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Interior sphere property of attainable sets and time optimal control problems

Published online by Cambridge University Press:  22 March 2006

Piermarco Cannarsa  and
Hélène Frankowska
Piermarco Cannarsa
Affiliation:
Dipartimento di Matematica, Università di Roma Tor Vergata, Via della Ricerca Scientifica 1, 00133 Roma, Italy; cannarsa@mat.uniroma2.it
Hélène Frankowska
Affiliation:
CREA, École Polytechnique, 1 Rue Descartes, 75005 Paris, France; franko@shs.polytechnique.fr
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Abstract

This paper studies the attainable set at time T>0 for the control system $$\dot y(t)=f(y(t),u(t))\,\qquad u(t)\in U$$ 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.

Keywords

Control theoryattainable setsminimum time functionsemiconcave functions.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 12 , Issue 2 , April 2006 , pp. 350 - 370
Copyright
© EDP Sciences, SMAI, 2006

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