| Issue |
ESAIM: COCV
Volume 12, Number 2, April 2006
|
|
|---|---|---|
| Page(s) | 350 - 370 | |
| DOI | https://doi.org/10.1051/cocv:2006002 | |
| Published online | 22 March 2006 | |
Interior sphere property of attainable sets and time optimal control problems
1
Dipartimento di Matematica, Università di Roma Tor Vergata,
Via della Ricerca Scientifica 1, 00133 Roma, Italy; This email address is being protected from spambots. You need JavaScript enabled to view it.
2
CREA, École Polytechnique,
1 Rue Descartes, 75005 Paris, France; This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
20
April
2004
Revised:
21
February
2005
Abstract
This paper studies the attainable set at time T>0 for the control system 
showing that, under suitable assumptions on f, such a set satisfies a uniform interior sphere
condition. The interior sphere property is
then applied to recover a semiconcavity result for the value
function of time optimal control problems with a general target, and to
deduce C1,1-regularity for boundaries of attainable sets.
Mathematics Subject Classification: 26B25 / 49K15 / 93B03
Key words: Control theory / attainable sets / minimum time function / semiconcave functions.
© EDP Sciences, SMAI, 2006
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