RUS  ENG
Полная версия
ЖУРНАЛЫ // Ural Mathematical Journal // Архив

Ural Math. J., 2022, том 8, выпуск 2, страницы 115–126 (Mi umj176)

Эта публикация цитируется 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).

Язык публикации: английский

DOI: 10.15826/umj.2022.2.009



Реферативные базы данных:


© МИАН, 2024