Geodesic
Interior sphere property of attainable sets and time optimal control problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 2, pp. 350-370

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This paper studies the attainable set at time T>0 for the control system

( ˙t)=f((t),u(t))u(t)∈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 C 1,1 -regularity for boundaries of attainable sets.

DOI : 10.1051/cocv:2006002
Classification : 26B25, 49K15, 93B03
Keywords: control theory, attainable sets, minimum time function, semiconcave functions 
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     title = {Interior sphere property of attainable sets and time optimal control problems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {350--370},
     publisher = {EDP-Sciences},
     volume = {12},
     number = {2},
     year = {2006},
     doi = {10.1051/cocv:2006002},
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     zbl = {1105.93007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006002/}
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Cannarsa, Piermarco; Frankowska, Hélène. Interior sphere property of attainable sets and time optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 2, pp. 350-370. doi: 10.1051/cocv:2006002

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