[Dottorcomp] avviso di seminario 23 febbraio, Politecnico di Milano

[Lorenzo Tamellini]

Buonasera a tutt*,

ricevo e inoltro l'avviso di seminario qui sotto.

Cordiali saluti,
Lorenzo Tamellini




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*Da:* Irene Maria Sabadini <irene.sabadini a polimi.it>
*Inviato:* venerdì 4 febbraio 2022 19:27
*Oggetto:* Avviso di seminario



Si avvisa che in data 23/2/2022, alle ore 17:00, Sala Consiglio 7 piano,
Edificio La Nave e on line, nell'ambito delle iniziative del Seminario
Matematico e Fisico di Milano, si svolgerà il seguente seminario:

Control of multiagent systems viewed as dynamical systems on the
Wasserstein space
Marc Quincampoix, Université de Brest, France
This talk is devoted to an overview of recent results on the optimal
control of dynamical systems on probability measures modelizing the
evolution of a large number of agents.

The system is composed by a number of agents so huge, that at each time
only a statistical description of the state is available. A common way to
model such kind of system is to consider a macroscopic point of view, where
the state of the system is
described by a (time-evolving) probability measure on $R^d$ (which the
underlying space where the agents move). So we are facing to a two-level
system where the mascroscopic dynamic concerns probability measure while
the microscopic dynamic - which describes the evolution of an individual
agent - is a controlled differential equation on $ R^d$.

Associated to this dynamics on the Wasserstein space, one can associate a
cost which allows to define a value function. We discuss the
characterization of this value function through a Hamilton Jacobi Bellman
equation stated on the Wasserstein space. We also discuss the problem of
compatibility of state constraints with a multiagent control system. Since
the Wasserstein space can be also viewed as the set of the laws of random
variables in a suitable $L^2$ space, one can hope to reduce our problems to
$L^2$ analysis. We discuss when this is possible.
This overview talk is based on several works in collaboration with I.
Averboukh, P. Cardaliaguet, G. Cavagnari, C. Jimenez and A. Marigonda.


È gradita la sua partecipazione.
Cordiali saluti.
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