We consider a model of cooperative control
system, that is a system where different controls act with non
conflictual purposes. For example one control is chosen in order to minimize some cost while another is designed
for safety purposes. In our main application, a model of Air Traffic Management, one control minimizes the
travel time while the other is applied to avoid crashes in a free flight environment.
The mathematical difficulties arise because of the use of
two discontinuous feedbacks at the same time.
We consider stratified feedbacks and
solutions in Krasowskii sense. Two refinements of this concept
are given to guarantee existence and good behavior of solutions.