Geodesic
Cut time in sub-riemannian problem on engel group
Ardentov, A.A.1 ; Sachkov, Yu.L.1
1 Program Systems Institute of RAS, Pereslavl-Zalessky 152020, Russia
ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 958-988 Cet article a éte moissonné depuis la source Numdam

Voir la notice de l'article

The left-invariant sub-Riemannian problem on the Engel group is considered. The problem gives the nilpotent approximation to generic rank two sub-Riemannian problems on four-dimensional manifolds. The global optimality of extremal trajectories is studied via geometric control theory. The global diffeomorphic structure of the exponential mapping is described. As a consequence, the cut time is proved to be equal to the first Maxwell time corresponding to discrete symmetries of the exponential mapping.

Reçu le :
DOI : 10.1051/cocv/2015027
Classification : 22E25, 58E25
Keywords: Sub-Riemannian geometry, optimal control, Engel group, Lie algebra, Maxwell time, cut time, exponential mapping, Euler’s elastica

Ardentov, A.A. 1 ; Sachkov, Yu.L. 1

1 Program Systems Institute of RAS, Pereslavl-Zalessky 152020, Russia 
@article{COCV_2015__21_4_958_0,
     author = {Ardentov, A.A. and Sachkov, Yu.L.},
     title = {Cut time in sub-riemannian problem on engel group},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {958--988},
     year = {2015},
     publisher = {EDP-Sciences},
     volume = {21},
     number = {4},
     doi = {10.1051/cocv/2015027},
     mrnumber = {3395751},
     zbl = {1330.53044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015027/}
}
TY  - JOUR
AU  - Ardentov, A.A.
AU  - Sachkov, Yu.L.
TI  - Cut time in sub-riemannian problem on engel group
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2015
SP  - 958
EP  - 988
VL  - 21
IS  - 4
PB  - EDP-Sciences
UR  - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015027/
DO  - 10.1051/cocv/2015027
LA  - en
ID  - COCV_2015__21_4_958_0
ER  - 
%0 Journal Article
%A Ardentov, A.A.
%A Sachkov, Yu.L.
%T Cut time in sub-riemannian problem on engel group
%J ESAIM: Control, Optimisation and Calculus of Variations
%D 2015
%P 958-988
%V 21
%N 4
%I EDP-Sciences
%U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2015027/
%R 10.1051/cocv/2015027
%G en
%F COCV_2015__21_4_958_0
Ardentov, A.A.; Sachkov, Yu.L. Cut time in sub-riemannian problem on engel group. ESAIM: Control, Optimisation and Calculus of Variations, Tome 21 (2015) no. 4, pp. 958-988. doi: 10.1051/cocv/2015027

Cité par Sources :