Optimal times for constrained nonlinear control problems without local controllability

We study optimal times to reach a given closed target for controlled systems with a state constraint. Our goal is to characterize these optimal time functions in such a way that it is possible to compute them numerically and we do not need to compute trajectories of the controlled system. In this paper we provide new results using viability theory. This allows us to study optimal time functions free from the controllability assumptions classically made in the partial differential equations approach.