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

Abstract

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This paper studies the attainable set at time T>0 for the control system y ˙ ( t ) = f ( y ( 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 C1,1-regularity for boundaries of attainable sets.

How to cite

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Cannarsa, 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 -

References

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Citations in EuDML Documents

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

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