Geodesic
On the structure of the singular set of solutions in one class of 3D time-optimal control problems
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 3, pp. 471-486

Voir la notice de l'article provenant de la source Math-Net.Ru

A class of time-optimal control problems in terms of speed in three-dimensional space with a spherical velocity vector is considered. A smooth regular curve $\Gamma$ was chosen as the target set. Pseudo-vertices — characteristic points on $\Gamma,$ responsible for the appearance of a singularity in the optimal result function, are selected. The characteristic features of the structure of a singular set belonging to the family of bisectors are revealed. An analytical representation is found for the extreme points of the bisector corresponding to a fixed pseudo-vertex. As an illustration of the effectiveness of the developed methods for solving nonsmooth dynamic problems, an example of the numerical-analytical construction of resolving structures of a control problem in terms of speed is given.
Keywords: time-optimal problem, dispersing surface, bisector, extreme point, curvature, singular set, Frene's trihedron.
Mots-clés : pseudo-vertex 
@article{VUU_2021_31_3_a8,
     author = {A. A. Uspenskii and P. D. Lebedev},
     title = {On the structure of the singular set of solutions in one class of {3D} time-optimal control problems},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {471--486},
     publisher = {mathdoc},
     volume = {31},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2021_31_3_a8/}
}
TY  - JOUR
AU  - A. A. Uspenskii
AU  - P. D. Lebedev
TI  - On the structure of the singular set of solutions in one class of 3D time-optimal control problems
JO  - Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
PY  - 2021
SP  - 471
EP  - 486
VL  - 31
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VUU_2021_31_3_a8/
LA  - ru
ID  - VUU_2021_31_3_a8
ER  - 
%0 Journal Article
%A A. A. Uspenskii
%A P. D. Lebedev
%T On the structure of the singular set of solutions in one class of 3D time-optimal control problems
%J Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki
%D 2021
%P 471-486
%V 31
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VUU_2021_31_3_a8/
%G ru
%F VUU_2021_31_3_a8
A. A. Uspenskii; P. D. Lebedev. On the structure of the singular set of solutions in one class of 3D time-optimal control problems. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, Tome 31 (2021) no. 3, pp. 471-486. http://geodesic.mathdoc.fr/item/VUU_2021_31_3_a8/