Differential Inclusions and Target Problems

Where and how solutions associated to a differential inclusion can or cannot enter a given target is studied. For this purpose, partitions of the target boundary are associated with the dynamic of the system. The behaviour of these solutions is qualitatively described in terms of viability and invariance kernels of sets. These kernels determine points such that there exist (respectively, all) solutions starting at these points remain in a given set of constraints. The sets that are reached in finite time by viable solutions to the system are also studied. Finally, some applications to control systems with one target are provided, and the concept of semipermeable barriers will be generalized.