Search results for "sous-riemannien"

showing 3 items of 3 documents

Etude asymptotique et transcendance de la fonctionvaleur en contrôle optimal. Catégorie log-exp en géométrie sous-Riemannienne dans le cas Martinet.

2000

The main subject of this work is the study and the role ofabnormal trajectories in optimal control theory.We first recall some fundamental results in optimal control. Thenwe investigate the optimality of abnormal trajectories forsingle-input affine systems with constraint on the control, firstfor the time-optimal problem, and then for any cost, the finaltime being fixed or not.Using such an affine system,we extend this theory to sub-Riemannian systems of rank 2.These results show that, under general conditions, an abnormaltrajectory is \it{isolated} among all solutions of the systemhaving the same limit conditions, and thus is \it{locallyoptimal}, until a first \it{conjugate point} which ca…

<br />fonction valeur[ MATH ] Mathematics [math]sphère<br />sous-Riemanniennecontrôle optimalgéométrie sous-Riemanniennecatégorie sous-analytiquethéorie spectrale[MATH] Mathematics [math]catégorie log-exp[MATH]Mathematics [math]trajectoire anormale
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Transport optimal sur les structures sous-Riemanniennes admettant des géodésiques minimisantes singulières

2017

This thesis is devoted to the study of the Monge transport problem for the quadratic cost in sub-Riemannian geometry and the essential conditions to obtain existence and uniqueness of solutions. These works consist in extending these results to the case of sub-Riemannian structures admitting singular minimizing geodesics. In a first part, we develop techniques inspired by works by Cavalletti and Huesmann in order to obtain significant results for structures of rank 2 in dimension 4. In a second part, we study analytical tools of the h-semiconcavity of the sub-Riemannian distance and we show how this type of regularity can lead to the well-posedness of the Monge problem in general cases.

Monge problem[MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG]Géométrie sous-RiemannienneGéodésiques minimisantes singulièresSingular minimizing geodesic[MATH.MATH-DG] Mathematics [math]/Differential Geometry [math.DG]Problème de MongeSub-Riemannian geometry
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R. Ghezzi - Volume measures in non equiregular sub-Riemannian manifolds

2017

In this talk we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it to a smooth volume. First we give the Lebesgue decomposition of the Hausdorff volume. Then we focus on the regular part, show that it is not commensurable with a smooth volume and give conditions under which it is a Radon measure. Finally we give a complete characterization of the singular part. This is a joint work with F. Jean (ENSTA).

volumesous-riemanniengrenoblemeasuressub-riemannian days 2017[MATH] Mathematics [math]journées sous-riemanniennes 2017non equiregularmanifoldssub-riemannian
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