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math.OC2021
Cut time in the sub-Riemannian problem on the Cartan group
Andrei Ardentov, Eero Hakavuori
We study the sub-Riemannian structure determined by a left-invariant distribution of rank 2 on a step 3 Carnot group of dimension 5. We prove the conjectured cut times of Y. Sachko…
math.OC2020
Extremals for a series of sub-Finsler problems with 2-dimensional control via convex trigonometry
A. A. Ardentov, L. V. Lokutsievskiy, Yu. L. Sachkov
We consider a series of optimal control problems with 2-dimensional control lying in an arbitrary convex compact set . The considered problems are well studied for the case when…
math.OC2012
Conjugate points in nilpotent sub-Riemannian problem on the Engel group
A. A. Ardentov, Yu. L. Sachkov
The left-invariant sub-Riemannian problem on the Engel group is considered. This problem is very important as nilpotent approximation of nonholonomic systems in four-dimensional sp…