  In this paper we consider a mean field optimal control problem with an
aggregation-diffusion constraint, where agents interact through a potential, in
the presence of a Gaussian noise term. Our analysis focuses on a PDE system
coupling a Hamilton-Jacobi and a Fokker-Planck equation, describing the optimal
control aspect of the problem and the evolution of the population of agents,
respectively. The main contribution of the paper is a result on the existence
of solutions for the aforementioned system. We notice this model is in close
connection with the theory of mean-field games systems. However, a distinctive
feature concerns the nonlocal character of the interaction; it affects the
drift term in the Fokker-Planck equation as well as the Hamiltonian of the
system, leading to new difficulties to be addressed.
