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Russia Yekaterinburg
Year
2021
Volume
31
Issue
3
Pages
471-486
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Section Mathematics
Title On the structure of the singular set of solutions in one class of 3D time-optimal control problems
Author(-s) Uspenskii A.A.a, Lebedev P.D.a
Affiliations Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciencesa
Abstract 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, pseudo-vertex, extreme point, curvature, singular set, Frene's trihedron
UDC 517.977
MSC 35A18, 14H20, 14J17
DOI 10.35634/vm210309
Received 19 July 2021
Language Russian
Citation Uspenskii A.A., Lebedev P.D. On the structure of the singular set of solutions in one class of 3D time-optimal control problems, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2021, vol. 31, issue 3, pp. 471-486.
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