Abstract: We are interested in developing necessary optimality conditions in the form of a Pontryagin maximum principle for the minimal time Bolza optimal control problem with constraints in the final time. In this problem, the dynamic is given by a non-local continuity equation in the Wasserstein space of probability measures, the set of controls are taken in open-loop form and the set of constraints is represented by functional inequalities applied to the terminal time. To this end, we relate the main challenges of this problem from which a fair amount is accounted by the fact that Wasserstein spaces are not Banach and hence its difficulties on defining differentiability.
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