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.

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.

Classification : 93B05, 93B03, 93C05, 93C10, 49J53
Mots clés : attainability, controlability, local variations, polynomial control, linear controls 
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     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},
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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://archive.numdam.org/item/COCV_2001__6__499_0/

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