Lorenz, Thomas
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Abstract
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.
| Document type: | Preprint |
|---|---|
| Date Deposited: | 08 May 2007 07:33 |
| Date: | 2007 |
| Faculties / Institutes: | Service facilities > Interdisciplinary Center for Scientific Computing |
| DDC-classification: | 510 Mathematics |
| Controlled Keywords: | Differentialinklusion, Kompakte Menge, Mengenwertige Abbildung |
| Uncontrolled Keywords: | Differential inclusion , reachable set (alias attainable set) , epi-Lipschitzian sets , Clarke tangent cone |
