Contribution à l'étude des jeux différentiels quantitatifs et qualitatifs avec contrainte sur l'état

This paper is devoted to a new approach of differential games with state constraints. We explain a new method, general enough to study discontinuous problems but efficient enough to provide numerical schemes. We present this method in a game of kind: the target problem and in a game of degree: the minimal time to reach a closed target. The solutions of these games are characterized by the mean of geometrical conditions. Algorithms for computing these solutions are presented.