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.

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 : https://doi.org/10.1051/cocv:2006002
Classification : 26B25,  49K15,  93B03
Mots clés : control theory, attainable sets, minimum time function, semiconcave functions
@article{COCV_2006__12_2_350_0,
     author = {Cannarsa, Piermarco and Frankowska, Halina},
     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},
     zbl = {1105.93007},
     mrnumber = {2209357},
     language = {en},
     url = {http://www.numdam.org/item/COCV_2006__12_2_350_0/}
}
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. http://www.numdam.org/item/COCV_2006__12_2_350_0/

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