Time-Optimal Trajectories of Generic Control-Affine Systems Have at Worst Iterated Fuller Singularities - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2017

Time-Optimal Trajectories of Generic Control-Affine Systems Have at Worst Iterated Fuller Singularities

Résumé

We consider in this paper the regularity problem for time-optimal trajectories of a single-input control-affine system on a n-dimensional manifold. We prove that, under generic conditions on the drift and the controlled vector field, any control u associated with an optimal trajectory is smooth out of a countable set of times. More precisely, there exists an integer K, only depending on the dimension n, such that the non-smoothness set of u is made of isolated points, accumulations of isolated points, and so on up to K-th order iterated accumulations.
Fichier principal
Vignette du fichier
notes.pdf (412.45 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-01528205 , version 1 (28-05-2017)
hal-01528205 , version 2 (11-07-2017)
hal-01528205 , version 3 (18-05-2018)

Identifiants

Citer

Francesco Boarotto, Mario Sigalotti. Time-Optimal Trajectories of Generic Control-Affine Systems Have at Worst Iterated Fuller Singularities. 2017. ⟨hal-01528205v2⟩
427 Consultations
534 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More