Safety controls and applications to the Dubins' car

In this paper we consider systems with cooperative controls. Such a model turns out to be efficient in those cases where one has to deal with different goals, as optimality and safety issues, at the same time. On the other hand, the drawback of this approach is the presence of discontinuities of the various controls. To deal with this problem, we give a general strategy, which is based on the concept of Krasowskii solution to discontinuous ODEs. Such a strategy is then applied to the safety driving of the Dubins' car.