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Эта публикация цитируется в 1 научной статье (всего в 1 статье)
Combined algorithms for constructing a solution to the time-optimal problem in three-dimensional space based on the selection of extreme points of the scattering surface
Pavel D. Lebedevab, Alexander A. Uspenskiia a Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University
Аннотация:
A class of time-optimal control problems in three-dimensional space with a spherical velocity vector is considered. A smooth regular curve $\Gamma$ is chosen as the target set. We distinguish pseudo-vertices that are characteristic points on $\Gamma$ and responsible for the appearance of a singularity in the function of the optimal result. We reveal analytical relationships between pseudo-vertices and extreme points of a singular set belonging to the family of bisectors. The found analytical representation for the extreme points of the bisector is taken as the basis for numerical algorithms for constructing a singular set. The effectiveness of the developed approach for solving non-smooth dynamic problems is illustrated by an example of numerical-analytical construction of resolving structures for the time-optimal control problem.
Ключевые слова:
time-optimal problem, dispersing surface, bisector, pseudo-vertex, extreme point, curvature, singular set, Frenet-Serret frame (TNB frame).
Образец цитирования:
Pavel D. Lebedev, Alexander A. Uspenskii, “Combined algorithms for constructing a solution to the time-optimal problem in three-dimensional space based on the selection of extreme points of the scattering surface”, Ural Math. J., 8:2 (2022), 115–126
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/umj176 https://www.mathnet.ru/rus/umj/v8/i2/p115
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Страница аннотации: | 96 | PDF полного текста: | 21 | Список литературы: | 18 |
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