Control problems with possibly infinite cost in the Wasserstein space

A population can be represented as a sum of individuals or as a continuum. Both approaches are unified if one uses probability measures, which are a very convenient tool when endowed with the Wasserstein distance. In this setting, one can study control problems over the dynamic of the population by using roughly the same tools as in classical Euclidian spaces. We present one of such extensions, namely the characterization of the value function of a control problem as the minimal viscosity supersolution of a Hamilton-Jacobi equation.