Optimal control in Wasserstein spaces.

Summary A large number of mathematical tools for modeling and analyzing multi-agent problems have recently been developed in the framework of optimal transport theory. In this thesis, we extend for the first time several of these concepts to problems from control theory. We prove several results on this subject, including necessary conditions for Pontryagin-like optimality in Wasserstein spaces, conditions ensuring the intrinsic regularity of optimal solutions, sufficient conditions for the emergence of different patterns, and an auxiliary result about the arrangements of certain singularities in sub-Riemannian geometry.