-
F. Dörfler and F. Bullo.
Synchronization in Complex Oscillator Networks: A survey.
Automatica,
50(6):1539-1564,
June 2014.
Keyword(s): Complex Oscillator Networks.
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. |
@article{FD-FB:13b,
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.},
author = {F. D{ö}rfler and F. Bullo},
date-added = {2013-04-23 00:07:17 +0000},
date-modified = {2015-01-06 18:59:29 +0000},
journal = {Automatica},
keywords = {Complex Oscillator Networks},
month = {June},
number = {6},
pages = {1539-1564},
pdf = {http://www.sciencedirect.com/science/article/pii/S0005109814001423/pdfft?md5=5bb96070ea4892d01141fac05f495195&pid=1-s2.0-S0005109814001423-main.pdf},
title = {Synchronization in Complex Oscillator Networks: A survey},
url = {http://www.sciencedirect.com/science/article/pii/S0005109814001423},
volume = {50},
year = 2014,
bdsk-url-1 = {http://www.sciencedirect.com/science/article/pii/S0005109814001423/pdfft?md5=5bb96070ea4892d01141fac05f495195&pid=1-s2.0-S0005109814001423-main.pdf}
}
-
F. Dörfler,
M. R. Jovanovic,
M. Chertkov,
and F. Bullo.
Sparsity-Promoting Optimal Wide-Area Control of Power Networks.
IEEE Transactions on Power Systems,
29(5):2281-2291,
September 2014.
Keyword(s): Wide-Area Control,
Linear Control Design,
Power Networks.
Abstract:
Inter-area oscillations in bulk power systems are typically poorly controllable by means of local decentralized control. Recent research efforts have been aimed at developing wide- area control strategies that involve communication of remote signals. In conventional wide-area control, the control structure is fixed a priori typically based on modal criteria. In contrast, here we employ the recently-introduced paradigm of sparsity- promoting optimal control to simultaneously identify the optimal control structure and optimize the closed-loop performance. To induce a sparse control architecture, we regularize the standard quadratic performance index with an l1-penalty on the feedback matrix. The quadratic objective functions are inspired by the classic slow coherency theory and are aimed at imitating homogeneous networks without inter-area oscillations. We use the New England power grid model to demonstrate that the proposed combination of the sparsity-promoting control design with the slow coherency objectives performs almost as well as the optimal centralized control while only making use of a single wide-area communication link. In addition to this nominal performance, we also demonstrate that our control strategy yields favorable robustness margins and that it can be used to identify a sparse control architecture for control design via alternative means. |
@article{FD-MJ-MC-FB:13a,
abstract = { Inter-area oscillations in bulk power systems are typically poorly controllable by means of local decentralized control. Recent research efforts have been aimed at developing wide- area control strategies that involve communication of remote signals. In conventional wide-area control, the control structure is fixed a priori typically based on modal criteria. In contrast, here we employ the recently-introduced paradigm of sparsity- promoting optimal control to simultaneously identify the optimal control structure and optimize the closed-loop performance. To induce a sparse control architecture, we regularize the standard quadratic performance index with an l1-penalty on the feedback matrix. The quadratic objective functions are inspired by the classic slow coherency theory and are aimed at imitating homogeneous networks without inter-area oscillations. We use the New England power grid model to demonstrate that the proposed combination of the sparsity-promoting control design with the slow coherency objectives performs almost as well as the optimal centralized control while only making use of a single wide-area communication link. In addition to this nominal performance, we also demonstrate that our control strategy yields favorable robustness margins and that it can be used to identify a sparse control architecture for control design via alternative means. },
author = {F. D{ö}rfler and M. R. Jovanovic and M. Chertkov and F. Bullo},
date-added = {2013-07-12 06:33:53 +0000},
date-modified = {2014-09-17 15:57:39 +0000},
funding = {UCLA Startup Funds},
journal = {IEEE Transactions on Power Systems},
keywords = {Wide-Area Control, Linear Control Design, Power Networks},
month = {September},
number = {5},
pages = {2281-2291},
pdf = {http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=6740090},
title = {Sparsity-Promoting Optimal Wide-Area Control of Power Networks},
url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6740090&queryText%3DSparsity-Promoting+Optimal+Wide-Area+Control+of+Power+Networks},
volume = {29},
year = 2014,
bdsk-url-1 = {http://arxiv.org/abs/1307.4342}
}
-
S. Dhople,
B. Johnson,
F. Dörfler,
and A. Hamadeh.
Synchronization of Nonlinear Circuits in Dynamic Electrical Networks with General Topologies.
IEEE Transactions on Circuits and Systems I: Regular Papers,
61(9):2677-2690,
September 2014.
Keyword(s): Complex Oscillator Networks,
Microgrids,
Algebraic Graph Theory,
Power Electronics Control,
Virtual Oscillator Control.
Abstract:
Sufficient conditions are derived for global asymptotic synchronization in a system of identical nonlinear electrical circuits coupled through linear time-invariant (LTI) electrical networks. In particular, the conditions we derive apply to settings where: i) the nonlinear circuits are composed of a parallel combination of passive LTI circuit elements and a nonlinear voltage-dependent current source with finite gain; and ii) a collection of these circuits are coupled through either uniform or homogeneous LTI electrical networks. Uniform electrical networks have identical per-unit-length impedances. Homogeneous electrical networks are characterized by having the same effective impedance between any two terminals with the others open circuited. Synchronization in these networks is guaranteed by ensuring the stability of an equivalent coordinate-transformed differential system that emphasizes signal differences. The applicability of the synchronization conditions to this broad class of networks follows from leveraging recent results on structural and spectral properties of Kron reduction---a model-reduction procedure that isolates the interactions of the nonlinear circuits in the network. The validity of the analytical results is demonstrated with simulations in networks of coupled Chua's circuits. |
@article{SD-BJ-FD-AH:13,
abstract = {Sufficient conditions are derived for global asymptotic synchronization in a system of identical nonlinear electrical circuits coupled through linear time-invariant (LTI) electrical networks. In particular, the conditions we derive apply to settings where: i) the nonlinear circuits are composed of a parallel combination of passive LTI circuit elements and a nonlinear voltage-dependent current source with finite gain; and ii) a collection of these circuits are coupled through either uniform or homogeneous LTI electrical networks. Uniform electrical networks have identical per-unit-length impedances. Homogeneous electrical networks are characterized by having the same effective impedance between any two terminals with the others open circuited. Synchronization in these networks is guaranteed by ensuring the stability of an equivalent coordinate-transformed differential system that emphasizes signal differences. The applicability of the synchronization conditions to this broad class of networks follows from leveraging recent results on structural and spectral properties of Kron reduction---a model-reduction procedure that isolates the interactions of the nonlinear circuits in the network. The validity of the analytical results is demonstrated with simulations in networks of coupled Chua's circuits.},
author = {S. Dhople and B. Johnson and F. D{ö}rfler and A. Hamadeh},
date-added = {2013-10-18 02:10:00 +0000},
date-modified = {2018-05-01 12:07:40 +0000},
funding = {UCLA Startup Funds},
journal = {IEEE Transactions on Circuits and Systems~I: Regular Papers},
keywords = {Complex Oscillator Networks, Microgrids, Algebraic Graph Theory, Power Electronics Control, Virtual Oscillator Control},
month = {September},
number = {9},
pages = {2677-2690},
pdf = {http://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6883261},
title = {Synchronization of Nonlinear Circuits in Dynamic Electrical Networks with General Topologies},
url = {http://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=6883261&queryText%3DSynchronization+of+Nonlinear+Circuits+in+Dynamic+Electrical+Networks+with+General+Topologies},
volume = {61},
year = 2014,
bdsk-url-1 = {http://arxiv.org/abs/1310.4550}
}
-
F. Dörfler,
S. Dhople,
B. Johnson,
and A. Hamadeh.
Synchronization of Nonlinear Circuits in Dynamic Electrical Networks.
In European Control Conference,
Strasbourg, France,
pages 552-557,
June 2014.
Keyword(s): Complex Oscillator Networks,
Algebraic Graph Theory,
Microgrids,
Virtual Oscillator Control,
Power Networks.
@inproceedings{FD-SD-BJ-AH:13,
address = {Strasbourg, France},
author = {F. D{ö}rfler and S. Dhople and B. Johnson and A. Hamadeh},
booktitle = {{E}uropean {C}ontrol {C}onference},
date-added = {2013-10-21 18:35:26 +0000},
date-modified = {2018-05-01 12:16:14 +0000},
funding = {IIS-0904501, CPS-1135819, UCLA Startup Funds},
keywords = {Complex Oscillator Networks, Algebraic Graph Theory, Microgrids, Virtual Oscillator Control, Power Networks},
month = {June},
pages = {552--557},
pdf = {http://people.ee.ethz.ch/~floriand/docs/Articles/Dorfler_ECC_2014.pdf},
title = {Synchronization of Nonlinear Circuits in Dynamic Electrical Networks},
year = 2014
}
-
F. Dörfler,
J. W. Simpson-Porco,
and F. Bullo.
Plug-and-Play Control and Optimization in Microgrids.
In IEEE Conf. on Decision and Control,
Los Angeles, CA, USA,
pages 211-216,
December 2014.
Keyword(s): Microgrids,
Complex Oscillator Networks,
Distributed Control Algorithms,
Frequency Control.
@inproceedings{FD-JWSP-FB:14b,
address = {Los Angeles, CA, USA},
author = {F. D{ö}rfler and J. W. Simpson-Porco and F. Bullo},
booktitle = {{IEEE} Conf.\ on Decision and Control},
date-added = {2014-03-12 00:33:50 +0000},
date-modified = {2016-05-31 09:48:28 +0000},
funding = {UCLA Startup Funds, NSF CNS-1135819},
keywords = {Microgrids, Complex Oscillator Networks, Distributed Control Algorithms, Frequency Control},
month = dec,
pages = {211-216},
pdf = {http://motion.me.ucsb.edu/pdf/2013y-dsb-conference.pdf},
title = {Plug-and-Play Control and Optimization in Microgrids},
url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7039383},
year = 2014,
bdsk-url-1 = {http://www.ifac-papersonline.net/Detailed/56785.html}
}
-
B. Gentile,
J. W. Simpson-Porco,
F. Dörfler,
S. Zampieri,
and F. Bullo.
On Reactive Power Flow and Voltage Stability in Microgrids.
In American Control Conference,
Portland, OR,
pages 759-764,
June 2014.
Keyword(s): Microgrids,
Distributed Control Algorithms,
Complex Polynomial Networks,
Voltage Control.
@conference{BG-JWSP-FD-SZ-FB:13a,
address = {Portland, OR},
author = {B. Gentile and J. W. Simpson-Porco and F. D{ö}rfler and S. Zampieri and F. Bullo},
booktitle = {{A}merican {C}ontrol {C}onference},
date-added = {2013-10-01 05:13:42 +0000},
date-modified = {2018-05-01 12:16:02 +0000},
keywords = {Microgrids, Distributed Control Algorithms, Complex Polynomial Networks, Voltage Control},
month = {June},
pages = {759--764},
pdf = {http://people.ee.ethz.ch/~floriand/docs/Articles/Gentile_ACC_2014.pdf},
title = {On Reactive Power Flow and Voltage Stability in Microgrids},
year = {2014}
}
-
X. Wu,
F. Dörfler,
and M. R. Jovanovic.
Analysis and Design Trade-Offs for Power Network Inter-Area Oscillations.
In International Symposium on Mathematical Theory of Network and Systems (MTNS),
July 2014.
Keyword(s): Linear Control Design,
Wide-Area Control,
Power Networks.
@inproceedings{XW-FD-MJ:13a,
author = {X. Wu and F. D{ö}rfler and M. R. Jovanovic},
booktitle = {International Symposium on Mathematical Theory of Network and Systems (MTNS)},
date-added = {2013-12-08 21:49:18 +0000},
date-modified = {2015-01-16 18:30:07 +0000},
funding = {IIS-0904501, CPS-1135819, UCLA Startup Funds},
keywords = {Linear Control Design, Wide-Area Control, Power Networks},
month = {July},
pdf = {control.ee.ethz.ch/~floriand/docs/Articles/WuDorflerJovanovic_MTNS_2014.pdf},
title = {Analysis and Design Trade-Offs for Power Network Inter-Area Oscillations},
year = 2014
}
-
Y. Xiao,
F. Dörfler,
and M. van der Schaar.
Rating and Matching in Peer Review Systems.
In Allerton Conf. on Communications, Control and Computing,
pages 54-61,
2014.
Keyword(s): Social Networks,
Distributed Control Algorithms,
Game Theory.
@conference{YX-FD-MS:14a,
author = {Y. Xiao and F. D{ö}rfler and M. van der Schaar},
booktitle = {Allerton Conf. on Communications, Control and Computing},
date-added = {2014-08-19 08:34:05 +0000},
date-modified = {2018-05-01 12:16:24 +0000},
funding = {ETH Zürich Funds},
keywords = {Social Networks, Distributed Control Algorithms, Game Theory},
pages = {54-61},
pdf = {http://people.ee.ethz.ch/~floriand/docs/Articles/PeerReviewAllerton.pdf},
title = {Rating and Matching in Peer Review Systems},
url = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7028435},
year = {2014},
bdsk-url-1 = {http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=7028435}
}
-
F. Dörfler and J. M. Hendrickx.
Synchronization of oscillators: Feasibility and Non-local analysis,
2014.
Keyword(s): Complex Oscillator Networks,
Power Networks.
@misc{FD-JH:14,
author = {F. D{ö}rfler and J. M. Hendrickx},
booktitle = {LCCC Focus Period on Dynamics and Control in Networks},
date-added = {2015-03-25 18:25:43 +0000},
date-modified = {2015-11-10 23:41:29 +0000},
keywords = {Complex Oscillator Networks, Power Networks},
pdf = {http://www.lccc.lth.se/media/2014/julien.pdf},
title = {Synchronization of oscillators: Feasibility and Non-local analysis},
year = {2014}
}
-
F. Dörfler,
J. W. Simpson-Porco,
and F. Bullo.
Breaking the Hierarchy: Distributed Control & Economic Optimality in Microgrids,
January 2014.
Note: Available at http://arxiv.org/abs/1401.1767.
Keyword(s): Microgrids,
Distributed Control Algorithms,
Power Electronics Control,
Power Networks.
Abstract:
Modeled after the hierarchical control architecture of power transmission systems, a layering of primary, secondary, and tertiary control has become the standard operation paradigm for microgrids. Despite this superficial similarity, the control objectives in microgrids across these three layers are varied and ambitious, and they must be achieved while allowing for robust plug-and-play operation and maximal flexibility, without hierarchical decision making and time-scale separations. In this work, we explore control strategies for these three layers and illuminate some possibly-unexpected connections and dependencies among them. Building from a first-principle analysis of decentralized primary droop control, we study centralized, decentralized, and distributed architectures for secondary frequency regulation. We find that averaging-based distributed controllers using communication among the generation units offer the best combination of flexibility and performance. We further leverage these results to study constrained AC economic dispatch in a tertiary control layer. Surprisingly, we show that the minimizers of the economic dispatch problem are in one-to-one correspondence with the set of steady-states reachable by droop control. In other words, the adoption of droop control is necessary and sufficient to achieve economic optimization. This equivalence results in simple guidelines to select the droop coefficients, which include the known criteria for power sharing. We illustrate the performance and robustness of our designs through simulations. |
@misc{FD-JWSP-FB:14a-arxiv,
abstract = {Modeled after the hierarchical control architecture of power transmission systems, a layering of primary, secondary, and tertiary control has become the standard operation paradigm for microgrids. Despite this superficial similarity, the control objectives in microgrids across these three layers are varied and ambitious, and they must be achieved while allowing for robust plug-and-play operation and maximal flexibility, without hierarchical decision making and time-scale separations. In this work, we explore control strategies for these three layers and illuminate some possibly-unexpected connections and dependencies among them. Building from a first-principle analysis of decentralized primary droop control, we study centralized, decentralized, and distributed architectures for secondary frequency regulation. We find that averaging-based distributed controllers using communication among the generation units offer the best combination of flexibility and performance. We further leverage these results to study constrained AC economic dispatch in a tertiary control layer. Surprisingly, we show that the minimizers of the economic dispatch problem are in one-to-one correspondence with the set of steady-states reachable by droop control. In other words, the adoption of droop control is necessary and sufficient to achieve economic optimization. This equivalence results in simple guidelines to select the droop coefficients, which include the known criteria for power sharing. We illustrate the performance and robustness of our designs through simulations. },
author = {F. D{ö}rfler and J. W. Simpson-Porco and F. Bullo},
date-added = {2014-01-09 03:11:05 +0000},
date-modified = {2018-05-01 12:23:35 +0000},
funding = {UCLA Startup Funds, NSF CNS-1135819, NSERC Canada},
journal = {IEEE Transactions on Control of Network Systems},
keywords = {Microgrids, Distributed Control Algorithms, Power Electronics Control, Power Networks},
month = {January},
note = {{Available at {http://arxiv.org/abs/1401.1767}}},
pdf = {http://arxiv.org/pdf/1401.1767v2.pdf},
title = {{Breaking the Hierarchy: Distributed Control \& Economic Optimality in Microgrids}},
url = {http://arxiv.org/abs/1401.1767},
year = 2014,
bdsk-url-1 = {http://dx.doi.org/10.1109/TCSI.2012.2215780}
}
-
D. Mehta,
N. Daleo,
F. Dörfler,
and J. D. Hauenstein.
Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis,
2014.
Note: Available at http://arxiv.org/abs/1412.0666.
Keyword(s): Complex Oscillator Networks,
Complex Polynomial Networks.
@misc{DM-NSD-FD-JDH:14-arxiv,
author = {D. Mehta and N. Daleo and F. D{ö}rfler and J. D. Hauenstein},
date-added = {2014-12-03 13:32:50 +0000},
date-modified = {2018-05-01 12:23:07 +0000},
funding = {ETH Zürich Funds},
keywords = {Complex Oscillator Networks, Complex Polynomial Networks},
note = {{Available at {http://arxiv.org/abs/1412.0666}}},
pdf = {https://arxiv.org/pdf/1412.0666v2.pdf},
title = {Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis},
url = {http://arxiv.org/abs/1412.0666},
year = {2014},
bdsk-url-1 = {http://arxiv.org/abs/1411.6973}
}
-
J. W. Simpson-Porco,
F. Dörfler,
and F. Bullo.
Voltage Stability of Droop-Controlled Microgrids (Extended Abstract),
July 2014.
Note: Available at http://people.ee.ethz.ch/ floriand/docs/Articles/SimpsonPorco_MTNS_2014.pdf.
Keyword(s): Complex Polynomial Networks,
Microgrids,
Voltage Control.
@misc{JWSP-FD-FB:MTNS14,
address = {Groningen, The Netherlands},
author = {J. W. Simpson-Porco and F. Dörfler and F. Bullo},
booktitle = {International Symposium on Mathematical Theory of Network and Systems},
date-added = {2014-07-02 22:40:19 +0000},
date-modified = {2016-05-31 09:51:42 +0000},
keywords = {Complex Polynomial Networks, Microgrids, Voltage Control},
month = {July},
note = {{Available at {http://people.ee.ethz.ch/~floriand/docs/Articles/SimpsonPorco_MTNS_2014.pdf}}},
pdf = {http://people.ee.ethz.ch/~floriand/docs/Articles/SimpsonPorco_MTNS_2014.pdf},
title = {Voltage Stability of Droop-Controlled Microgrids {(Extended Abstract)}},
year = {2014}
}
-
M. Sinha,
F. Dörfler,
B. Johnson,
and S. Dhople.
Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of Van der Pol Oscillators,
2014.
Note: Available at http://arxiv.org/abs/1411.6973.
Keyword(s): Microgrids,
Complex Oscillator Networks,
Virtual Oscillator Control,
Power Electronics Control.
@misc{MS-FD-BJ-SD:14b-arxiv,
author = {M. Sinha and F. D{ö}rfler and B. Johnson and S. Dhople},
date-added = {2014-11-26 11:53:46 +0000},
date-modified = {2018-05-01 12:23:23 +0000},
funding = {ETH Zürich Funds},
keywords = {Microgrids, Complex Oscillator Networks, Virtual Oscillator Control, Power Electronics Control},
note = {{Available at {http://arxiv.org/abs/1411.6973}}},
pdf = {http://arxiv.org/pdf/1411.6973v1.pdf},
title = {Uncovering Droop Control Laws Embedded Within the Nonlinear Dynamics of {Van der Pol} Oscillators},
url = {http://arxiv.org/abs/1411.6973},
year = {2014},
bdsk-url-1 = {http://arxiv.org/abs/1411.6973}
}
-
T. Summers,
I. Shames,
J. Lygeros,
and F. Dörfler.
Topology Design for Optimal Network Coherence,
2014.
Note: Available at http://arxiv.org/abs/1411.4884.
Keyword(s): Distributed Control Algorithms,
Wide-Area Control.
@misc{TS-IS-JL-FD:15-arxiv,
author = {Summers, T. and Shames, I. and Lygeros, J. and D{ö}rfler, F.},
date-added = {2014-11-26 11:55:35 +0000},
date-modified = {2016-05-31 09:52:02 +0000},
keywords = {Distributed Control Algorithms, Wide-Area Control},
note = {{Available at {http://arxiv.org/abs/1411.4884}}},
pdf = {http://arxiv.org/pdf/1411.4884v1.pdf},
title = {Topology Design for Optimal Network Coherence},
url = {http://arxiv.org/abs/1411.4884},
year = {2014},
bdsk-url-1 = {http://arxiv.org/abs/1411.4884}
}
-
Y. Xiao,
F. Dörfler,
and M. van der Schaar.
Incentive Design in Peer Review: Rating and Repeated Endogenous Matching,
November 2014.
Note: Available at http://arxiv.org/abs/1411.2139.
Keyword(s): Social Networks,
Distributed Control Algorithms,
Game Theory.
@misc{YX-FD-MVDS:14b-arxiv,
author = {Y. Xiao and F. D{ö}rfler and M. van der Schaar},
date-added = {2014-11-11 09:11:01 +0000},
date-modified = {2018-05-01 12:22:44 +0000},
funding = {ETH Zürich Funds},
keywords = {Social Networks, Distributed Control Algorithms, Game Theory},
month = {November},
note = {{Available at {http://arxiv.org/abs/1411.2139}}},
pdf = {http://arxiv.org/pdf/1411.2139v1.pdf},
title = {Incentive Design in Peer Review: Rating and Repeated Endogenous Matching},
year = 2014
}