Optimal control problems in transport dynamics with additive noise

Motivated by the applications in leader-follower multi-agent dynamics, a class of optimal control prob-lems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. The evolution of the systems obeys a non-linear Fokker-Planck-type equation as 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 rig-orous mean-field limit of a stochastic particle approximation.& COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).