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Asymptotics of accessibility sets along anabnormal trajectory

Published online by Cambridge University Press:  15 August 2002

Emmanuel Trélat
Emmanuel Trélat*
Affiliation:
Université de Bourgogne, Laboratoire de Topologie, UMR 5584 du CNRS, BP. 47870, 21078 Dijon Cedex, France; [email protected].
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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.

Keywords

Accessibility setabnormal trajectoryend-point mappingsingle-input affine control systemsub-Riemannian geometry.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 6 , 2001 , pp. 387 - 414
Copyright
© EDP Sciences, SMAI, 2001

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