The reachable sets of a differential inclusion have nonsmooth topological boundaries in general. The main result of this paper is that under the well-known assumptions of Filippov's existence theorem (about differential inclusions), every epi-Lipschitzian initial compact set (of the Euclidean space) preserves this regularity for a (possibly short) time, i.e. its reachable set is also epi-Lipschitzian for all small times. The proof is based on Rockafellar's geometric characterization of epi-Lipschitzian sets and uses a new result about the "inner semicontinuity" of Clarke tangent cone (to reachable sets) with respect to both time and base point.
|Faculties / Institutes:||Service facilities > Interdisciplinary Center for Scientific Computing|
|Controlled Keywords:||Differentialinklusion, Kompakte Menge, Mengenwertige Abbildung|
|Uncontrolled Keywords:||Differential inclusion , reachable set (alias attainable set) , epi-Lipschitzian sets , Clarke tangent cone|