Résumé
In this work, we provide a reformulation of the minimal time crisis problem associated to a given domain as a free terminal time control problem. This is made possible supposing that the viability kernel is non-empty, and that it is reachable from the state space. Moreover, an additional hypothesis on consecutive crossing time of the constraint set is required. Thanks to this result, we compute an optimal synthesis for the minimal time crisis problem governed by the Lotka-Volterra prey-predator model, with a controlled mortality on the predators. Finally, we compare the time spent in the crisis set by optimal trajectories of the minimal time crisis problem and the minimal time problem to reach the viability kernel.