Boundary regularity of reachable sets of control systems |
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| Authors: | Thomas Lorenz |
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| Affiliation: | Interdisciplinary Center for Scientific Computing (IWR), Ruprecht-Karls University of Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany |
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| Abstract: | The reachable set of a differential inclusion has nonsmooth boundary in general. Now we give sufficient conditions on the compact initial set and the differential inclusion (a.e.) so that this topological boundary has “positive erosion”, i.e. it satisfies a uniform interior sphere condition. The proof is based on the close relation between the semiconcave value function of a suitable Mayer problem and its epigraph with positive erosion. |
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| Keywords: | Differential inclusion Control system Reachable set Interior sphere condition Set of positive erosion Set of positive reach Proximally smooth set Semiconcave function |
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