- Università di Pavia
Wednesday, April 17, 2019
This talk aims to explore the relations between various formulations of an optimal control problem for interacting multi-particles systems.
Different research fields come 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.
In particular, we consider an abstract parametrization space for the mass of agents. Here, we are interested in the time-evolution of a random variable subject to non-local dynamics where the control appears under different natures. We consider related nonlocal cost functionals and we study the equivalence of their infima. Then, we state a suitable Eulerian formulation of the problem, i.e. an optimal control problem for the corresponding laws in the space of probability measures, and we discuss conditions in order to have the equivalence with the corresponding value function. Finally we deal with stability and $\Gamma$-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).
Wed 17.4.2019 12:30 Room C