Geodesic
On the Small-time Local Controllability
Journal of convex analysis, Tome 19 (2012) no. 4, pp. 1073-109.

Voir la notice de l'article provenant de la source Heldermann Verlag

The convexity of a set of "control variations" is one of the crucial properties needed to prove sufficient controllability conditions or necessary optimality conditions. Heuristically, if one can construct control variations in all possible directions, then the considered control system is small-time locally controllable. As it was shown by R.-M. Bianchini and M. Kawski ["Needle variations that cannot be summed", SIAM J. Control Optimization 42 (2003) 218--238] the cones generated by needle variations may fail to be convex. The purpose of the present paper is to define a convex set of high-order control variations and to prove a sufficient controllability condition. The proof is based on a general Lie series formalism. One illustrative example is also presented.
Classification : 93B05, 93C10
Mots-clés : High-order control variations, smooth control systems, small-time local controllability 
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     author = {M. I. Krastanov},
     title = {On the {Small-time} {Local} {Controllability}},
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     number = {4},
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M. I. Krastanov. On the Small-time Local Controllability. Journal of convex analysis, Tome 19 (2012) no. 4, pp. 1073-109. http://geodesic.mathdoc.fr/item/JCA_2012_19_4_JCA_2012_19_4_a10/