[Dottorcomp] Avviso di Seminario, Politecnico di Milano

[Stefano Lisini]

Segnalo il seguente seminario:

Da: Iniziative di Dipartimento <giovanni.catino a polimi.it>
Oggetto: Avviso di seminario
Data: 21 febbraio 2020 09:55:18 CET
Rispondi a: Iniziative di Dipartimento <giovanni.catino a polimi.it>

Si avvisa che in data 26/2/2020, alle ore 15:15 , presso il
Politecnico di Milano, Dipartimento di Matematica, Aula seminari 3°
piano, nell'ambito delle iniziative della sezione di Analisi, si
svolgerà il seguente seminario:

Titolo: Lagrangian and Eulerian formulations for multi-agent optimal
control problems
Relatore: Giulia Cavagnari, Politecnico di Milano
Abstract:
In this talk we present and compare two approaches to study
deterministic optimal control problems for interacting multi-agent
systems: Lagrangian and Eulerian.
Different research fields comes into play: optimal control and
transport theory to set out the variational model and analyze the
underlying principles, and a random variable approach to deal with the
problem in its various Lagrangian formulations on a fixed probability
space Ω (space of parametrizations).
On one side, the state of the system is expressed by a random variable
in L^2(Ω) and the nonlocal velocity field driving the dynamics depends
on the realizations of a Borel measurable control map. The lack of
existence of minimizers for a generic cost functional, even after
relaxation, makes it fundamental to recover optimality through the
study of the problem from an Eulerian viewpoint. Here the problem is
set in the 2-Wasserstein space of probability measures. The relation
with the previous approach lies on the identification of the
time-dependent measure, solving a controlled continuity equation, as
the law of the evolving random variable.
After stating the problem, we prove the equivalence between the
Lagrangian and Eulerian value functions through an intermediate
formulation based on the Superposition Principle by
Ambrosio-Gigli-Savaré.
Finally we deal with stability and Г-convergence results for the
corresponding problems involving a finite number of agents to the
mean-field ones.
This is a joint work with Stefano Lisini (University of Pavia), Carlo
Orrieri (University of Trento) and Giuseppe Savaré (University of
Pavia).