About minimal time impulsive control of sequential batch reactors with several species

We consider the optimal control problem of feeding in minimal time a tank where several species compete on a single resource. We allow controls to be bounded measurable functions of time as well as impulses. For the one species case, we extend former results given by Moreno to the framework of impulse controls. For the two species case with increasing growth functions, we show that the solution of the minimal time problem consists in either one impulse control at initial time filling the whole tank, either reaching a singular arc. This last one is optimally reached with an impulse or waiting, and consists in keeping the system at a constant resource level until the tank is filled. We give conditions under which the first strategy is optimal, as well as an example where it is not.