Interior sphere property of attainable sets and time optimal control problems
Dipartimento di Matematica, Università di Roma Tor Vergata,
Via della Ricerca Scientifica 1, 00133 Roma, Italy; firstname.lastname@example.org
2 CREA, École Polytechnique, 1 Rue Descartes, 75005 Paris, France; email@example.com
Revised: 21 February 2005
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