@article{JRPF:56,
author = {J. R. P. French},
journal = {Psychological Review},
number = {3},
pages = {181--194},
title = {A formal theory of social power},
volume = {63},
year = {1956},
doi = {10.1037/h0046123},
}
@incollection{FH:59,
author = {F. Harary},
booktitle = {Studies in Social Power},
editor = {D. Cartwright},
pages = {168--182},
publisher = {University of Michigan},
title = {A criterion for unanimity in {F}rench's theory of
social power},
year = {1959},
isbn = {0879442301},
url = {http://psycnet.apa.org/psycinfo/1960-06701-006},
}
@article{MHDG:74,
author = {M. H. DeGroot},
journal = {Journal of the American Statistical Association},
number = {345},
pages = {118-121},
title = {Reaching a Consensus},
volume = {69},
year = {1974},
abstract = {Consider a group of individuals who must act together
as a team or committee, and suppose that each
individual in the group has his own subjective
probability distribution for the unknown value of
some parameter. A model is presented which describes
how the group might reach agreement on a common
subjective probability distribution for the parameter
by pooling their individual opinions. The process
leading to the consensus is explicitly described and
the common distribution that is reached is explicitly
determined. The model can also be applied to problems
of reaching a consensus when the opinion of each
member of the group is represented simply as a point
estimate of the parameter rather than as a
probability distribution.},
doi = {10.1080/01621459.1974.10480137},
}
@article{INM:73,
author = {I. Noy-Meir},
journal = {Annual Review of Ecology and Systematics},
pages = {25--51},
title = {Desert ecosystems. {I}. {E}nvironment and producers},
year = {1973},
url = {http://www.jstor.org/stable/2096803},
}
@article{MSK-DJN:71,
author = {M. S. Klamkin and D. J. Newman},
journal = {American Mathematical Monthly},
number = {6},
pages = {631-639},
title = {Cyclic pursuit or "the three bugs problem"},
volume = {78},
year = {1971},
doi = {10.4169/amer.math.monthly.122.04.377},
}
@techreport{AMB-NC-AE:91,
address = {Haifa, Israel},
author = {A. M. Bruckstein and N. Cohen and A. Efrat},
institution = {Center for Intelligent Systems, Technion},
month = jul,
number = {CIS 9105},
title = {Ants, crickets, and frogs in cyclic pursuit},
year = {1991},
url = {http://www.cs.technion.ac.il/tech-reports},
}
@inproceedings{LX-SB-SL:05,
address = {Los Angeles, CA, USA},
author = {L. Xiao and S. Boyd and S. Lall},
booktitle = {Symposium on Information Processing of Sensor
Networks},
month = apr,
pages = {63-70},
title = {A scheme for robust distributed sensor fusion based
on average consensus},
year = {2005},
doi = {10.1109/IPSN.2005.1440896},
}
@incollection{FG-LS:10,
author = {F. Garin and L. Schenato},
booktitle = {Networked Control Systems},
editor = {A. Bemporad and M. Heemels and M. Johansson},
pages = {75-107},
publisher = {Springer},
series = {LNCIS},
title = {A Survey on Distributed Estimation and Control
Applications Using Linear Consensus Algorithms},
year = {2010},
doi = {10.1007/978-0-85729-033-5_3},
}
@book{VHP:98,
author = {V. H. Poor},
edition = {2},
publisher = {Springer},
title = {An Introduction to Signal Detection and Estimation},
year = {1998},
isbn = {0387941738},
}
@article{BSYR-HFDH:93,
author = {B. S. Y. Rao and H. F. Durrant-Whyte},
journal = {IEEE Transactions on Systems, Man \& Cybernetics},
number = {6},
pages = {1683-1698},
title = {A decentralized {B}ayesian algorithm for
identification of tracked targets},
volume = {23},
year = {1993},
abstract = {The problem of identification of objects being
tracked by a fully decentralized surveillance system
is considered. A decentralized multisensor system is
used to track targets (people and mobile robots) as
they enter and move around a factory assembly room
performing tasks. The sensors used in this system
(CCD cameras) reveal information about the targets
that is sufficiently rich to allow them not only to
be tracked, but also identified as a person, a robot,
etc. This identity information can be used to aid in
man-machine interface design and to facilitate
situation assessment. After defining the
identification problem, a centralized Bayesian
algorithm is developed for determining the identity
of each target based on each sensor's information.
The algorithm is decentralized and its performance
compared to the centralized version. Results of an
implementation of the algorithm working on real data
from the surveillance system are presented},
doi = {10.1109/21.257763},
}
@incollection{ROS-EF-EF-JSS:06,
author = {R. Olfati-Saber and E. Franco and E. Frazzoli and
J. S. Shamma},
booktitle = {Network Embedded Sensing and Control. (Proceedings of
NESC'05 Worskhop)},
editor = {P. J. Antsaklis and P. Tabuada},
pages = {169-182},
publisher = {Springer},
series = {Lecture Notes in Control and Information Sciences},
title = {Belief consensus and distributed hypothesis testing
in sensor networks},
year = {2006},
doi = {10.1007/11533382_11},
isbn = {3540327940},
}
@incollection{MWS-NC:07,
author = {M. W. Spong and N. Chopra},
booktitle = {Lagrangian and Hamiltonian Methods for Nonlinear
Control 2006},
pages = {47-59},
publisher = {Springer},
series = {Lecture Notes in Control and Information Sciences},
title = {Synchronization of Networked {L}agrangian Systems},
volume = {366},
year = {2007},
isbn = {978-3-540-73889-3},
}
@article{NC-MWS:08,
author = {N. Chopra and M. W. Spong},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {353-357},
title = {On exponential synchronization of {K}uramoto
oscillators},
volume = {54},
year = {2009},
doi = {10.1109/TAC.2008.2007884},
}
@article{JRM-GA-JSS:09,
author = {J. R. Marden and G. Arslan and J. S. Shamma},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {208--220},
title = {Joint strategy fictitious play with inertia for
potential games},
volume = {54},
year = {2009},
doi = {10.1109/TAC.2008.2010885},
}
@article{DB-GN:15,
author = {D. Bauso and G. Notarstefano},
journal = {IEEE Transactions on Automatic Control},
number = {11},
pages = {3107--3112},
title = {Distributed $n$-Player Approachability and Consensus
in Coalitional Games},
volume = {60},
year = {2015},
doi = {10.1109/TAC.2015.2411873},
}
@article{TH-YI-MF-MWS:12,
author = {T. Hatanaka and Y. Igarashi and M. Fujita and
M. W. Spong},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {360--375},
title = {Passivity-based pose synchronization in three
dimensions},
volume = {57},
year = {2012},
doi = {10.1109/TAC.2011.2166668},
}
@article{LS-FF:11,
author = {L. Schenato and F. Fiorentin},
journal = {Automatica},
number = {9},
pages = {1878--1886},
title = {{Average TimeSynch: A} consensus-based protocol for
clock synchronization in wireless sensor networks},
volume = {47},
year = {2011},
doi = {10.1016/j.automatica.2011.06.012},
}
@article{MA:07,
author = {M. Arcak},
journal = {IEEE Transactions on Automatic Control},
number = {8},
pages = {1380-1390},
title = {Passivity as a design tool for group coordination},
volume = {52},
year = {2007},
doi = {10.1109/TAC.2007.902733},
}
@article{JTW-MA:04,
author = {J. T. Wen and M. Arcak},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {162-174},
title = {A unifying passivity framework for network flow
control},
volume = {49},
year = {2004},
doi = {10.1109/TAC.2003.822858},
}
@article{EM-RAF-AKT:16,
author = {E. Mallada and R. A. Freeman and A. K. Tang},
journal = {IEEE Transactions on Control of Network Systems},
number = {1},
pages = {1-12},
title = {Distributed synchronization of heterogeneous
oscillators on networks with arbitrary topology},
volume = {3},
year = {2016},
doi = {10.1109/TCNS.2015.2428371},
}
@book{WR-RWB:08,
author = {W. Ren and R. W. Beard},
publisher = {Springer},
series = {Communications and Control Engineering},
title = {Distributed Consensus in Multi-vehicle Cooperative
Control},
year = {2008},
isbn = {978-1-84800-014-8},
}
@book{FB-JC-SM:09,
author = {F. Bullo and J. Cort{\'e}s and S. Mart{\'\i}nez},
publisher = {Princeton University Press},
title = {Distributed Control of Robotic Networks},
year = {2009},
isbn = {978-0-691-14195-4},
url = {http://www.coordinationbook.info},
}
@book{MM-ME:10,
author = {M. Mesbahi and M. Egerstedt},
publisher = {Princeton University Press},
title = {Graph Theoretic Methods in Multiagent Networks},
year = {2010},
isbn = {9781400835355},
}
@book{HB-MA-JW:11,
author = {H. Bai and M. Arcak and J. Wen},
publisher = {Springer},
title = {Cooperative Control Design},
year = {2011},
isbn = {1461429072},
}
@book{EC-BP-AT:14,
author = {E. Cristiani and B. Piccoli and A. Tosin},
publisher = {Springer},
title = {Multiscale Modeling of Pedestrian Dynamics},
year = {2014},
isbn = {978-3-319-06619-6},
}
@book{PAF-UH:15,
author = {P. A. Fuhrmann and U. Helmke},
publisher = {Springer},
title = {The Mathematics of Networks of Linear Systems},
year = {2015},
isbn = {3319166468},
}
@book{BAF-MM:16,
author = {B. A. Francis and M. Maggiore},
publisher = {Springer},
title = {Flocking and Rendezvous in Distributed Robotics},
year = {2016},
isbn = {978-3-319-24727-4},
}
@book{MA-CM-AP:16,
author = {M. Arcak and C. Meissen and A. Packard},
publisher = {Springer},
title = {Networks of Dissipative Systems: Compositional
Certification of Stability, Performance, and Safety},
year = {2016},
doi = {10.1007/978-3-319-29928-0},
isbn = {978-3-319-29928-0},
}
@book{MAP-JPG:16,
author = {M. A. Porter and J. P. Gleeson},
publisher = {Springer},
title = {Dynamical Systems on Networks: A Tutorial},
year = {2016},
doi = {10.1007/978-3-319-26641-1},
isbn = {978-3-319-26641-1},
}
@article{SM-JC-FB:04n,
author = {S. Mart{\'\i}nez and J. Cort{\'e}s and F. Bullo},
journal = {{IEEE} Control Systems},
number = {4},
pages = {75-88},
title = {Motion Coordination with Distributed Information},
volume = {27},
year = {2007},
abstract = {This paper surveys recently-developed theoretical
tools for the analysis and design of coordination
algorithms for networks of mobile autonomous agents.
First, various motion coordination tasks are encoded
into aggregate cost functions from Geometric
Optimization. Second, the limited communication
capabilities of the mobile agents are modeled via the
notions of proximity graphs from Computational
Geometry and of spatially distributed maps. Finally,
we illustrate how to apply these tools to design and
analyze scalable cooperative strategies in a variety
of motion coordination problems such as deployment,
rendezvous, and flocking.},
doi = {10.1109/MCS.2007.384124},
}
@article{WR-RWB-EMA:07,
author = {W. Ren and R. W. Beard and E. M. Atkins},
journal = {{IEEE} Control Systems},
number = {2},
pages = {71-82},
title = {Information consensus in multivehicle cooperative
control},
volume = {27},
year = {2007},
doi = {10.1109/MCS.2007.338264},
}
@article{YC-WY-WR-GC:13,
author = {Y. Cao and W. Yu and W. Ren and G. Chen},
journal = {IEEE Transactions on Industrial informatics},
number = {1},
pages = {427--438},
title = {An overview of recent progress in the study of
distributed multi-agent coordination},
volume = {9},
year = {2013},
doi = {10.1109/TII.2012.2219061},
}
@article{KKO-MCP-HSA:15,
author = {K.-K. Oh and M.-C. Park and H.-S. Ahn},
journal = {Automatica},
pages = {424--440},
title = {A survey of multi-agent formation control},
volume = {53},
year = {2015},
doi = {10.1016/j.automatica.2014.10.022},
}
@article{MEJN:03,
author = {Newman, M. E. J.},
journal = {SIAM Review},
number = {2},
pages = {167--256},
title = {The structure and function of complex networks},
volume = {45},
year = {2003},
doi = {10.1137/S003614450342480},
}
@article{SB-VL-YM-MC-DUH:06,
author = {Boccaletti, S. and Latora, V. and Moreno, Y. and
Chavez, M. and Hwang, D. U.},
journal = {Physics Reports},
number = {4-5},
pages = {175--308},
title = {Complex networks: {S}tructure and dynamics},
volume = {424},
year = {2006},
doi = {10.1016/j.physrep.2005.10.009},
}
@article{CC-SF-VL:09,
author = {Castellano, C. and Fortunato, S. and Loreto, V.},
journal = {Reviews of Modern Physics},
number = {2},
pages = {591--646},
title = {Statistical Physics of Social Dynamics},
volume = {81},
year = {2009},
doi = {10.1103/RevModPhys.81.591},
}
@book{DE-JK:10,
author = {D. Easley and J. Kleinberg},
publisher = {Cambridge University Press},
title = {Networks, Crowds, and Markets: Reasoning About a
Highly Connected World},
year = {2010},
isbn = {0521195330},
}
@book{MOJ:10,
author = {M. O. Jackson},
publisher = {Princeton University Press},
title = {Social and Economic Networks},
year = {2010},
isbn = {0691148201},
}
@book{MEJN:10,
author = {Newman, M. E. J.},
publisher = {Oxford University Press},
title = {Networks: An Introduction},
year = {2010},
isbn = {0199206651},
}
@article{DS:17,
author = {D. Spielman},
journal = {Bulletin of the American Mathematical Society},
number = {1},
pages = {45--61},
title = {Graphs, Vectors, and Matrices},
volume = {54},
year = {2017},
doi = {10.1090/bull/1557},
}
@incollection{RPA:64,
author = {R. P. Abelson},
booktitle = {Contributions to Mathematical Psychology},
editor = {N. Frederiksen and H. Gulliksen},
pages = {142--160},
publisher = {Holt, Rinehart, \& Winston},
title = {Mathematical models of the distribution of attitudes
under controversy},
volume = {14},
year = {1964},
isbn = {0030430100},
}
@book{NEF-ECJ:11,
author = {N. E. Friedkin and E. C. Johnsen},
publisher = {Cambridge University Press},
title = {Social Influence Network Theory: {A} Sociological
Examination of Small Group Dynamics},
year = {2011},
isbn = {9781107002463},
}
@techreport{AC-HL-JX:16,
author = {A. G. Chandrasekhar and H. Larreguy and J. P. Xandri},
institution = {National Bureau of Economic Research},
month = {August},
number = {21468},
series = {Working Paper Series},
type = {Working Paper},
title = {Testing Models of Social Learning on Networks:
Evidence from a Lab Experiment in the Field},
year = {2015},
abstract = {Agents often use noisy signals from their neighbors
to update their beliefs about a state of the world.
The effectiveness of social learning relies on the
details of how agents aggregate information from
others. There are two prominent models of information
aggregation in networks: (1) Bayesian learning, where
agents use Bayes' rule to assess the state of the
world and (2) DeGroot learning, where agents instead
consider a weighted average of their neighbors'
previous period opinions or actions. Agents who
engage in DeGroot learning often double-count
information and may not converge in the long run. We
conduct a lab experiment in the field with 665
subjects across 19 villages in Karnataka, India,
designed to structurally test which model best
describes social learning. Seven subjects were placed
into a network with common knowledge of the network
structure. Subjects attempted to learn the underlying
(binary) state of the world, having received
independent identically distributed signals in the
first period. Thereafter, in each period, subjects
made guesses about the state of the world, and these
guesses were transmitted to their neighbors at the
beginning of the following round. We structurally
estimate a model of Bayesian learning, relaxing
common knowledge of Bayesian rationality by allowing
agents to have incomplete information as to whether
others are Bayesian or DeGroot. Our estimates show
that, despite the flexibility in modeling learning in
these networks, agents are robustly best described by
DeGroot-learning models wherein they take a simple
majority of previous guesses in their neighborhood.},
doi = {10.3386/w21468},
}
@article{NEF-PJ-FB:14n,
author = {N. E. Friedkin and P. Jia and F. Bullo},
journal = {Sociological Science},
pages = {444-472},
title = {A Theory of the Evolution of Social Power: {N}atural
Trajectories of Interpersonal Influence Systems along
Issue Sequences},
volume = {3},
year = {2016},
abstract = {This article reports new advancements in the theory
of influence system evolution in small deliberative
groups, and a novel set of empirical findings on such
evolution. The theory elaborates the specification of
the single-issue opinion dynamics of such groups,
which has been the focus of theory development in the
field of opinion dynamics, to include group dynamics
that occur along a sequence of issues. The theory
predicts an evolution of influence centralities along
issue sequences based on elementary reflected
appraisal mechanisms that modify influence network
structure and flows of influence in the group. The
new empirical findings, which are also reported in
this article, present a remarkable suite of
issue-sequence effects on influence network structure
consistent with theoretical predictions.},
doi = {10.15195/v3.a20},
}
@article{AVP-RT:17,
author = {A. V. Proskurnikov and R. Tempo},
journal = {Annual Reviews in Control},
pages = {65-79},
title = {A Tutorial on Modeling and Analysis of Dynamic Social
Networks. {Part I}},
volume = {43},
year = {2017},
doi = {10.1016/j.arcontrol.2017.03.002},
}
@article{AW-DWK:69,
author = {A. Watton and D. W. Kydon},
journal = {American Journal of Physics},
number = {2},
pages = {220--221},
title = {Analytical Aspects of the {$N$}-Bug Problem},
volume = {37},
year = {1969},
doi = {10.1119/1.1975458},
}
@article{JAM-MEB-BAF:04c,
author = {J. A. Marshall and M. E. Broucke and B. A. Francis},
journal = {IEEE Transactions on Automatic Control},
number = {11},
pages = {1963-1974},
title = {Formations of vehicles in cyclic pursuit},
volume = {49},
year = {2004},
abstract = {Inspired by the so-called "bugs" problem from
mathematics, we study the geometric formations of
multi-vehicle systems under cyclic pursuit. First, we
introduce the notion of cyclic pursuit by examining a
system of identical linear agents in the plane. This
idea is then extended to a system of wheeled
vehicles, each subject to a single nonholonomic
constraint (i.e., unicycles), which is the principal
focus of this article. The pursuit framework is
particularly simple in that the n identical vehicles
are ordered such that vehicle i pursues vehicle i + 1
modulo n. In this article, we assume each vehicle has
the same constant forward speed. We show that the
system's equilibrium formations are generalized
regular polygons and it is exposed how the
multi-vehicle system's global behavior can be shaped
through appropriate controller gain assignments. We
then study the local stability of these equilibrium
polygons, revealing which formations are stable and
which are not. Index Terms: Cooperative control,
multi-agent systems, circulant matrices, pursuit
problems.},
doi = {10.1109/TAC.2004.837589},
}
@article{SLS-MEB-BAF:05,
author = {S. L. Smith and M. E. Broucke and B. A. Francis},
journal = {Automatica},
number = {6},
pages = {1045-1053},
title = {A hierarchical cyclic pursuit scheme for vehicle
networks},
volume = {41},
year = {2005},
doi = {10.1016/j.automatica.2005.01.001},
}
@book{RAH-CRJ:85,
author = {R. A. Horn and C. R. Johnson},
publisher = {Cambridge University Press},
title = {Matrix Analysis},
year = {1985},
isbn = {0521386322},
}
@book{CDM:01,
author = {C. D. Meyer},
publisher = {SIAM},
title = {Matrix Analysis and Applied Linear Algebra},
year = {2001},
annote = {http://www.matrixanalysis.com},
isbn = {0898714540},
}
@book{FRG:59ab,
address = {New York},
author = {Felix R. Gantmacher},
note = {Translation of German edition by K.~A.~Hirsch},
publisher = {Chelsea},
title = {The Theory of Matrices},
volume = {1 and 2},
year = {1959},
isbn = {0-8218-1376-5 and 0-8218-2664-6},
}
@article{OK:1907,
author = {Oskar Perron},
journal = {Mathematische Annalen},
number = {2},
pages = {248--263},
title = {{Zur Theorie der Matrices}},
volume = {64},
year = {1907},
doi = {10.1007/BF01449896},
}
@article{FGF:1912,
author = {Frobenius, Ferdinand Georg},
note = {K{\"o}nigliche Gesellschaft der Wissenschaften},
title = {{\"U}ber Matrizen aus nicht negativen {E}lementen},
year = {1912},
doi = {10.3931/e-rara-18865},
}
@book{LB:92,
author = {L. Breiman},
note = {Corrected reprint of the 1968 original},
publisher = {SIAM},
series = {Classics in Applied Mathematics},
title = {Probability},
volume = {7},
year = {1992},
isbn = {0-89871-296-3},
}
@book{LH:13,
edition = {2},
editor = {L. Hogben},
publisher = {Chapman and Hall/CRC},
title = {Handbook of Linear Algebra},
year = {2013},
isbn = {1466507284},
}
@article{JRS:00,
author = {J. R. Silvester},
journal = {The Mathematical Gazette},
number = {501},
pages = {460--467},
title = {Determinants of Block Matrices},
volume = {84},
year = {2000},
doi = {10.2307/3620776},
}
@inproceedings{JK:13,
address = {Rio de Janeiro, Brazil},
author = {J. Kunegis},
booktitle = {International Conference on World Wide Web Companion},
month = may,
pages = {1343--1350},
title = {{KONECT:} the {K}oblenz network collection},
year = {2013},
doi = {10.1145/2487788.2488173},
}
@article{TAM-YU:11,
author = {T. A. Davis and Y. Hu},
journal = {ACM Transactions on Mathematical Software},
number = {1},
pages = {1-25},
title = {The {University of Florida} sparse matrix collection},
volume = {38},
year = {2011},
abstract = {We describe the University of Florida Sparse Matrix
Collection, a large and actively growing set of
sparse matrices that arise in real applications. The
Collection is widely used by the numerical linear
algebra community for the development and performance
evaluation of sparse matrix algorithms. It allows for
robust and repeatable experiments: robust because
performance results with artificially-generated
matrices can be misleading, and repeatable because
matrices are curated and made publicly available in
many formats. Its matrices cover a wide spectrum of
domains, include those arising from problems with
underlying 2D or 3D geometry (as structural
engineering, computational fluid dynamics, model
reduction, electromagnetics, semiconductor devices,
thermodynamics, materials, acoustics, computer
graphics/vision, robotics/kinematics, and other
discretizations) and those that typically do not have
such geometry (optimization, circuit simulation,
economic and financial modeling, theoretical and
quantum chemistry, chemical process simulation,
mathematics and statistics, power networks, and other
networks and graphs). We provide software for
accessing and managing the Collection, from MATLAB,
Mathematica, Fortran, and C, as well as an online
search capability. Graph visualization of the
matrices is provided, and a new multilevel coarsening
scheme is proposed to facilitate this task.},
doi = {10.1145/2049662.2049663},
}
@misc{CLDB:08,
author = {Christopher L. DuBois},
institution = {University of California, Irvine, School of
Information and Computer Sciences},
title = {{UCI} {N}etwork {D}ata {R}epository},
year = {2008},
url = {http://networkdata.ics.uci.edu},
}
@book{FH:69,
author = {F. Harary},
publisher = {Addison-Wesley},
title = {Graph Theory},
year = {1969},
url = {http://www.dtic.mil/dtic/tr/fulltext/u2/705364.pdf},
}
@article{LE:1741,
author = {Leonhard Euler},
journal = {Commentarii Academiae Scientiarum Imperialis
Petropolitanae},
note = {Also in Opera Omnia (1), Vol. 7, 1-10.},
pages = {128-140},
title = {{Solutio Problematis ad Geometriam Situs
Pertinentis}},
volume = {8},
year = {1741},
}
@article{GK:1847,
author = {Gustav Kirchhoff},
journal = {Annalen der Physik und Chemie},
number = {12},
pages = {497-508},
title = {{\"Uber die Aufl\"osung der Gleichungen, auf welche
man bei der Untersuchung der linearen Verteilung
galvanischer Str\"ome gef\"uhrt wird}},
volume = {148},
year = {1847},
doi = {10.1002/andp.18471481202},
}
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author = {Arthur Cayley},
journal = {Philosophical Magazine},
pages = {19-30},
title = {{On the Theory of Analytic Forms Called Trees}},
volume = {13},
year = {1857},
}
@book{RD:00,
author = {R. Diestel},
edition = {2},
publisher = {Springer},
series = {Graduate Texts in Mathematics},
title = {Graph Theory},
volume = {173},
year = {2000},
annote = {Reference for Metric Graphs},
isbn = {3642142788},
}
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author = {B. Bollob{\'a}s},
publisher = {Springer},
title = {Modern Graph Theory},
year = {1998},
isbn = {0387984887},
}
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author = {T. M. J. Fruchterman and and E. M. Reingold},
journal = {Software: Practice and Experience},
number = {11},
pages = {1129--1164},
title = {Graph drawing by force-directed placement},
volume = {21},
year = {1991},
doi = {10.1002/spe.4380211102},
}
@article{YH:05,
author = {Y. Hu},
journal = {Mathematica Journal},
number = {1},
pages = {37--71},
title = {Efficient, high-quality force-directed graph drawing},
volume = {10},
year = {2005},
url = {http://www.mathematica-journal.com/issue/v10i1/},
}
@article{ZL-BF-MM:05,
author = {Z. Lin and B. Francis and M. Maggiore},
journal = {IEEE Transactions on Automatic Control},
number = {1},
pages = {121-127},
title = {Necessary and sufficient graphical conditions for
formation control of unicycles},
volume = {50},
year = {2005},
doi = {10.1109/TAC.2004.841121},
}
@article{LM:05,
author = {L. Moreau},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {169-182},
title = {Stability of multiagent systems with time-dependent
communication links},
volume = {50},
year = {2005},
abstract = {We study a simple but compelling model of network of
agents interacting via time-dependent communication
links. The model finds application in a variety of
fields including synchronization, swarming and
distributed decision making. In the model, each agent
updates his current state based upon the current
information received from neighboring agents.
Necessary and/or sufficient conditions for the
convergence of the individual agentsÃ states to a
common value are presented, thereby extending recent
results reported in the literature. The stability
analysis is based upon a blend of graph-theoretic and
system-theoretic tools with the notion of convexity
playing a central role. The analysis is integrated
within a formal framework of set-valued Lyapunov
theory, which may be of independent interest. Among
others, it is observed that more communication does
not necessarily lead to faster convergence and may
eventually even lead to a loss of convergence, even
for the simple models discussed in the present
paper.},
doi = {10.1109/TAC.2004.841888},
}
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year = {1994},
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@book{CDG-GFR:01,
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title = {Algebraic Graph Theory},
year = {2001},
isbn = {0387952411},
}
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number = {4},
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year = {2003},
doi = {10.2307/3219081},
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year = {2002},
doi = {10.1017/S0963548301004928},
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volume = {281},
year = {2004},
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year = {1945},
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edition = {2},
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title = {Matrix Population Models},
year = {2006},
isbn = {087893121X},
}
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note = {A Wiley-Interscience Publication, Pure and Applied
Mathematics},
publisher = {John Wiley \& Sons},
title = {Circulant Matrices},
year = {1979},
isbn = {0-471-05771-1},
}
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year = {1987},
doi = {10.1016/0378-8733(87)90009-8},
}
@phdthesis{SFS:69,
author = {Sampson, S. F.},
school = {Department of Sociology, Cornell University},
title = {Crisis in a Cloister},
year = {1969},
}
@article{PMD-DV-JZ:03,
author = {DeMarzo, P. M. and Vayanos, D. and Zwiebel, J.},
journal = {The Quarterly Journal of Economics},
number = {3},
pages = {909-968},
title = {Persuasion Bias, Social Influence, and Unidimensional
Opinions},
volume = {118},
year = {2003},
doi = {10.1162 /00335530360698469},
}
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author = {P. Bonacich},
journal = {Journal of Mathematical Sociology},
number = {1},
pages = {113--120},
title = {Factoring and weighting approaches to status scores
and clique identification},
volume = {2},
year = {1972},
doi = {10.1080/0022250X.1972.9989806},
}
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pages = {39--43},
title = {A new status index derived from sociometric analysis},
volume = {18},
year = {1953},
doi = {10.1007/BF02289026},
}
@article{HI-RT:14,
author = {H. Ishii and R. Tempo},
journal = {{IEEE} Control Systems},
number = {3},
pages = {34--53},
title = {The {PageRank} Problem, Multiagent Consensus, and Web
Aggregation: {A} Systems and Control Viewpoint},
volume = {34},
year = {2014},
doi = {10.1109/MCS.2014.2308672},
}
@article{DFG:14,
author = {D. F. Gleich},
journal = {SIAM Review},
number = {3},
pages = {321-363},
title = {{PageRank} beyond the {W}eb},
volume = {57},
year = {2015},
doi = {10.1137/140976649},
}
@article{SPB-MGE:06,
author = {S. P. Borgatti and M. G. Everett},
journal = {Social Networks},
number = {4},
pages = {466--484},
title = {A graph-theoretic perspective on centrality},
volume = {28},
year = {2006},
doi = {10.1016/j.socnet.2005.11.005},
}
@misc{UB:06,
address = {Bloomington, IN, USA},
author = {U. Brandes},
howpublished = {Slides},
month = may,
note = {The International Workshop/School and Conference on
Network Science},
title = {Centrality: concepts and methods},
year = {2006},
url = {http://vw.indiana.edu/netsci06},
}
@book{UB-TE:05,
author = {U. Brandes and T. Erlebach},
journal = {Lecture Notes in Computer Science},
publisher = {Springer},
title = {Network Analysis: Methodological Foundations},
year = {2005},
isbn = {3540249796},
}
@article{AB:50,
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year = {1950},
doi = {10.1121/1.1906679},
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author = {L. C. Freeman},
journal = {Sociometry},
number = {1},
pages = {35-41},
title = {A set of measures of centrality based on betweenness},
volume = {40},
year = {1977},
doi = {10.2307/3033543},
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journal = {Sociological Methodology},
pages = {176--185},
title = {Technique for analyzing overlapping memberships},
volume = {4},
year = {1972},
doi = {10.2307/270732},
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@article{JMK:99,
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number = {5},
pages = {604--632},
title = {Authoritative Sources in a Hyperlinked Environment},
volume = {46},
year = {1999},
doi = {10.1145/324133.324140},
}
@article{SB-LP:98,
author = {S. Brin and L. Page},
journal = {Computer Networks},
pages = {107-117},
title = {The anatomy of a large-scale hypertextual {W}eb
search engine},
volume = {30},
year = {1998},
doi = {10.1016/S0169-7552(98)00110-X},
}
@misc{LP:01,
author = {L. Page},
month = sep,
note = {US Patent 6,285,999},
publisher = {Google Patents},
title = {Method for node ranking in a linked database},
year = {2001},
url = {https://www.google.com/patents/US6285999},
}
@article{NEF:91,
author = {N. E. Friedkin},
journal = {American Journal of Sociology},
number = {6},
pages = {1478-1504},
title = {Theoretical foundations for centrality measures},
volume = {96},
year = {1991},
doi = {10.1086/229694},
}
@article{NEF-ECJ:14,
author = {N. E. Friedkin and E. C. Johnsen},
journal = {Social Networks},
pages = {12--13},
title = {Two steps to obfuscation},
volume = {39},
year = {2014},
doi = {10.1016/j.socnet.2014.03.008},
}
@article{YN:12,
author = {Y. Nesterov},
journal = {SIAM Journal on Optimization},
number = {2},
pages = {341-362},
title = {Efficiency of coordinate descent methods on
huge-scale optimization problems},
volume = {22},
year = {2012},
doi = {10.1137/100802001},
}
@article{HI-RT:10,
author = {H. Ishii and R. Tempo},
journal = {IEEE Transactions on Automatic Control},
number = {9},
pages = {1987-2002},
title = {Distributed Randomized Algorithms for the {PageRank}
Computation},
volume = {55},
year = {2010},
doi = {10.1109/TAC.2010.2042984},
}
@article{WXZ-HFC-HTF:13,
author = {W. X. Zhao and H. F. Chen and H. T. Fang},
journal = {IEEE Transactions on Automatic Control},
number = {12},
pages = {3255-3259},
title = {Convergence of distributed randomized {PageRank}
algorithms},
volume = {58},
year = {2013},
doi = {10.1109/TAC.2013.2264553},
}
@incollection{NEF-ECJ:99,
author = {N. E. Friedkin and E. C. Johnsen},
booktitle = {Advances in Group Processes},
editor = {S. R. Thye and E. J. Lawler and M. W. Macy and
H. A. Walker},
pages = {1-29},
publisher = {Emerald Group Publishing Limited},
title = {Social influence networks and opinion change},
volume = {16},
year = {1999},
isbn = {0762304529},
}
@article{DB-JK-SO:15,
author = {D. Bindel and J. Kleinberg and S. Oren},
journal = {Games and Economic Behavior},
pages = {248-265},
title = {How bad is forming your own opinion?},
volume = {92},
year = {2015},
abstract = {Abstract The question of how people form their
opinion has fascinated economists and sociologists
for long time. In many of the models, a group of
people in a social network, each holding a numerical
opinion, arrive at a shared opinion through repeated
averaging with their neighbors in the network.
Motivated by the observation that in reality
consensus is rarely reached, we study a related
sociological model in which individuals' intrinsic
beliefs counterbalance the averaging process and
yield a diversity of opinions. We interpret the
repeated averaging process as best-response dynamics
in an underlying game with natural payoffs and its
limit as an equilibrium. This allows us to study the
cost of disagreement by comparing between the cost at
equilibrium and the social optimum. We also consider
a natural network design problem in this setting:
which links can we add to the underlying network to
reduce the cost at equilibrium?},
doi = {10.1016/j.geb.2014.06.004},
}
@article{CR-PF-RT-HI:15,
author = {C. Ravazzi and P. Frasca and R. Tempo and H. Ishii},
journal = {IEEE Transactions on Control of Network Systems},
number = {1},
pages = {78-87},
title = {Ergodic randomized algorithms and dynamics over
networks},
volume = {2},
year = {2015},
doi = {10.1109/TCNS.2014.2367571},
}
@inproceedings{DK-AD-JG:03,
address = {Washington, DC},
author = {D. Kempe and A. Dobra and J. Gehrke},
booktitle = {IEEE Symposium on Foundations of Computer Science},
month = oct,
pages = {482-491},
title = {Gossip-Based Computation of Aggregate Information},
year = {2003},
doi = {10.1109/SFCS.2003.1238221},
}
@article{AO-JNT:07,
author = {A. Olshevsky and J. N. Tsitsiklis},
journal = {SIAM Journal on Control and Optimization},
number = {1},
pages = {33-55},
title = {Convergence Speed in Distributed Consensus and
Averaging},
volume = {48},
year = {2009},
annote = {We study the convergence speed of distributed
iterative algorithms for the consensus and averaging
problems, with emphasis on the latter. We first
consider the case of a fixed communication topology.
We show that a simple adaptation of a consensus
algorithm leads to an averaging algorithm. We prove
lower bounds on the worst-case convergence time for
various classes of linear, time-invariant,
distributed consensus methods, and provide an
algorithm that essentially matches those lower
bounds. We then consider the case of a time-varying
topology, and provide a polynomial-time averaging
algorithm.},
doi = {10.1137/060678324},
}
@inproceedings{FB-VB-PT-JT-MV:10,
author = {F. Benezit and V. Blondel and P. Thiran and
J. Tsitsiklis and M. Vetterli},
booktitle = {IEEE International Symposium on Information Theory},
month = jun,
pages = {1753-1757},
title = {Weighted gossip: {D}istributed averaging using
non-doubly stochastic matrices},
year = {2010},
doi = {10.1109/ISIT.2010.5513273},
}
@article{ZB-JD-JML-BW:09,
author = {Z. Burda and J. Duda and J. M. Luck and B. Waclaw},
journal = {Physical Review Letters},
pages = {160602},
title = {Localization of the Maximal Entropy Random Walk},
volume = {102},
year = {2009},
doi = {10.1103/PhysRevLett.102.160602},
}
@article{MF:73,
author = {M. Fiedler},
journal = {Czechoslovak Mathematical Journal},
number = {2},
pages = {298--305},
publisher = {Institute of Mathematics, Academy of Sciences of the
Czech Republic},
title = {Algebraic connectivity of graphs},
volume = {23},
year = {1973},
url = {http://dml.cz/dmlcz/101168},
}
@misc{DG:06,
author = {D. Gleich},
institution = {Purdue University},
month = jan,
note = {(Last retrieved on May 30, 2016.)},
title = {{Spectral Graph Partitioning and the Laplacian with
Matlab}},
year = {2006},
url = {https://www.cs.purdue.edu/homes/dgleich/demos/matlab/
spectral/spectral.html},
}
@incollection{BM:91,
author = {B. Mohar},
booktitle = {Graph Theory, Combinatorics, and Applications},
editor = {Y. Alavi and G. Chartrand and O. R. Oellermann and
A. J. Schwenk},
pages = {871-898},
publisher = {John Wiley \& Sons},
title = {The {L}aplacian spectrum of graphs},
volume = {2},
year = {1991},
isbn = {0471532452},
url = {http://citeseerx.ist.psu.edu/viewdoc/summary?
doi=10.1.1.96.2577},
}
@article{RM:94,
author = {R. Merris},
journal = {Linear Algebra and its Applications},
pages = {143-176},
title = {Laplacian matrices of a graph: {A} survey},
volume = {197},
year = {1994},
doi = {10.1016/j.laa.2011.11.032 3374},
}
@article{DF:72,
author = {D. Fife},
journal = {Mathematical Biosciences},
number = {3},
pages = {311--315},
title = {Which linear compartmental systems contain traps?},
volume = {14},
year = {1972},
doi = {10.1016/0025-5564(72)90082-X},
}
@article{DMF-JAJ:75,
author = {D. M. Foster and J. A. Jacquez},
journal = {Mathematical Biosciences},
number = {1},
pages = {89--97},
title = {Multiple zeros for eigenvalues and the multiplicity
of traps of a linear compartmental system},
volume = {26},
year = {1975},
doi = {10.1016/0025-5564(75)90096-6},
}
@article{RPA-PYC:00,
author = {R. P. Agaev and P. Y. Chebotarev},
journal = {Automation and Remote Control},
number = {9},
pages = {1424-1450},
title = {The matrix of maximum out forests of a digraph and
its applications},
volume = {61},
year = {2000},
abstract = {We study the maximum out forests of a (weighted)
digraph and the matrix of maximum out forests. A
maximum out forest of a digraph Gamma is a spanning
subgraph of Gamma that consists of disjoint diverging
trees and has the maximum possible number of arcs. If
a digraph contains out arborescences, then maximum
out forests coincide with them. We consider Markov
chains related to a weighted digraph and prove that
the matrix of Cesaro limiting probabilities of such a
chain coincides with the normalized matrix of maximum
out forests. This provides an interpretation for the
matrix of Cesasro limiting probabilities of an
arbitrary stationary finite Markov chain in terms of
the weight of maximum out forests. We discuss the
applications of the matrix of maximum out forests and
its transposition, the matrix of limiting
accessibilities of a digraph, to the problems of
preference aggregation, measuring the vertex
proximity, and uncovering the structure of a
digraph.},
url = {https://arxiv.org/pdf/math/0602059},
}
@article{WR-RWB:05,
author = {W. Ren and R. W. Beard},
journal = {IEEE Transactions on Automatic Control},
number = {5},
pages = {655-661},
title = {Consensus seeking in multiagent systems under
dynamically changing interaction topologies},
volume = {50},
year = {2005},
abstract = {This note considers the problem of information
consensus among multiple agents in the presence of
limited and unreliable information exchange with
dynamically changing interaction topologies. Both
discrete and continuous update schemes are proposed
for information consensus. This note shows that
information consensus under dynamically changing
interaction topologies can be achieved asymptotically
if the union of the directed interaction graphs have
a spanning tree frequently enough as the system
evolves.},
doi = {10.1109/TAC.2005.846556},
}
@article{IG-WX:04,
author = {I. Gutman and W. Xiao},
journal = {Bulletin (Académie serbe des sciences et des arts.
Classe des sciences mathématiques et naturelles.
Sciences mathématiques)},
number = {29},
pages = {15--23},
title = {Generalized inverse of the {L}aplacian matrix and
some applications},
volume = {129},
year = {2004},
url = {http://emis.ams.org/journals/BSANU/29/2.html},
}
@article{MAP-JPO-PJM:09,
author = {M. A. Porter and J.-P. Onnela and P. J. Mucha},
journal = {Notices of the AMS},
number = {9},
pages = {1082--1097},
title = {Communities in networks},
volume = {56},
year = {2009},
url = {http://www.ams.org/notices/200909/rtx090901082p.pdf},
}
@article{SF:10,
author = {S. Fortunato},
journal = {Physics Reports},
number = {3-5},
pages = {75--174},
title = {Community detection in graphs},
volume = {486},
year = {2010},
doi = {10.1016/j.physrep.2009.11.002},
}
@inproceedings{RC-AC-LS-SZ:08,
author = {R. Carli and A. Chiuso and L. Schenato and
S. Zampieri},
booktitle = {{IFAC} {W}orld {C}ongress},
pages = {10289-10294},
title = {A {PI} Consensus Controller for Networked Clocks
Synchronization},
volume = {41},
year = {2008},
doi = {10.3182/20080706-5-KR-1001.01741},
}
@article{RC-SZ:14,
author = {R. Carli and S. Zampieri},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {409-422},
title = {Network Clock Synchronization Based on the
Second-Order Linear Consensus Algorithm},
volume = {59},
year = {2014},
doi = {10.1109/TAC.2013.2283742},
}
@article{BS-UB-ADK:05,
author = {B. Sundararaman and U. Buy and A. D. Kshemkalyani},
journal = {Ad Hoc Networks},
number = {3},
pages = {281-323},
title = {Clock synchronization for wireless sensor networks: a
survey},
volume = {3},
year = {2005},
doi = {10.1016/j.adhoc.2005.01.002},
}
@article{FS-BY:04,
author = {F. Sivrikaya and B. Yener},
journal = {IEEE Network},
number = {4},
pages = {45--50},
title = {Time synchronization in sensor networks: {A} survey},
volume = {18},
year = {2004},
doi = {10.1109/MNET.2004.1316761},
}
@article{OS-US-YBN-SS:08,
author = {Simeone, O. and Spagnolini, U. and Bar-Ness, Y. and
Strogatz, S. H.},
journal = {IEEE Signal Processing Magazine},
number = {5},
pages = {81--97},
title = {Distributed synchronization in wireless networks},
volume = {25},
year = {2008},
doi = {10.1109/MSP.2008.926661},
}
@article{NR:12,
author = {N. Reff},
journal = {Linear Algebra and its Applications},
number = {9},
pages = {3165--3176},
title = {Spectral properties of complex unit gain graphs},
volume = {436},
year = {2012},
doi = {10.1016/j.laa.2011.10.021},
}
@article{ZL-WD-GY-CY-AG:13,
author = {Z. Lin and W. Ding and G. Yan and C. Yu and A. Giua},
journal = {Automatica},
number = {6},
pages = {1900--1906},
title = {Leader--follower formation via complex {L}aplacian},
volume = {49},
year = {2013},
doi = {10.1016/j.automatica.2013.02.055},
}
@misc{JGD-LQ:14,
author = {J.-G. Dong and L. Qiu},
title = {Complex {L}aplacians and Applications in Multi-Agent
Systems},
year = {2014},
url = {https://arxiv.org/pdf/1406.1862},
}
@article{CG-JC-FB:06o,
author = {C. Gao and J. Cort{\'e}s and F. Bullo},
journal = {Automatica},
number = {8},
pages = {2120-2127},
title = {Notes on Averaging over Acyclic Digraphs and Discrete
Coverage Control},
volume = {44},
year = {2008},
abstract = {In this paper, we show the relationship between two
algorithms and optimization problems that are the
subject of recent attention in the networking and
control literature. First, we obtain some results on
averaging algorithms over acyclic digraphs with fixed
and controlled-switching topology. Second, we discuss
continuous and discrete coverage control laws.
Further, we show how discrete coverage control laws
can be cast as averaging algorithms defined over
discrete Voronoi graphs.},
doi = {10.1016/j.automatica.2007.12.017},
}
@book{DGL-YY:08,
author = {D. G. Luenberger and Y. Ye},
edition = {4},
publisher = {Springer},
title = {Linear and Nonlinear Programming},
year = {2008},
isbn = {9780387745022},
}
@book{JPH:09,
author = {J. P. Hespanha},
publisher = {Princeton University Press},
title = {Linear Systems Theory},
year = {2009},
isbn = {0691140219},
}
@inproceedings{WR-WA:05,
address = {San Francisco, CA, USA},
author = {W. Ren and W. Atkins},
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year = {2017},
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month = sep,
note = {Submitted},
title = {Electrical Networks and Algebraic Graph Theory:
{M}odels, Properties, and Applications},
year = {2017},
abstract = {Algebraic graph theory is a cornerstone in the study
of electrical networks ranging from miniature
integrated circuits to continental-scale power
systems. Conversely, many fundamental results of
algebraic graph theory were laid out by early
electrical circuit analysts. In this paper we survey
some fundamental and historic as well as recent
results on how algebraic graph theory informs
electrical network analysis, dynamics, and design. In
particular, we review the algebraic and spectral
properties of graph adjacency, Laplacian, incidence,
and resistance matrices and how they relate to the
analysis, network-reduction, and dynamics of certain
classes of electrical networks. We study these
relations for models of increasing complexity ranging
from static resistive DC circuits, over dynamic RLC
circuits, to nonlinear AC power flow. We conclude
this paper by presenting a set of fundamental open
questions at the intersection of algebraic graph
theory and electrical networks.},
}
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month = aug,
school = {University of Washington},
title = {Graph-Theoretic Methods for the Analysis and
Synthesis of Networked Dynamic Systems},
year = {2009},
}
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title = {On Frame and Orientation Localization for Relative
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author = {T. Kavitha and C. Liebchen and K. Mehlhorn and
D. Michail and R. Rizzi and T. Ueckerdt and
K. A. Zweig},
journal = {Computer Science Review},
number = {4},
pages = {199-243},
title = {Cycle bases in graphs characterization, algorithms,
complexity, and applications},
volume = {3},
year = {2009},
abstract = {Abstract Cycles in graphs play an important role in
many applications, e.g., analysis of electrical
networks, analysis of chemical and biological
pathways, periodic scheduling, and graph drawing.
From a mathematical point of view, cycles in graphs
have a rich structure. Cycle bases are a compact
description of the set of all cycles of a graph. In
this paper, we survey the state of knowledge on cycle
bases and also derive some new results. We introduce
different kinds of cycle bases, characterize them in
terms of their cycle matrix, and prove structural
results and a priori length bounds. We provide
polynomial algorithms for the minimum cycle basis
problem for some of the classes and prove
APX-hardness for others. We also discuss three
applications and show that they require different
kinds of cycle bases.},
doi = {10.1016/j.cosrev.2009.08.001},
}
@article{SJ-FB:16h,
author = {S. Jafarpour and F. Bullo},
journal = {IEEE Transactions on Automatic Control},
month = nov,
note = {Submitted},
title = {Synchronization of {K}uramoto Oscillators via Cutset
Projections},
year = {2017},
abstract = {Synchronization coupled oscillators networks is a
remarkable phenomenon of relevance in numerous
fields. A key question is how to characterize the
transition from synchrony to incoherence. For
Kuramoto oscillators the loss of synchronization is
determined by a trade-off between coupling strength
and oscillator heterogeneity. Despite extensive prior
work, the existing sufficient conditions for
synchronization are either very conservative or
heuristic and approximate. This paper proposes a
novel approach to the study of Kuramoto oscillators
based on an oblique projection operator, called the
cutset projection. We propose a novel family of
sufficient synchronization conditions; these
conditions rigorously identify the correct functional
form of the trade-off between coupling strength and
oscillator heterogeneity. To overcome the need to
solve a nonconvex optimization problem, we then
provide two explicit bounding methods, thereby
obtaining (i) the best-known sufficient condition
based on the 2-norm, and (ii) the first-know
generally-applicable sufficient condition based on
the $\infty$-norm. We conclude with a comparative
study of the novel conditions for specific topologies
and IEEE test cases; for IEEE test cases our new
sufficient conditions are always more accurate, in
most cases by one to two orders of magnitude, than
previous rigorous tests.},
}
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network systems typically can be described with the
aid of the incidence matrix of a directed graph, and
an associated symmetric Laplacian matrix. Some basic
examples are discussed, and the extension to k
-complexes is indicated. Physical distribution
networks often involve a non-symmetric Laplacian
matrix. It is shown how, in case the connected
components of the graph are strongly connected, such
systems can be converted into a form with balanced
Laplacian matrix by constructive use of Kirchhoff’s
Matrix Tree theorem, giving rise to a
port-Hamiltonian description. Application to the dual
case of asymmetric consensus algorithms is given.
Finally it is shown how the minimal storage function
for physical network systems with controlled flows
can be explicitly computed.},
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author = {F. D{\"o}rfler and F. Bullo},
journal = {IEEE Transactions on Circuits and Systems~I: Regular
Papers},
number = {1},
pages = {150-163},
title = {Kron Reduction of Graphs with Applications to
Electrical Networks},
volume = {60},
year = {2013},
abstract = {Consider a weighted and undirected graph, possibly
with self-loops, and its corresponding Laplacian
matrix, possibly augmented with additional diagonal
elements corresponding to the self-loops. The Kron
reduction of this graph is again a graph whose
Laplacian matrix is obtained by the Schur complement
of the original Laplacian matrix with respect to a
subset of nodes. The Kron reduction process is
ubiquitous in classic circuit theory and in related
disciplines such as electrical impedance tomography,
smart grid monitoring, transient stability assessment
in power networks, or analysis and simulation of
induction motors and power electronics. More general
applications of Kron reduction occur in sparse matrix
algorithms, multi-grid solvers, finite-element
analysis, and Markov chains. The Schur complement of
a Laplacian matrix and related concepts have also
been studied under different names and as purely
theoretic problems in the literature on linear
algebra. In this paper we propose a general
graph-theoretic framework for Kron reduction that
leads to novel and deep insights both on the
mathematical and the physical side. We show the
applicability of our framework to various practical
problem setups arising in engineering applications
and computation. Furthermore, we provide a
comprehensive and detailed graph-theoretic analysis
of the Kron reduction process encompassing
topological, algebraic, spectral, resistive, and
sensitivity analyses. Throughout our theoretic
elaborations we especially emphasize the practical
applicability of our results.},
doi = {10.1109/TCSI.2012.2215780},
}
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author = {M. Pirani and S. Sundaram},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {509-514},
title = {On the Smallest Eigenvalue of Grounded {L}aplacian
Matrices},
volume = {61},
year = {2016},
doi = {10.1109/TAC.2015.2444191},
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pages = {10-16},
title = {Analysis and applications of spectral properties of
grounded {L}aplacian matrices for directed networks},
volume = {80},
year = {2017},
doi = {10.1016/j.automatica.2017.01.009},
}
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month = oct,
title = {{CVX}: Matlab Software for Disciplined Convex
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year = {2016},
url = {http://cvxr.com/cvx},
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@unpublished{FF:14,
author = {F. Fagnani},
month = jan,
note = {Lecture notes for Winter School on Complex Networks,
INRIA. Downloaded on 12/23/2016},
title = {Consensus dynamics over networks},
year = {2014},
url = {http://www-sop.inria.fr/members/Giovanni.Neglia/
complexnetworks14},
}
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author = {A. Olshevsky},
title = {Linear time average consensus on fixed graphs and
implications for decentralized optimization and
multi-agent control},
year = {2014},
url = {https://arxiv.org/pdf/1411.4186},
}
@inproceedings{RC-FG-SZ:09,
address = {San Diego, CA, USA},
author = {R. Carli and F. Garin and S. Zampieri},
booktitle = {IEEE Information Theory and Applications Workshop},
month = feb,
pages = {96--104},
title = {Quadratic indices for the analysis of consensus
algorithms},
year = {2009},
doi = {10.1109/ITA.2009.5044929},
}
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author = {R. Carli and F. Fagnani and A. Speranzon and
S. Zampieri},
journal = {Automatica},
number = {3},
pages = {671-684},
title = {Communication constraints in the average consensus
problem},
volume = {44},
year = {2008},
abstract = {The rendezvous problem can be seen as the simplest
instance of coordinated control of autonomous agents.
This problem has been widely investigated in the
recent years. It is clear that the information
exchange must have an important influence on the
performance of the control strategy. In this
contribution the information flow is modelled by a
graph representing the information transmission from
one vehicle to another one. In this graph there exist
two kinds of edges. One kind represents the exact
data transmission. This is very expensive with
respect to the communication rate required. A second
kind of edges represents the transmission logarithmic
quantized data. On the contrary this is very cheap
with respect to communication rate required. The
final goal of the present paper is to determine how
the degree of connection of this graph influences the
performance of the coordinated control system.},
doi = {10.1016/j.automatica.2007.07.009},
}
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number = {4},
pages = {331--354},
title = {First-and second-order diffusive methods for rapid,
coarse, distributed load balancing},
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@inproceedings{NB-RC-LS:16,
address = {Aalborg, Denmark},
author = {N. Bof and R. Carli and L. Schenato},
booktitle = {{E}uropean {C}ontrol {C}onference},
month = jun,
pages = {160--165},
title = {On the performance of consensus based versus
{L}agrangian based algorithms for quadratic cost
functions},
year = {2016},
doi = {10.1109/ECC.2016.7810280},
}
@phdthesis{JMH:08,
author = {J. M. Hendrickx},
month = feb,
school = {Departement d'Ingenierie Mathematique, Universit{\'e}
Catholique de Louvain, Belgium},
title = {Graphs and Networks for the Analysis of Autonomous
Agent Systems},
year = {2008},
annote = {Available at
\textt{http://perso.uclouvain.be/julien.hendrickx}},
}
@article{VDB-AO:14,
author = {V. D. Blondel and A. Olshevsky},
journal = {SIAM Journal on Control and Optimization},
number = {5},
pages = {2707--2726},
title = {How to decide consensus? {A} combinatorial necessary
and sufficient condition and a proof that consensus
is decidable but {NP}-hard},
volume = {52},
year = {2014},
doi = {10.1137/12086594X},
}
@article{WX-MC:14,
author = {W. Xia and M. Cao},
journal = {IEEE Transactions on Automatic Control},
number = {8},
pages = {2228--2233},
title = {Sarymsakov matrices and asynchronous implementation
of distributed coordination algorithms},
volume = {59},
year = {2014},
doi = {10.1109/TAC.2014.2301571},
}
@phdthesis{JNT:84,
author = {J. N. Tsitsiklis},
month = nov,
school = {Massachusetts Institute of Technology},
title = {Problems in Decentralized Decision Making and
Computation},
year = {1984},
}
@article{JNT-DPB-MA:86,
author = {J. N. Tsitsiklis and D. P. Bertsekas and M. Athans},
journal = {IEEE Transactions on Automatic Control},
number = {9},
pages = {803-812},
title = {Distributed asynchronous deterministic and stochastic
gradient optimization algorithms},
volume = {31},
year = {1986},
abstract = {Asynchronous distributed iterative optimization
algorithms are modeled for the following cases in
which each processor does not need to communicate to
each other processor at each time instance:
processors may keep performing computations without
having to wait until they receive the messages that
have been transmitted to them; processors are allowed
to remain idle some of the time; some processors may
perform computations faster than others. A model for
asynchronous distributed computation is presented and
then the convergence of natural asynchronous
distributed versions of a large class of
deterministic and stochastic gradient-like algorithms
is analyzed. It is shown that such algorithms retain
the desirable convergence properties of their
centralized counterparts, provided that the time
between consecutive communications between processors
and communication delays is not too large. (19
References).},
doi = {10.1109/TAC.1986.1104412},
}
@article{YH-JH-LG:06,
author = {Y. Hong and J. Hu and L. Gao},
journal = {Automatica},
number = {7},
pages = {1177--1182},
title = {Tracking control for multi-agent consensus with an
active leader and variable topology},
volume = {42},
year = {2006},
doi = {10.1016/j.automatica.2006.02.013},
}
@article{YH-LG-DC-JH:07,
author = {Y. Hong and L. Gao and D. Cheng and J. Hu},
journal = {IEEE Transactions on Automatic Control},
number = {5},
pages = {943-948},
title = {Lyapunov-Based Approach to Multiagent Systems With
Switching Jointly Connected Interconnection},
volume = {52},
year = {2007},
doi = {10.1109/TAC.2007.895860},
}
@article{MC-ASM-BDOA:08,
author = {M. Cao and A. S. Morse and B. D. O. Anderson},
journal = {IEEE Transactions on Automatic Control},
number = {8},
pages = {1826--1838},
title = {Agreeing asynchronously},
volume = {53},
year = {2008},
doi = {10.1109/TAC.2008.929387},
}
@inproceedings{LM:04,
address = {Nassau, Bahamas},
author = {L. Moreau},
booktitle = {{IEEE} Conf.\ on Decision and Control},
pages = {3998--4003},
title = {Stability of continuous-time distributed consensus
algorithms},
year = {2004},
doi = {10.1109/CDC.2004.1429377},
}
@article{ZL-BF-MM:07,
author = {Z. Lin and B. Francis and M. Maggiore},
journal = {SIAM Journal on Control and Optimization},
number = {1},
pages = {288-307},
title = {State agreement for continuous-time coupled nonlinear
systems},
volume = {46},
year = {2007},
abstract = {Two related problems are treated in continuous time.
First, the state agreement problem is studied for
coupled nonlinear differential equations. The vector
fields can switch within a finite family. Associated
to each vector field is a directed graph based in a
natural way on the interaction structure of the
subsystems. Generalizing the work of Moreau, under
the assumption that the vector fields satisfy a
certain subtangentiality condition, it is proved that
asymptotic state agreement is achieved if and only if
the dynamic interaction digraph has the property of
being sufficiently connected over time. The proof
uses nonsmooth analysis. Second, the rendezvous
problem for kinematic point-mass mobile robots is
studied when the robotsÃ fields of view have a
fixed radius. The circumcenter control law of Ando et
al. [IEEE Trans. Robotics Automation, 15 (1999), pp.
818Ã 828] is shown to solve the problem. The
rendezvous problem is a kind of state agreement
problem, but the interaction structure is state
dependent.},
doi = {10.1137/050626405},
}
@article{JMH-JNT:13,
author = {J. M. Hendrickx and J. N. Tsitsiklis},
journal = {IEEE Transactions on Automatic Control},
number = {1},
pages = {214--218},
title = {Convergence of type-symmetric and cut-balanced
consensus seeking systems},
volume = {58},
year = {2013},
doi = {10.1109/TAC.2012.2203214},
}
@article{AJ-JL-ASM:02,
author = {A. Jadbabaie and J. Lin and A. S. Morse},
journal = {IEEE Transactions on Automatic Control},
number = {6},
pages = {988-1001},
title = {Coordination of groups of mobile autonomous agents
using nearest neighbor rules},
volume = {48},
year = {2003},
abstract = {In a recent Physical Review Letters article, Vicsek
et al. propose a simple but compelling discrete-time
model of n autonomous agents (i.e., points or
particles) all moving in the plane with the same
speed but with different headings. Each agent's
heading is updated using a local rule based on the
average of its own heading plus the headings of its
"neighbors." In their paper, Vicsek et al. provide
simulation results which demonstrate that the nearest
neighbor rule they are studying can cause all agents
to eventually move in the same direction despite the
absence of centralized coordination and despite the
fact that each agent's set of nearest neighbors
change with time as the system evolves. This paper
provides a theoretical explanation for this observed
behavior. In addition, convergence results are
derived for several other similarly inspired models.
The Vicsek model proves to be a graphic example of a
switched linear system which is stable, but for which
there does not exist a common quadratic Lyapunov
function.},
doi = {10.1109/TAC.2003.812781},
}
@article{FF-SZ:08a,
author = {F. Fagnani and S. Zampieri},
journal = {IEEE Journal on Selected Areas in Communications},
number = {4},
pages = {634-649},
title = {Randomized consensus algorithms over large scale
networks},
volume = {26},
year = {2008},
doi = {10.1109/JSAC.2008.080506},
}
@article{ATS-AJ:08,
author = {A. Tahbaz-Salehi and A. Jadbabaie},
journal = {IEEE Transactions on Automatic Control},
number = {3},
pages = {791-795},
title = {A necessary and sufficient condition for consensus
over random networks},
volume = {53},
year = {2008},
doi = {10.1109/TAC.2008.917743},
}
@article{SC-ES:77,
author = {S. Chatterjee and E. Seneta},
journal = {Journal of Applied Probability},
number = {1},
pages = {89-97},
title = {Towards Consensus: {S}ome Convergence Theorems on
Repeated Averaging},
volume = {14},
year = {1977},
annote = {The problem of tendency to consensus in an
information-exchanging operation is connected with
the ergodicity problem for backwards products of
stochastic matrices. For such products, weak and
strong ergodicity, defined analogously to these
concepts for forward products of inhomogeneous Markov
chain theory, are shown (in contrast to that theory)
to be equivalent. Conditions for ergodicity are
derived and their relation to the consensus problem
is considered.},
doi = {10.2307/3213262},
}
@article{RC:84,
author = {R. Cogburn},
journal = {Zeitschrift f\"ur Wahrscheinlichkeitstheorie und
Verwandte Gebiete},
number = {1},
pages = {109-128},
title = {The ergodic theory of {M}arkov chains in random
environments},
volume = {66},
year = {1984},
doi = {10.1007/BF00532799},
}
@article{ATS-AJ:10,
author = {A. Tahbaz-Salehi and A. Jadbabaie},
journal = {IEEE Transactions on automatic Control},
number = {1},
pages = {225--230},
title = {Consensus over ergodic stationary graph processes},
volume = {55},
year = {2010},
doi = {10.1109/TAC.2009.2034054},
}
@article{YH-MM:05,
author = {Y. Hatano and M. Mesbahi},
journal = {IEEE Transactions on Automatic Control},
number = {11},
pages = {1867-1872},
title = {Agreement over random networks},
volume = {50},
year = {2005},
doi = {10.1109/TAC.2005.858670},
}
@article{DB-JX-JMFM-BS:13,
author = {D. Bajovi{\'c} and J. Xavier and J. M. F. Moura and
B. Sinopoli},
journal = {IEEE Transactions on Signal Processing},
number = {10},
pages = {2557--2571},
title = {Consensus and products of random stochastic matrices:
Exact rate for convergence in probability},
volume = {61},
year = {2013},
doi = {10.1109/TSP.2013.2248003},
}
@article{IM-JSB-CS:13,
author = {I. Matei and J. S. Baras and C. Somarakis},
journal = {SIAM Journal on Control and Optimization},
number = {2},
pages = {1574--1591},
title = {Convergence results for the linear consensus problem
under {Markovian} random graphs},
volume = {51},
year = {2013},
doi = {10.1137/100816870},
}
@article{BT-AN:14,
author = {B. Touri and A. Nedi{\'c}},
journal = {IEEE Transactions on Automatic Control},
number = {2},
pages = {437--448},
title = {Product of random stochastic matrices},
volume = {59},
year = {2014},
doi = {10.1109/TAC.2013.2283750},
}
@article{SB-AG-BP-DS:06,
author = {S. Boyd and A. Ghosh and B. Prabhakar and D. Shah},
journal = {IEEE Transactions on Information Theory},
number = {6},
pages = {2508-2530},
title = {Randomized gossip algorithms},
volume = {52},
year = {2006},
doi = {10.1109/TIT.2006.874516},
}
@article{DA-AO:11,
author = {D. Acemoglu and A. Ozdaglar},
journal = {Dynamic Games and Applications},
number = {1},
pages = {3-49},
title = {Opinion Dynamics and Learning in Social Networks},
volume = {1},
year = {2011},
doi = {10.1007/s13235-010-0004-1},
}
@article{DA-GC-FF-AO:10,
author = {D. Acemoglu and G. Como and F. Fagnani and
A. Ozdaglar},
journal = {Mathematics of Operation Research},
number = {1},
pages = {1-27},
title = {Opinion fluctuations and disagreement in social
networks},
volume = {38},
year = {2013},
doi = {10.1287/moor.1120.0570},
}
@article{AK-TB-RS:07,
author = {A. Kashyap and T. Ba{\c s}ar and R. Srikant},
journal = {Automatica},
number = {7},
pages = {1192-1203},
title = {Quantized consensus},
volume = {43},
year = {2007},
doi = {10.1016/j.automatica.2007.01.002},
}
@article{AN-AO-AO-JNT:09,
author = {Nedi{\'c}, A. and Olshevsky, A. and Ozdaglar, A. and
Tsitsiklis, J. N.},
journal = {IEEE Transactions on Automatic Control},
number = {11},
pages = {2506-2517},
title = {On distributed averaging algorithms and quantization
effects},
volume = {54},
year = {2009},
doi = {10.1109/TAC.2009.2031203},
}
@article{PF-RC-FF-SZ:09,
author = {P. Frasca and R. Carli and F. Fagnani and
S. Zampieri},
journal = {International Journal of Robust and Nonlinear
Control},
number = {16},
pages = {1787--1816},
title = {Average consensus on networks with quantized
communication},
volume = {19},
year = {2009},
doi = {10.1002/rnc.1396},
}
@article{LX-SB-SJK:07,
author = {L. Xiao and S. Boyd and S.-J. Kim},
journal = {Journal of Parallel and Distributed Computing},
number = {1},
pages = {33-46},
title = {Distributed Average Consensus with Least-Mean-Square
Deviation},
volume = {67},
year = {2007},
doi = {10.1016/j.jpdc.2006.08.010},
}
@article{BB-MRJ-PM-SP:12,
author = {B. Bamieh and M. R. Jovanovic and P. Mitra and
S. Patterson},
journal = {IEEE Transactions on Automatic Control},
number = {9},
pages = {2235-2249},
title = {Coherence in Large-Scale Networks:
Dimension-Dependent Limitations of Local Feedback},
volume = {57},
year = {2012},
doi = {10.1109/TAC.2012.2202052},
}
@article{EL-FG-SZ:13,
author = {E. Lovisari and F. Garin and S. Zampieri},
journal = {SIAM Journal on Control and Optimization},
number = {5},
pages = {3918--3945},
title = {Resistance-based performance analysis of the
consensus algorithm over geometric graphs},
volume = {51},
year = {2013},
doi = {10.1137/110857428},
}
@misc{AJ-AO:16,
author = {A. Jadbabaie and A. Olshevsky},
title = {On performance of consensus protocols subject to
noise: {R}ole of hitting times and network structure},
year = {2015},
url = {https://arxiv.org/pdf/1508.00036},
}
@article{ROS-RMM:03c,
author = {R. Olfati-Saber and R. M. Murray},
journal = {IEEE Transactions on Automatic Control},
number = {9},
pages = {1520-1533},
title = {Consensus problems in networks of agents with
switching topology and time-delays},
volume = {49},
year = {2004},
doi = {10.1109/TAC.2004.834113},
}
@article{JH-YH:07,
author = {J. Hu and Y. Hong},
journal = {Physica A: Statistical Mechanics and its
Applications},
number = {2},
pages = {853-863},
title = {Leader-following coordination of multi-agent systems
with coupling time delays},
volume = {374},
year = {2007},
abstract = {In this paper, we consider a leader-following
consensus problem of a group of autonomous agents
with time-varying coupling delays. Two different
cases of coupling topologies are investigated. At
first, a necessary and sufficient condition is proved
in the case when the interconnection topology is
fixed and directed. Then a sufficient condition is
proposed in the case when the coupling topology is
switched and balanced. Numerical examples are also
given to illustrate our results.},
doi = {10.1016/j.physa.2006.08.015},
}
@article{PL-YJ:08,
author = {P. Lin and Y. Jia},
journal = {Physica A: Statistical Mechanics and its
Applications},
number = {1},
pages = {303-313},
title = {Average consensus in networks of multi-agents with
both switching topology and coupling time-delay},
volume = {387},
year = {2008},
abstract = {This paper is devoted to the study of the
average-consensus problem in directed networks of
agents with both switching topology and time-delay.
The stability analysis is performed based on a
proposed Lyapunov-Krasovskii function. Sufficient
conditions in terms of linear matrix inequalities
(LMIs) are given to guarantee the average consensus
under arbitrary switching of the network topology
even if the time-delay is time-varying. Numerical
simulations show the effectiveness of our theoretical
results.},
doi = {10.1016/j.physa.2007.08.040},
}
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number = {7},
pages = {410-415},
title = {Analytical note on certain rhythmic relations in
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volume = {6},
year = {1920},
doi = {10.1073/pnas.6.7.410},
}
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individuals in animal species living together},
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year = {1928},
doi = {10.1093/icesjms/3.1.3},
}
@book{EPO:59,
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year = {1959},
}
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@incollection{YK:75,
author = {Y. Kuramoto},
booktitle = {Int. Symposium on Mathematical Problems in
Theoretical Physics},
editor = {H. Araki},
pages = {420-422},
publisher = {Springer},
series = {Lecture Notes in Physics},
title = {Self-entrainment of a population of coupled
non-linear oscillators},
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year = {1975},
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author = {F. D{\"o}rfler and F. Bullo},
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number = {6},
pages = {1539-1564},
title = {Synchronization in Complex Networks of Phase
Oscillators: {A} Survey},
volume = {50},
year = {2014},
abstract = {The emergence of synchronization in a network of
coupled oscillators is a fascinating subject of
multidisciplinary research. This survey reviews the
vast literature on the theory and the applications of
complex oscillator networks. We focus on phase
oscillator models that are widespread in real-world
synchronization phenomena, that generalize the
celebrated Kuramoto model, and that feature a rich
phenomenology. We review the history and the
countless applications of this model throughout
science and engineering. We justify the importance of
the widespread coupled oscillator model as a locally
canonical model and describe some selected
applications relevant to control scientists,
including vehicle coordination, electric power
networks, and clock synchronization. We introduce the
reader to several synchronization notions and
performance estimates. We propose analysis approaches
to phase and frequency synchronization, phase
balancing, pattern formation, and partial
synchronization. We present the sharpest known
results about synchronization in networks of
homogeneous and heterogeneous oscillators, with
complete or sparse interconnection topologies, and in
finite-dimensional and infinite-dimensional settings.
We conclude by summarizing the limitations of
existing analysis methods and by highlighting some
directions for future research.},
doi = {10.1016/j.automatica.2014.04.012},
}
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note = {Istituto di Geometria, Dipartimento di Matematica,
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@book{JLL:88,
address = {Paris},
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publisher = {Chez la Veuve Desaint},
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@book{AML:1892,
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note = {Translation:~\cite{AML:1992}},
publisher = {Fakul\cprime{}teta i Khar\cprime{}kovskogo
Matematicheskogo Obshchestva},
title = {Ob\v{s}\v{c}aya zada\v{c}a ob usto\u{\i}\v{c}ivosti
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title = {On Global Stability of Motion},
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year = {1952},
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author = {N. N. Krasovski\u\i},
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publisher = {Stanford University Press},
title = {Stability of Motion. Applications of Lyapunov's
Second Method to Differential Systems and Equations
with Delay},
year = {1963},
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@book{JPL:76,
author = {J. P. LaSalle},
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title = {The Stability of Dynamical Systems},
year = {1976},
doi = {10.1137/1.9781611970432},
isbn = {9780898710229},
}
@book{NGC:61,
author = {Nikolai Gurevich Chetaev},
note = {Translation from Russian by M.~Nadler},
publisher = {Pergamon},
title = {The Stability of Motion},
year = {1961},
}
@book{WH:67,
author = {W. Hahn},
publisher = {Springer},
title = {Stability of Motion},
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title = {Nonlinear Systems Analysis},
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isbn = {9780898715262},
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note = {Translation of the third Russian edition by R.~Cooke},
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title = {Ordinary Differential Equations},
year = {1992},
isbn = {3-540-54813-0},
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author = {J. Guckenheimer and P. Holmes},
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title = {Nonlinear Dynamical Systems and Control: A
Lyapunov-Based Approach},
year = {2008},
isbn = {9780691133294},
}
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author = {R. Goebel and R. G. Sanfelice and A. R. Teel},
publisher = {Princeton University Press},
title = {Hybrid Dynamical Systems: Modeling, Stability, and
Robustness},
year = {2012},
isbn = {9780691153896},
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publisher = {Springer},
title = {Set-Theoretic Methods in Control},
year = {2015},
isbn = {9783319179322},
}
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author = {A. Rantzer},
journal = {European Journal of Control},
pages = {72-80},
title = {Scalable control of positive systems},
volume = {24},
year = {2015},
doi = {10.1016/j.ejcon.2015.04.004},
}
@book{FHC-YSL-RJS-PRW:98,
author = {F. H. Clarke and Y.S. Ledyaev and R. J. Stern and
P. R. Wolenski},
publisher = {Springer},
title = {Nonsmooth Analysis and Control Theory},
year = {1998},
isbn = {0387983368},
}
@article{JC:08-csm,
author = {J. Cort{\'e}s},
journal = {{IEEE} Control Systems},
number = {3},
pages = {36-73},
title = {Discontinuous dynamical systems},
volume = {28},
year = {2008},
abstract = {This paper considers discontinuous dynamical systems,
i.e., systems whose associated vector field is a
discontinuous function of the state. Discontinuous
dynamical systems arise in a large number of
applications, including optimal control, nonsmooth
mechanics, and robotic manipulation. Independently of
the particular application, one always faces similar
questions when dealing with discontinuous dynamical
systems. The most basic one is the notion of
solution. We begin by introducing the notions of
Caratheodory, Filippov and sample-and-hold solutions,
discuss existence and uniqueness results for them,
and examine various examples. We also give specific
pointers to other notions of solution defined in the
literature. Once the notion of solution has been
settled, we turn our attention to the analysis of
stability of discontinuous systems. We introduce the
concepts of generalized gradient of locally Lipschitz
functions and proximal subdifferential of lower
semicontinuous functions. Building on these notions,
we establish monotonic properties of candidate
Lyapunov functions along the solutions. These results
are key in providing suitable generalizations of
Lyapunov stability theorems and the LaSalle
Invariance Principle. We illustrate the applicability
of these results in a class of nonsmooth gradient
flows.},
doi = {10.1109/MCS.2008.919306},
}
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author = {Y. Takeuchi},
publisher = {World Scientific Publishing},
title = {Global Dynamical Properties of {Lotka-Volterra}
Systems},
year = {1996},
isbn = {9810224710},
}
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note = {Unpublished Lecture Notes, reproduced with permission
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title = {{Introduction to Inequalities}},
year = {1982},
url = {http://www.mediafire.com/?1mw1tkgozzu},
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author = {S. Baigent},
month = mar,
note = {Unpublished Lecture Notes, University of College,
London},
title = {{Lotka-Volterra Dynamics \textemdash{} An
Introduction}},
year = {2010},
annote = {Downloaded on 12/23/2016},
url = {http://www.ltcc.ac.uk/media/london-taught-course-centre/
documents/Bio-Mathematics-(APPLIED).pdf},
}
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number = {3},
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volume = {62},
year = {1978},
doi = {10.1016/0022-247X(78)90139-7},
}
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author = {B. S. Goh},
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pages = {261--275},
title = {Stability in models of mutualism},
year = {1979},
doi = {10.1086/283384},
}
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author = {B.-S. Goh},
publisher = {Elsevier},
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year = {1980},
isbn = {978-0-444-41793-0},
}
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author = {J. Hofbauer and K. Sigmund},
publisher = {Cambridge University Press},
title = {Evolutionary Games and Population Dynamics},
year = {1998},
isbn = {052162570X},
}
@book{WHS:10,
author = {W. H. Sandholm},
publisher = {MIT Press},
title = {Population Games and Evolutionary Dynamics},
year = {2010},
isbn = {0262195879},
}
@article{WM-SM-SZ-FB:16f,
author = {W. Mei and S. Mohagheghi and S. Zampieri and
F. Bullo},
journal = {Annual Reviews in Control},
pages = {116-128},
title = {On the Dynamics of Deterministic Epidemic Propagation
over Networks},
volume = {44},
year = {2017},
abstract = {In this work we review a class of deterministic
nonlinear models for the propagation of infectious
diseases over contact networks with
strongly-connected topologies. We consider network
models for susceptible-infected (SI),
susceptible-infected-susceptible (SIS), and
susceptible-infected-recovered (SIR) settings. In
each setting, we provide a comprehensive nonlinear
analysis of equilibria, stability properties,
convergence, monotonicity, positivity, and threshold
conditions. For the network SI setting, specific
contributions include establishing its equilibria,
stability, and positivity properties. For the network
SIS setting, we review a well- known deterministic
model, provide novel results on the computation and
characterization of the endemic state (when the
system is above the epidemic threshold), and present
alternative proofs for some of its properties.
Finally, for the network SIR setting, we propose
novel results for transient behavior, threshold
conditions, stability properties, and asymptotic
convergence. These results are analogous to those
well-known for the scalar case. In addition, we
provide a novel iterative algorithm to compute the
asymptotic state of the network SIR system.},
doi = {10.1016/j.arcontrol.2017.09.002},
}
@article{AF-AI-GS-JJT:07,
author = {A. Fall and A. Iggidr and G. Sallet and J.-J. Tewa},
journal = {Mathematical Modelling of Natural Phenomena},
number = {1},
pages = {62--68},
title = {Epidemiological models and {L}yapunov functions},
volume = {2},
year = {2007},
doi = {10.1051/mmnp:2008011},
}
@article{AK-TB-BG:16,
author = {A. Khanafer and T. Ba{\c s}ar and B. Gharesifard},
journal = {Automatica},
pages = {126-134},
title = {Stability of Epidemic Models over Directed Graphs:
{A} Positive Systems Approach},
volume = {74},
year = {2016},
doi = {10.1016/j.automatica.2016.07.037},
}
@article{LJSA:94,
author = {L. J. S. Allen},
journal = {Mathematical Biosciences},
number = {1},
pages = {83-105},
title = {Some discrete-time {SI, SIR, and SIS} epidemic
models},
volume = {124},
year = {1994},
abstract = {Discrete-time models, or difference equations, of
some well-known SI, SIR, and SIS epidemic models are
considered. The discrete-time SI and SIR models give
rise to systems of nonlinear difference equations
that are similar in behavior to their continuous
analogues under the natural restriction that
solutions to the discrete-time models be positive. It
is important that the entire system be considered
since the difference equation for infectives I in an
SI model has a logistic form which can exhibit
period-doubling and chaos for certain parameter
values. Under the restriction that S and I be
positive, these parameter values are excluded. In the
case of a discrete SIS model, positivity of solutions
is not enough to guarantee asymptotic convergence to
an equilibrium value (as in the case of the
continuous model). The positive feedback from the
infective class to the susceptible class allows for
more diverse behavior in the discrete model.
Period-doubling and chaotic behavior is possible for
some parameter values. In addition, if births and
deaths are included in the SI and SIR models
(positive feedback due to births) the discrete models
exhibit periodicity and chaos for some parameter
values. Single-population and multi-population,
discrete-time epidemic models are analyzed.},
doi = {10.1016/0025-5564(94)90025-6},
}
@inproceedings{YW-DC-CW-CF:03,
address = {Florence, Italy},
author = {Y. Wang and D. Chakrabarti and C. Wang and
C. Faloutsos},
booktitle = {IEEE Int. Symposium on Reliable Distributed Systems},
month = oct,
pages = {25-34},
title = {Epidemic Spreading in Real Networks: {A}n Eigenvalue
Viewpoint},
year = {2003},
doi = {10.1109/RELDIS.2003.1238052},
}
@inproceedings{HJA-BH:13,
address = {Florence, Italy},
author = {H. J. Ahn and B. Hassibi},
booktitle = {{IEEE} Conf.\ on Decision and Control},
month = dec,
pages = {4579-4585},
title = {Global Dynamics of Epidemic Spread over Complex
Networks},
year = {2013},
doi = {10.1109/CDC.2013.6760600},
}
@inproceedings{NAR-BH:15,
author = {N. {Azizan~Ruhi} and B. Hassibi},
booktitle = {{IEEE} Conf.\ on Decision and Control},
month = dec,
pages = {2919-2926},
title = {{SIRS} epidemics on complex networks: {C}oncurrence
of exact {M}arkov chain and approximated models},
year = {2015},
doi = {10.1109/CDC.2015.7402660},
}
@article{PvM-JO-RK:09,
author = {P. {Van~Mieghem} and J. Omic and R. Kooij},
journal = {IEEE/ACM Transactions on Networking},
number = {1},
pages = {1-14},
title = {Virus spread in networks},
volume = {17},
year = {2009},
doi = {10.1109/TNET.2008.925623},
}
@article{FDS-CS-PvM:13,
author = {F. D. Sahneh and C. Scoglio and P. {Van~Mieghem}},
journal = {IEEE/ACM Transactions on Networking},
number = {5},
pages = {1609--1620},
title = {Generalized Epidemic Mean-Field Model for Spreading
Processes Over Multilayer Complex Networks},
volume = {21},
year = {2013},
doi = {10.1109/TNET.2013.2239658},
}
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author = {H. Guo and M. Li and Z. Shuai},
journal = {Proceedings of the American Mathematical Society},
number = {8},
pages = {2793--2802},
title = {A graph-theoretic approach to the method of global
{L}yapunov functions},
volume = {136},
year = {2008},
doi = {10.1090/S0002-9939-08-09341-6},
}
@article{MY-CS:11,
author = {M. Youssef and C. Scoglio},
journal = {Journal of Theoretical Biology},
number = {1},
pages = {136--144},
title = {An individual-based approach to {SIR} epidemics in
contact networks},
volume = {283},
year = {2011},
doi = {10.1016/j.jtbi.2011.05.029},
}
@book{AB-MB-AV:08,
author = {A. Barrat and M. Barthlemy and A. Vespignani},
publisher = {Cambridge University Press},
title = {Dynamical Processes on Complex Networks},
year = {2008},
isbn = {0521879507},
}
@article{CN-VMP-GJP:16,
author = {C. Nowzari and V. M. Preciado and G. J. Pappas},
journal = {{IEEE} Control Systems},
number = {1},
pages = {26-46},
title = {Analysis and Control of Epidemics: {A} Survey of
Spreading Processes on Complex Networks},
volume = {36},
year = {2016},
doi = {10.1109/MCS.2015.2495000},
}
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author = {R. Potrie and P. Monz{\'o}n},
journal = {Dynamical Systems},
number = {1},
pages = {109-115},
title = {Local implications of almost global stability},
volume = {24},
year = {2009},
doi = {10.1080/14689360802474657},
}
@article{FD-FB:10w,
author = {F. D{\"o}rfler and F. Bullo},
journal = {SIAM Journal on Applied Dynamical Systems},
number = {3},
pages = {1070-1099},
title = {On the Critical Coupling for {K}uramoto Oscillators},
volume = {10},
year = {2011},
abstract = {The celebrated Kuramoto model captures various
synchronization phenomena in biological and man-made
dynamical systems of coupled oscillators. It is
well-known that there exists a critical coupling
strength among the oscillators at which a phase
transition from incoherency to synchronization
occurs. This paper features four contributions.
First, we characterize and distinguish the different
notions of synchronization used throughout the
literature and formally introduce the concept of
phase cohesiveness as an analysis tool and
performance index for synchronization. Second, we
review the vast literature providing necessary,
sufficient, implicit, and explicit estimates of the
critical coupling strength in the finite and
infinite-dimensional case and for both first-order
and second-order Kuramoto models. Third, we present
the first explicit necessary and sufficient condition
on the critical coupling strength to achieve
synchronization in the finite-dimensional Kuramoto
model for an arbitrary distribution of the natural
frequencies. The multiplicative gap in the
synchronization condition yields a practical
stability result determining the admissible initial
and the guaranteed ultimate phase cohesiveness as
well as the guaranteed asymptotic magnitude of the
order parameter. As supplementary results, we provide
a statistical comparison of our synchronization
condition with other conditions proposed in the
literature, and we show that our results also hold
for switching and smoothly time-varying natural
frequencies. Fourth and finally, we extend our
analysis to multi-rate Kuramoto models consisting of
second-order Kuramoto oscillators with inertia and
viscous damping together with first-order Kuramoto
oscillators with multiple time constants. We prove
that such a heterogeneous network is locally
topologically conjugate to a first-order Kuramoto
model with scaled natural frequencies. Finally, we
present necessary and sufficient conditions for
almost global phase synchronization and local
frequency synchronization in the multi-rate Kuramoto
model. Interestingly, our provably correct
synchronization conditions do not depend on the
inertiae which contradicts prior observations on the
role of inertial effects in synchronization of
second-order Kuramoto oscillators.},
doi = {10.1137/10081530X},
}
@misc{FD-FB:12i-arxiv+url,
author = {F. D{\"o}rfler and F. Bullo},
note = {{E}xtended version including proofs.},
title = {Exploring Synchronization in Complex Oscillator
Networks},
year = {2012},
url = {http://arxiv.org/pdf/1209.1335},
}
@book{CH:1673,
address = {Paris, France},
author = {C. Huygens},
title = {Horologium Oscillatorium},
year = {1673},
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author = {A. T. Winfree},
journal = {Journal of Theoretical Biology},
number = {1},
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title = {Biological rhythms and the behavior of populations of
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volume = {16},
year = {1967},
doi = {10.1016/0022-5193(67)90051-3},
}
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author = {Y. Kuramoto},
publisher = {Springer},
title = {Chemical Oscillations, Waves, and Turbulence},
year = {1984},
isbn = {0387133224},
}
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journal = {Physica D: Nonlinear Phenomena},
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title = {From {K}uramoto to {C}rawford: {E}xploring the onset
of synchronization in populations of coupled
oscillators},
volume = {143},
year = {2000},
doi = {10.1016/S0167-2789(00)00094-4},
}
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{A} new hypothesis},
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S. M. Reppert},
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number = {6},
pages = {855--860},
title = {Cellular construction of a circadian clock: {P}eriod
determination in the suprachiasmatic nuclei},
volume = {91},
year = {1997},
doi = {10.1016/S0092-8674(00)80473-0},
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Martinerie, J.},
journal = {Nature Reviews Neuroscience},
number = {4},
pages = {229--239},
publisher = {Nature Publishing Group},
title = {The brainweb: {P}hase synchronization and large-scale
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volume = {2},
year = {2001},
doi = {10.1038/35067550},
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author = {E. Brown and P. Holmes and J. Moehlis},
booktitle = {Perspectives and Problems in Nonlinear Science: A
Celebratory Volume in Honor of Larry Sirovich},
editor = {E. Kaplan and J. E. Marsden and K. R. Sreenivasan},
pages = {183--215},
publisher = {Springer},
title = {Globally coupled oscillator networks},
year = {2003},
doi = {10.1007/978-0-387-21789-5_5},
}
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J. M. Bower},
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number = {2},
pages = {161--172},
title = {The role of axonal delay in the synchronization of
networks of coupled cortical oscillators},
volume = {4},
year = {1997},
doi = {10.1023/A:1008843412952},
}
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author = {Ghosh, A. K. and Chance, B. and Pye, E. K.},
journal = {Archives of Biochemistry and Biophysics},
number = {1},
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title = {Metabolic coupling and synchronization of {NADH}
oscillations in yeast cell populations},
volume = {145},
year = {1971},
doi = {10.1016/0003-9861(71)90042-7},
}
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number = {3},
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title = {Synchronous rhythmic flashing of fireflies. {II}.},
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year = {1988},
doi = {10.1086/415929},
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@article{TJW:69,
author = {T. J. Walker},
journal = {Science},
number = {3907},
pages = {891--894},
title = {Acoustic synchrony: {Two} mechanisms in the snowy
tree cricket},
volume = {166},
year = {1969},
doi = {10.1126/science.166.3907.891},
}
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Brechet, Y. and Barab{\'a}si, A.-L.},
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}
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author = {Daido, H.},
journal = {Physical Review Letters},
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Coolen, A. C. C. and Perez-Vicente, C.},
journal = {Journal of Physics A: Mathematical and General},
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interactions in the {XY} spin glass},
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year = {2001},
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}
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author = {J. Pantaleone},
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year = {1998},
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author = {Kiss, I. Z. and Zhai, Y. and Hudson, J. L.},
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title = {Emerging coherence in a population of chemical
oscillators},
volume = {296},
year = {2002},
doi = {10.1126/science.1070757},
}
@article{PAT:03,
author = {P. A. Tass},
journal = {Biological Cybernetics},
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with a demand-controlled coordinated reset of neural
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volume = {89},
year = {2003},
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author = {R. Sepulchre and D. A. Paley and N. E. Leonard},
journal = {IEEE Transactions on Automatic Control},
number = {5},
pages = {811-824},
title = {Stabilization of Planar Collective Motion:
{A}ll-to-all Communication},
volume = {52},
year = {2007},
doi = {10.1109/TAC.2007.898077},
}
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T. Javidi},
journal = {IEEE Journal on Selected Areas in Communications},
number = {4},
pages = {695--705},
title = {Integration of communication and control using
discrete time {K}uramoto models for multivehicle
coordination over broadcast networks},
volume = {26},
year = {2008},
doi = {10.1109/JSAC.2008.080511},
}
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semiconductor lasers},
volume = {85},
year = {2000},
doi = {10.1103/PhysRevLett.85.3809},
}
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}
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journal = {IEEE Transactions on Microwave Theory and Techniques},
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@article{JWSP-FD-FB:12u,
author = {J. W. Simpson-Porco and F. D{\"o}rfler and F. Bullo},
journal = {Automatica},
number = {9},
pages = {2603-2611},
title = {Synchronization and Power Sharing for
Droop-Controlled Inverters in Islanded Microgrids},
volume = {49},
year = {2013},
abstract = {Motivated by the recent and growing interest in smart
grid technology, we study the operation of DC/AC
inverters in a lossless microgrid. We show that a
network of loads and DC/AC inverters equipped with
power-frequency droop controllers can be cast as a
Kuramoto model of phase-coupled oscillators. This
novel description, together with results from the
theory of coupled oscillators, allows us to
characterize the behavior of the network of inverters
and loads. Specifically, we provide a necessary and
sufficient condition for the existence of a
synchronized solution that is unique and locally
exponentially stable. We present a selection of
controller gains leading to a desirable sharing of
power among the inverters, and specify the set of
loads which can be serviced without violating given
actuation constraints. Moreover, we propose a
distributed integral controller based on averaging
algorithms, which dynamically regulates the system
frequency in the presence of a time-varying load.
Remarkably, this distributed-averaging integral
controller has the additional property that it
preserves the power sharing properties of the primary
droop controller. Our results hold without
assumptions on identical line characteristics or
voltage magnitudes.},
doi = {10.1016/j.automatica.2013.05.018},
}
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@inproceedings{AM-PS-RJS:12,
address = {Maui, HI, USA},
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pages = {7171-7183},
title = {Kick Synchronization versus Diffusive
Synchronization},
year = {2012},
doi = {10.1109/CDC.2012.6425821},
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Autonomous Robots},
volume = {55},
year = {2010},
doi = {10.1109/TAC.2010.2053735},
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@article{BDOA-CY-BF-JMH:08,
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title = {The algebraic geometry of stresses in frameworks},
volume = {4},
year = {1983},
abstract = {A bar-and-joint framework, with rigid bars and
flexible joints, is said to be generically isostatic
if it has just enough bars to be infinitesimally
rigid in some realization in Euclidean n-space. We
determine the equation that must be satisfied by the
coordinates of the joints in a given realization in
order to have a nonzero stress, and hence an
infinitesimal motion, in the framework. This
equation, called the pure condition, is expressed in
terms of certain determinants, called brackets. The
pure condition is obtained by choosing a way to tie
down the framework to eliminate the Euclidean
motions, computing a bracket expression by a method
due to Rosenberg and then factoring out part of the
expression related to the tie-down. A major portion
of this paper is devoted to proving that the
resulting pure condition is independent of the
tie-down chosen. We then catalog a number of small
examples and their pure conditions, along with the
geometric conditions for the existence of a stress
which are equivalent to the algebraic pure
conditions. We also explain our methods for
calculating these conditions and determining their
factorization. We then use the pure conditions to
investigate stresses and tension-compression splits
in 1-overbraced frameworks. Finally we touch briefly
upon some of the problems arising when multiple
factors occur in the pure condition.},
doi = {10.1137/0604049},
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for the problem of network localization in which some
nodes know their locations and other nodes determine
their locations by measuring the distances to their
neighbors. We construct grounded graphs to model
network localization and apply graph rigidity theory
to test the conditions for unique localizability and
to construct uniquely localizable networks. We
further study the computational complexity of network
localization and investigate a subclass of grounded
graphs where localization can be computed
efficiently. We conclude with a discussion of
localization in sensor networks where the sensors are
placed randomly},
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}
@book{JLL:97,
address = {Dordrecht},
author = {Joseph Louis Lagrange},
note = {Translation of the 1811 edition in French by
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publisher = {Kluwer Academic Publishers},
series = {Boston Studies in the Philosophy of Science},
title = {Analytical Mechanics},
year = {1997},
isbn = {0-7923-4349-2},
}
@book{AML:1992,
author = {Aleksandr Mikhailovich Lyapunov},
note = {Translation from Russian by A.~T.~Fuller},
publisher = {Taylor \& Francis},
title = {The General Problem of the Stability of Motion},
year = {1992},
}