# Asymptotics of accessibility sets along an abnormal trajectory

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

- Volume: 6, page 387-414
- ISSN: 1292-8119

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topTrélat, Emmanuel. "Asymptotics of accessibility sets along an abnormal trajectory." ESAIM: Control, Optimisation and Calculus of Variations 6 (2010): 387-414. <http://eudml.org/doc/197282>.

@article{Trélat2010,

abstract = {
We describe precisely, under generic conditions, the contact of
the accessibility set at time T with an abnormal direction,
first for a single-input affine control system with constraint on
the control, and then as an
application for a sub-Riemannian system of rank 2. As a
consequence we obtain in sub-Riemannian geometry a new
splitting-up of the sphere near an abnormal minimizer γ
into two sectors, bordered by the first Pontryagin's cone along
γ, called the L∞-sector and the
L2-sector.
Moreover we find again necessary and sufficient conditions of
optimality of an abnormal trajectory for such systems,
for any optimization problem.
},

author = {Trélat, Emmanuel},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Accessibility set;
abnormal trajectory; end-point mapping; single-input
affine control system; sub-Riemannian geometry.; accessibilty set; abnormal trajectory; single-input affine control system; sub-Riemannian geometry; bounded control; normal form; spectral analytic tools},

language = {eng},

month = {3},

pages = {387-414},

publisher = {EDP Sciences},

title = {Asymptotics of accessibility sets along an abnormal trajectory},

url = {http://eudml.org/doc/197282},

volume = {6},

year = {2010},

}

TY - JOUR

AU - Trélat, Emmanuel

TI - Asymptotics of accessibility sets along an abnormal trajectory

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2010/3//

PB - EDP Sciences

VL - 6

SP - 387

EP - 414

AB -
We describe precisely, under generic conditions, the contact of
the accessibility set at time T with an abnormal direction,
first for a single-input affine control system with constraint on
the control, and then as an
application for a sub-Riemannian system of rank 2. As a
consequence we obtain in sub-Riemannian geometry a new
splitting-up of the sphere near an abnormal minimizer γ
into two sectors, bordered by the first Pontryagin's cone along
γ, called the L∞-sector and the
L2-sector.
Moreover we find again necessary and sufficient conditions of
optimality of an abnormal trajectory for such systems,
for any optimization problem.

LA - eng

KW - Accessibility set;
abnormal trajectory; end-point mapping; single-input
affine control system; sub-Riemannian geometry.; accessibilty set; abnormal trajectory; single-input affine control system; sub-Riemannian geometry; bounded control; normal form; spectral analytic tools

UR - http://eudml.org/doc/197282

ER -

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