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 Γ was chosen as the target set. Pseudo-vertices — characteristic points on Γ, 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.
The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (Agreement number 075-02-2021-1383).
Citation:
A. A. Uspenskii, P. D. Lebedev, “On the structure of the singular set of solutions in one class of 3D time-optimal control problems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 31:3 (2021), 471–486
\Bibitem{UspLeb21}
\by A.~A.~Uspenskii, P.~D.~Lebedev
\paper On the structure of the singular set of solutions in one class of 3D time-optimal control problems
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2021
\vol 31
\issue 3
\pages 471--486
\mathnet{http://mi.mathnet.ru/vuu782}
\crossref{https://doi.org/10.35634/vm210309}
\elib{https://elibrary.ru/item.asp?id=46616518}
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https://www.mathnet.ru/eng/vuu782
https://www.mathnet.ru/eng/vuu/v31/i3/p471
This publication is cited in the following 2 articles:
P. D. Lebedev, A. A. Uspenskii, “Ob usloviyakh gladkosti i vydelenii kraya rasseivayuschei poverkhnosti v odnom klasse prostranstvennykh zadach bystrodeistviya”, Izv. IMI UdGU, 63 (2024), 37–48
P. D. Lebedev, A. A. Uspenskii, “Analytic-Numerical Approach to Construction of Minimax Solution to the Hamilton–Jacobi Equation in Three-Dimensional Space”, J Math Sci, 262:3 (2022), 291
Citation in format AMSBIB
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