Cut time in sub-riemannian problem on engel group

Ardentov, A.A.; Sachkov, Yu.L.

doi:10.1051/cocv/2015027

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.

Résumé

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 : 2014-08-28

MR Zbl

DOI : 10.1051/cocv/2015027

Classification : 22E25, 58E25
Mots-clés : Sub-Riemannian geometry, optimal control, Engel group, Lie algebra, Maxwell time, cut time, exponential mapping, Euler’s elastica

Affiliations des auteurs :

Ardentov, A.A. ¹ ; Sachkov, Yu.L. ¹

¹ Program Systems Institute of RAS, Pereslavl-Zalessky 152020, Russia

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     title = {Cut time in sub-riemannian problem on engel group},
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     publisher = {EDP-Sciences},
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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. http://www.numdam.org/articles/10.1051/cocv/2015027/

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