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The emergence of the graphon theory of large networks and their infinite limits has enabled the formulation of a theory of the centralized control of dynamical systems distributed on asymptotically infinite networks (Gao and Caines, IEEE CDC 2017, 2018).
Joseph L Doob, Stochastic processes , Wiley, New York, 1953
1953
Earlier work this paper cites.
Olga Aleksandrovna Ladyzhenskaya, NN Ural’ceva, and VA Solonnikov, Linear and quasi-linear equations of parabolic type , American Mathematical Society, 1968
1968
Earlier work this paper cites.
Wendell H. Fleming and Raymond W. Rishel, Deterministic and stochastic optimal control , Springer-Verlag, New York, 1975
1975
Earlier work this paper cites.
I. P. Natanson, Theory of functions of a real variable, vol. I , F. Ungar Publishing Co., 1983, 5th printing
1983
Earlier work this paper cites.
Alain-Sol Sznitman, Topics in propagation of chaos , Ecole d’été de probabilités de Saint-Flour XIX—1989, Springer, 1991, pp. 165–251
1991
Earlier work this paper cites.
Wolfgang Pauli and Charles P Enz, Thermodynamics and the kinetic theory of gases , vol. 3, Courier Corporation, 2000
2000
Earlier work this paper cites.
Christian Borgs, Jennifer Chayes, László Lovász, Vera T Sós, Balázs Szegedy, and Katalin Vesztergombi, Graph limits and parameter testing , Proc. the thirty-eighth annual ACM symposium on Theory of computing, 2006, pp. 261–270
2006
Earlier work this paper cites.
Minyi Huang, Roland P Malhamé, and Peter E Caines, Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle , Communications in Information & Systems 6
2006
Earlier work this paper cites.
Jean-Michel Lasry and Pierre-Louis Lions, Jeux á champ moyen. I - le cas stationnaire , Comptes Rendus Mathématique 343
2006
Earlier work this paper cites.
by same author, Jeux á champ moyen. II horizon fini et controle optimal , Comptes Rendus Mathématique 343
2006
Earlier work this paper cites.
László Lovász and Balázs Szegedy, Limits of dense graph sequences , Journal of Combinatorial Theory, Series B 96
2006
Earlier work this paper cites.
Minyi Huang, Peter E Caines, and Roland P Malhamé, Large-population cost-coupled LQG problems with nonuniform agents: individual-mass behavior and decentralized ε \varepsilon -Nash equilibria , IEEE Transactions on Automatic Control 52
2007
Earlier work this paper cites.
Christian Borgs, Jennifer T Chayes, László Lovász, Vera T Sós, and Katalin Vesztergombi, Convergent sequences of dense graphs I: Subgraph frequencies, metric properties and testing , Advances in Mathematics 219
2008
Earlier work this paper cites.
Isom H Herron and Michael R Foster, Partial differential equations in fluid dynamics , Cambridge University Press, 2008
2008
Earlier work this paper cites.
by same author, The NCE (mean field) principle with locality dependent cost interactions , IEEE Transactions on Automatic Control 55
2010
Cited alongside, same era.
by same author, Convergent sequences of dense graphs II. multiway cuts and statistical physics , Annals of Mathematics 176
2012
Cited alongside, same era.
Ioannis Karatzas and Steven Shreve, Brownian motion and stochastic calculus , vol. 113, Springer Science & Business Media, 2012
2012
Cited alongside, same era.
László Lovász, Large networks and graph limits , vol. 60, American Mathematical Soc., 2012
2012
Cited alongside, same era.
Isabelle Gallagher, From Newton to Navier-Stokes, or how to connect fluid mechanics equations from microscopic to macroscopic scales , Bulletin of the American Math. Society 56
2013
Cited alongside, same era.
François Delarue, Mean field games: A toy model on an Erdös-Renyi graph , ESAIM: Proceedings and Surveys 60
2017
Later among the works it cites.
Shuang Gao and Peter E. Caines, The control of arbitrary size networks of linear systems via graphon limits: An initial investigation , Proc. 56th IEEE CDC (Melbourne, Australia), December 2017, pp. 1052–1057
2017
Later among the works it cites.
by same author, Controlling complex networks of linear systems via graphon limits , Presented at the Symposium of Controlling Complex Networks of NetSci17, Indianapolis, IN, USA (2017)
2017
Later among the works it cites.
by same author, Minimum energy control of arbitrary size networks of linear systems via graphon limits , Presented at the SIAM Workshop on Network Science, Pittsburgh, PA, USA (2017)
2017
Later among the works it cites.
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Isabelle Gallagher, Laure Saint-Raymond, and Benjamin Texier, From Newton to Boltzmann: hard spheres and short-range potentials , European Mathematical Society, 2013
2013
Cited alongside, same era.
Georgi S Medvedev, The nonlinear heat equation on dense graphs and graph limits , SIAM J. Math. Anal. 46
2014
Cited alongside, same era.
by same author, The nonlinear heat equation on w-random graphs , Archive for Rational Mechanics and Analysis 212
2014
Cited alongside, same era.
Peter E Caines, Mean field games , Encyclopedia of Systems and Control (2015), 706–712
2015
Cited alongside, same era.
Olivier Guéant, Existence and uniqueness result for mean field games with congestion effect on graphs , Applied Mathematics & Optimization 72
2015
Cited alongside, same era.
2015
Cited alongside, same era.
Cristobal Quininao and Jonathan Touboul, Limits and dynamics of randomly connected neuronal networks , Acta Appl Math 136
2015
Cited alongside, same era.
2017
Later among the works it cites.
Peter E Caines and Minyi Huang, Graphon mean field games and the GMFG equations , Proc. 57th IEEE CDC (Miami Beach, FL, USA), 2018, pp. 4129–4134
2018
Later among the works it cites.
Rene Carmona and Francois Delarue, Probabilistic theory of mean field games with applications I , vol. 83, Springer International Publishing, 2018
2018
Later among the works it cites.
by same author, Probabilistic theory of mean field games with applications II , vol. 84, Springer International Publishing, 2018
2018
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by same author, Graphon linear quadratic regulation of large-scale networks of linear systems , Proc. 57th IEEE Conference on Decision and Control (Miami Beach, FL, USA), December 2018, pp. 5892–5897
2018
Later among the works it cites.
Francesca Parise and Asuman Ozdaglar, Graphon games , arXiv preprint arXiv:1802.00080 (2018)
2018
Later among the works it cites.
by same author, Graphon mean field games and the GMFG equations: ϵ \epsilon -Nash equilibria , Proc. the 58th IEEE CDC (Nice, France), 2019, pp. 286–292
2019
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2020
Closest in time.
by same author, Graphon control of large-scale networks of linear systems , IEEE Transactions on Automatic Control 65
2020
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