Calculus of Variations and Geometric Measure Theory

S. Almi - M. Morandotti - F. Solombrino

Optimal control problems in transport dynamics with additive noise

created by morandott on 06 Mar 2023
modified by solombrino on 20 Jul 2023


Published Paper

Inserted: 6 mar 2023
Last Updated: 20 jul 2023

Journal: Journal of Differential Equations
Volume: 373
Pages: 1-47
Year: 2023
Doi: 10.1016/j.jde.2023.07.010

ArXiv: 2303.04877 PDF


Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for randomness in the evolution are taken into account. A well-posedness theory under very low regularity of the control vector fields is developed, as well as a rigorous derivation from stochastic particle systems.

Keywords: $\Gamma$-convergence, superposition principle, mean-field optimal control, population dynamics, optimal control with SDE constraints