilityandobservabilityofrandomnetworks,and(c)thedegree
ofcontrollability,observability, andachievable performancefor these networks.
The third facet of the dissertation is on the applications of these results in
distributed estimation over sensor networks, distributed localization for robotic
applications, and optimal marketing strategies in social networks. These applica-
tions are very novel and contribute in a unique way to our fundamental under-
standing of dynamics and control of these complex dynamic networks.
Lastly, the fourth facet of Marzieh’s dissertation is on the use of data-driven
distributed optimization in an uncertain model free setting, which has direct and
important applications to pricing mechanisms and energy efficiency. Once again,
I believe the application of online distributed optimization to complex and large-
scaleengineeredsystemsasexaminedinMarzieh’sworkisnovelandleadstonew
insights and directions for research and development for networked power
systems, as well as energy and financial markets.
Seattle, September 2013 Prof. Mehran Mesbahi
ix
Acknowledgments
BeforestartingmyPh.D.atUniversityofWashington,foracoupleofmonthsmy
imagination of UW was filled by asmileypicture ofWanda Frederick and anold
picture of Prof. Mehran Mesbahi that I found on the web. My arrival coincided
with many nice surprises; the beautiful campus, moving to a new and spacious
office, and going to work on rainy days.
Now looking back at more than 5 years of being at UW and as a member of
Distributed Space System Lab, my memory is filled with so many reminiscences
of discussions, collaborations, conferences, laughs and cries, ups and downs,
spendinglongdaysinthelaboratory,hiking,everyotherFridayafternoongrocery
shoppingwithRanDai,andmanymore.Onecommonelementofthesememories
is the presence of my supervisor, Prof. Mesbahi. Words cannot express my grat-
itude and respect toward him. His patience, knowledge, philosophical point of
view, and in one word his personality have influenced me in different ways and
mademewhoIamtoday.Workingwithasupervisorwhoconsidersbothpersonal
and professional growth of his students was a big fortune for me. He taught me
having passions is one side of the story, but how we can have meaningful
approaches toward them is another. He taught me that ‘‘enough is never enough’’
andthereisnoendtoperfectingthequalityofworkwedeliver.Hetaughtmehow
to be a good teacher, a good researcher, and a better person. His lifetime lessons
will stay with me forever.
I would also like to deeply thank my qualification exam, general exam, final
exam, and reading committees Prof. Arthur Mattick, Prof. Soumik Pal, Prof. Eric
Klavins, Prof. Uy-Loi Ly, Prof. Santosh Devasia, Prof. Kristi Morgansen, and
Prof. Maryam Fazel for their time, insightful comments, and their support. In
particular,IwouldliketosincerelyacknowledgeProf.MorgansenandProf.Fazel
fortheirsupportindifferentstagesofmystudy.Theirassistancetaughtmethatat
the end of the day, the academic environment is a big community of people who
are aiming to help develop the world by fostering a new generation. Prof. Mor-
gansen granted me the opportunity to work with the experimental data on the
Seaglider. Her welcoming personality and unconditional support have always
inspiredme.GreatdiscussionswithProf.Fazel havealwaysbeenrevitalizingand
inspiring too. I would like to greatly acknowledge and thank the William E.
Boeing Department of Aeronautics and Astronautics and, in particular, Wanda
Frederick for creating a friendly environment to conduct research.
xi
xii Acknowledgments
IwouldalsoliketothankmycolleaguesatDistributedSpaceSystemsLab.The
laboratoryhas been the secondhome for me. Ihave learned quite alot fromeach
member of the laboratory, especially, Dr. Ran Dai, Airlie Chapman, Joshua
Maximoff, and Dr. Dan Zelazo. Great discussions and fun collaborations with
Airlie Chapman and Joshua Maximoff have influenced my research. Airlie’s pas-
sionsforresearchandherefforttosucceedhavesetmyprofessionalstandardsand
changedmydefinitionofperfection.IwouldalsoliketodeeplythankDr.RanDai
formakingmyexperienceinthelaboratoryunforgettableandaverypleasantone.
I like to express my sincere gratitude to many good friends who made my expe-
rience in the USA, in Seattle, and at UW so colourful; in particular, Mr. Gregory
Both and his wife Tuba who were my host family the first week of arriving to
Seattle and became people who were there for me whenever I needed help.
Thelastandnottheleastis myfamily. Iwouldliketothankmyfamily forall
theirloveandencouragementsfromthousandsofmilesaway.Theirpureloveand
their memories have enabled me to go on. Let me start with my best friend
Mojtaba who has always been beside me, whose love, silent support, calm,
complex, and flawless personality, and beautifuleyes have redefined the meaning
oflifeforme.IhavebeenextremelyfortunatetohaveawisesisterorIshouldsay
an angel such as Sareh, who can give wise advice whenever I need it the most, a
responsible brother such as Aboozar, who I can trust the most to finish whatever
Iaskhimtodo,ahardworkingangelsuchasSoheila,whocanplaymysupportive
roleathomewhenIamaway,asmartsistersuchasRazieh,whocanmakemyday
by just talking to her for 5 minutes, and my little angel Negin whose kindness is
endless.WhateverIdoinmylifeisanappreciationtoourparentswhotaughtusto
love, be wise, responsible, supportive, kind, and have good morals.
Contents
1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Preliminaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.1 Dynamical Systems and Control. . . . . . . . . . . . . . . . 5
1.2.2 Graph Theory. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.3 Cartesian Product. . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.4 Kronecker Product . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Organization and Contribution. . . . . . . . . . . . . . . . . . . . . . . 11
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Part I Can One Hear the Shape of Coordination?
2 Network Identification via Node Knockout . . . . . . . . . . . . . . . . . 17
2.1 Problem Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 System Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Characterization of the Network Topology
via Node Knockout. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.4 Edge Faults in the Network. . . . . . . . . . . . . . . . . . . . . . . . . 28
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
3 A Sieve Method for Consensus-Type Network Tomography. . . . . 31
3.1 Graph Characterization via Characteristic Polynomial. . . . . . . 31
3.2 Graph Characterization via Graph Sieve . . . . . . . . . . . . . . . . 32
3.2.1 Integer Partitioning Algorithms and Complexity
Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.2.2 Degree Based Graph Construction Algorithms
and Complexity Analysis. . . . . . . . . . . . . . . . . . . . . 35
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4 Network Identification via Graph Realization . . . . . . . . . . . . . . . 39
4.1 Summary of the Previous Two Chapters . . . . . . . . . . . . . . . . 39
4.2 Similarity Transformation Approach. . . . . . . . . . . . . . . . . . . 41
4.2.1 Numerical Considerations . . . . . . . . . . . . . . . . . . . . 45
xiii