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Documents  Piccoli, Benedetto | enregistrements trouvés : 9

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Research talks

Very large networks linking dynamical agents are now ubiquitous and there is significant interest in their analysis, design and control. The emergence of the graphon theory of large networks and their infinite limits has recently 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]. Furthermore, the study of the decentralized control of such systems has been initiated in [Caines and Huang, IEEE CDC 2018] where Graphon Mean Field Games (GMFG) and the GMFG equations are formulated for the analysis of non-cooperative dynamical games on unbounded networks. In this talk the GMFG framework will be first be presented followed by the basic existence and uniqueness results for the GMFG equations, together with an epsilon-Nash theorem relating the infinite population equilibria on infinite networks to that of finite population equilibria on finite networks. Very large networks linking dynamical agents are now ubiquitous and there is significant interest in their analysis, design and control. The emergence of the graphon theory of large networks and their infinite limits has recently 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]. Furthermore, the study of the decentralized ...

91A13 ; 49N70 ; 93E20 ; 93E35

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- xiv; 497 p.
ISBN 978-3-642-32159-7

Lecture notes in mathematics , 2062

Localisation : Collection 1er étage

analyse de systèmes # EDP # équations aux dérivées partielles # optimisation # modèle en réseau # logistique # problèmes de traffic # lois de consevation # programmation mathématique

35L65 ; 90B20 ; 90-06 ; 90B10 ; 90B06 ; 90C90 ; 00B25

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Research talks

Mean field games (MFG) are dynamic games with infinitely many infinitesimal agents. In this joint work with Catherine Rainer (U. Brest), we study the efficiency of Nash MFG equilibria: Namely, we compare the social cost of a MFG equilibrium with the minimal cost a global planner can achieve. We find a structure condition on the game under which there exists efficient MFG equilibria and, in case this condition is not fulfilled, quantify how inefficient MFG equilibria are. Mean field games (MFG) are dynamic games with infinitely many infinitesimal agents. In this joint work with Catherine Rainer (U. Brest), we study the efficiency of Nash MFG equilibria: Namely, we compare the social cost of a MFG equilibrium with the minimal cost a global planner can achieve. We find a structure condition on the game under which there exists efficient MFG equilibria and, in case this condition is not fulfilled, quantify how ...

91A13 ; 35Q91

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Research talks

We present a Godunov type numerical scheme for a class of scalar conservation laws with nonlocal flux arising for example in traffic flow modeling. The scheme delivers more accurate solutions than the widely used Lax-Friedrichs type scheme and also allows to show well-posedness of the model. In a second step, we consider the extension of the non-local traffic flow model to road networks by defining appropriate conditions at junctions. Based on the proposed numerical scheme we show some properties of the approximate solution and provide several numerical examples. We present a Godunov type numerical scheme for a class of scalar conservation laws with nonlocal flux arising for example in traffic flow modeling. The scheme delivers more accurate solutions than the widely used Lax-Friedrichs type scheme and also allows to show well-posedness of the model. In a second step, we consider the extension of the non-local traffic flow model to road networks by defining appropriate conditions at junctions. Based on ...

35L65 ; 65M12 ; 90B20

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Research talks

In the talk, I will first present a typical Mean Field Game problem, as in the theory introduced by Lasry-Lions and Huang-Caines-Malhamé, concentrating on the case where the game has a variational structure (i.e., the equilibrium can be found by minimizing a global energy) and is purely deterministic (no diffusion, no stochastic control). From the game-theoretical point of view, we look for a Nash equilibrium for a non-atomic congestion game, involving a penalization on the density of the players at each point. I will explain why regularity questions are natural and useful for rigorously proving that minimizers are equilibria, making the connection with what has been done for the incompressible Euler equation in the Brenier’s variational formalism. I will also introduce a variant where the penalization on the density is replaced by a constraint, which lets a price (which is a pressure, in the incompressible fluid language) appears on saturated regions. Then, I will sketch some regularity results which apply to these settings.
The content of the talk mainly comes from joint works with A. Mészáros, P. Cardaliaguet, and H. Lavenant.
In the talk, I will first present a typical Mean Field Game problem, as in the theory introduced by Lasry-Lions and Huang-Caines-Malhamé, concentrating on the case where the game has a variational structure (i.e., the equilibrium can be found by minimizing a global energy) and is purely deterministic (no diffusion, no stochastic control). From the game-theoretical point of view, we look for a Nash equilibrium for a non-atomic congestion game, ...

49J45 ; 91A10 ; 35Q91

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Research talks

The talk summarize the empirical state of knowledge on bottleneck flow and introduces an approach to describe crowd disasters. The approach combines quantities well known in natural sciences with concepts of social psychology. It allows to describe crowds at bottlenecks in case of exceptional (life-threatening) or normal circumstances.
On the basis of empirical data, the influence of the spatial structure of the boundaries (width and length of the bottleneck) and the motivation of pedestrians on flow and density will be presented. The phenomenon of clogging and its effects on the flow will be discussed in connection with congestion, rewards, motivation and pushing. Positive effects of pillars in front of bottlenecks are critically questioned by recent experiments. Results of two experiments including questionnaire studies connect flow and density with factors of social psychology like rewards, social norms, expectations or fairness.
The talk summarize the empirical state of knowledge on bottleneck flow and introduces an approach to describe crowd disasters. The approach combines quantities well known in natural sciences with concepts of social psychology. It allows to describe crowds at bottlenecks in case of exceptional (life-threatening) or normal circumstances.
On the basis of empirical data, the influence of the spatial structure of the boundaries (width and length of ...

91D10 ; 35L65 ; 90B20

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ISBN 978-0-8218-2066-7

Memoirs of the american mathematical society , 0694

Localisation : Collection 1er étage

loi de conservation # problème de Cauchy # système n fois n

35L65

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- 261 p.
ISBN 978-3-540-20306-3

Mathématiques & applications , 0043

Localisation : Collection 1er étage

théorie du contrôle # méthode géométrique # variété de dimension 2 # synthèse optimale # système feedback # singularité # projection # contrôle en temps minimal

49J15 ; 49N35

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- x; 206 p.
ISBN 978-0-898717-00-6

Localisation : Ouvrage RdC (MODE)

optimisation # files d'attentes # simulation # modélisation mathématique # chaîne d'appovisionnement # modèle en réseau

90-02 ; 90B22 ; 00A71 ; 00A72 ; 90B10

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