Optimal control problems in transport dynamics with additive noise (Q6072858)

Motivated by the applications in leader-follower multi-agent dynamics, the authors study a class of optimal control problems, 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. In particular, the authors extend the work by \textit{M. Bongini} and \textit{G. Buttazzo} [Math. Models Methods Appl. Sci. 27, No. 3, 427--451 (2017; Zbl 1365.49004)]. A well-posedness theory under very low regularity of the control vector fields is developed. The mean-field limit of a stochastic particle approximation is also detailed.