Local small time controllability and attainability of a set for nonlinear control system

Mikhail Krastanov; Marc Quincampoix

ESAIM: Control, Optimisation and Calculus of Variations (2010)

  • Volume: 6, page 499-516
  • ISSN: 1292-8119

Abstract

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In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set is a hyperplane.

How to cite

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Krastanov, Mikhail, and Quincampoix, Marc. "Local small time controllability and attainability of a set for nonlinear control system." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 499-516. <http://eudml.org/doc/197313>.

@article{Krastanov2010,
abstract = { In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set is a hyperplane. },
author = {Krastanov, Mikhail, Quincampoix, Marc},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {Attainability; controlability; local variations; polynomial control; linear controls.; attainability; controllability; linear controls},
language = {eng},
month = {3},
pages = {499-516},
publisher = {EDP Sciences},
title = {Local small time controllability and attainability of a set for nonlinear control system},
url = {http://eudml.org/doc/197313},
volume = {6},
year = {2010},
}

TY - JOUR
AU - Krastanov, Mikhail
AU - Quincampoix, Marc
TI - Local small time controllability and attainability of a set for nonlinear control system
JO - ESAIM: Control, Optimisation and Calculus of Variations
DA - 2010/3//
PB - EDP Sciences
VL - 6
SP - 499
EP - 516
AB - In the present paper, we study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set well adapted to a given closed set and prove a new attainability result for a general dynamical system. This provide our main result for nonlinear control systems. Some applications to linear and polynomial systems are discussed and STLA necessary and sufficient conditions are obtained when the considered set is a hyperplane.
LA - eng
KW - Attainability; controlability; local variations; polynomial control; linear controls.; attainability; controllability; linear controls
UR - http://eudml.org/doc/197313
ER -

References

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