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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.
@article{COCV_2001__6__499_0,
author = {Krastanov, Mikhail and Quincampoix, Marc},
title = {Local small time controllability and attainability of a set for nonlinear control system},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {499--516},
publisher = {EDP-Sciences},
volume = {6},
year = {2001},
mrnumber = {1849413},
zbl = {1082.93003},
language = {en},
url = {http://geodesic.mathdoc.fr/item/COCV_2001__6__499_0/}
}
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 PY - 2001 SP - 499 EP - 516 VL - 6 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/item/COCV_2001__6__499_0/ LA - en ID - COCV_2001__6__499_0 ER -
%0 Journal Article %A Krastanov, Mikhail %A Quincampoix, Marc %T Local small time controllability and attainability of a set for nonlinear control system %J ESAIM: Control, Optimisation and Calculus of Variations %D 2001 %P 499-516 %V 6 %I EDP-Sciences %U http://geodesic.mathdoc.fr/item/COCV_2001__6__499_0/ %G en %F COCV_2001__6__499_0
Krastanov, Mikhail; Quincampoix, Marc. Local small time controllability and attainability of a set for nonlinear control system. ESAIM: Control, Optimisation and Calculus of Variations, Tome 6 (2001), pp. 499-516. http://geodesic.mathdoc.fr/item/COCV_2001__6__499_0/