Mattia Bongini's seminar at SISSA

[Emanuele Tuillier Illingworth]

SEMINAR ANNOUNCEMENT

Mattia Bongini (TU München)

TITLE
Mean-field Pontryagin maximum principle

ABSTRACT
The mean-field approach is a powerful tool for giving sense to the 
notion that a discrete dynamical system converges to a continuous one as 
the number of agents increases. This technique has been recently used in 
connection with $\Gamma$-convergence to show that a two-populations 
discrete optimal control problem converges to an ODE-PDE constrainted 
optimal control problem: in this model, a discrete population of agents 
(called "leaders") interacts with a continuous one (the mass of 
"followers"), and its target is to steer the entire population towards 
configurations minimizing a given cost. In this paper we address the 
problem of deriving optimality conditions for this optimal control 
problem. We show that these optimality conditions can be seen as the 
mean-field limit $N\to\infty$ of the Pontryagin Maximum Principle 
applied to the two-population discrete system with $N$ followers. This, 
in turn, enables us a constructive method to derive solutions as limits 
of solutions of the discrete optimality conditions, which in the end let 
us establish existence results for these kinds of Hamiltonian systems. 
Finally, we prove that the resulting optimality conditions are indeed 
Hamiltonian flows in the Wasserstein space of probability measures.

Venue: SISSA, room 005 (ground floor), Thursday 19 March at 11:00