Differential Inclusions and Target Problems

The author studies where and how solutions associated to a differential inclusion can or cannot enter a given target. For this purpose, he associates partitions of the target boundary with the dynamics of the system. He qualitatively describes the behavior of these solutions in terms of viability and invariance kernels of sets. These kernels determine points such that there exist (respectively all) solutions starting at these point remain in a given set of constraints. He also studies the sets which are reached in finite time by viable solutions to the system. Finally, he provides some applications to control systems with one target and he generalizes the concept of semipermeable barrier.