# Interior sphere property of attainable sets and time optimal control problems

Piermarco Cannarsa; Hélène Frankowska

ESAIM: Control, Optimisation and Calculus of Variations (2006)

- Volume: 12, Issue: 2, page 350-370
- ISSN: 1292-8119

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topCannarsa, Piermarco, and Frankowska, Hélène. "Interior sphere property of attainable sets and time optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 12.2 (2006): 350-370. <http://eudml.org/doc/249673>.

@article{Cannarsa2006,

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.
},

author = {Cannarsa, Piermarco, Frankowska, Hélène},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Control theory; attainable sets; minimum time function; semiconcave
functions.; semiconcave functions},

language = {eng},

month = {3},

number = {2},

pages = {350-370},

publisher = {EDP Sciences},

title = {Interior sphere property of attainable sets and time optimal control problems},

url = {http://eudml.org/doc/249673},

volume = {12},

year = {2006},

}

TY - JOUR

AU - Cannarsa, Piermarco

AU - Frankowska, Hélène

TI - Interior sphere property of attainable sets and time optimal control problems

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2006/3//

PB - EDP Sciences

VL - 12

IS - 2

SP - 350

EP - 370

AB -
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.

LA - eng

KW - Control theory; attainable sets; minimum time function; semiconcave
functions.; semiconcave functions

UR - http://eudml.org/doc/249673

ER -

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## Citations in EuDML Documents

top- Marco Castelpietra, Interior sphere property for level sets of the value function of an exit time problem
- Lino J. Alvarez-Vázquez, Francisco J. Fernández, Aurea Martínez, Analysis of a time optimal control problem related to the management of a bioreactor
- Lino J. Alvarez-Vázquez, Francisco J. Fernández, Aurea Martínez, Analysis of a time optimal control problem related to the management of a bioreactor
- Thomas Lorenz, Evolution equations in ostensible metric spaces: First-order evolutions of nonsmooth sets with nonlocal terms

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