On the structure of the singular set of solutions in one class of 3D time-optimal control problems

DOI10.35634/vm210309zbMath1484.35011OpenAlexW3203236799MaRDI QIDQ5037477

Pabel Dmitrievich Lebedev, A. A. Uspenskii

Publication date: 1 March 2022

Published in: Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/vuu782

zbMATH Keywords

extreme pointcurvaturebisectoreikonal equationtime-optimal problemsingular setpseudo-vertexdispersing surfaceFrene's trihedron

Mathematics Subject Classification ID

Singularities of surfaces or higher-dimensional varieties (14J17) Singularities of curves, local rings (14H20) Boundary value problems for nonlinear first-order PDEs (35F30) Wave front sets in context of PDEs (35A18) Hamilton-Jacobi equations (35F21)

Related Items (1)

Analytic-numerical approach to construction of minimax solution to the Hamilton-Jacobi equation in three-dimensional space

Cites Work

• Calculation formulas for nonsmooth singularities of the optimal result function in a time-optimal problem
• On Euler characteristics of manifolds of singularities of wave fronts
• Construction of a minimax solution for an eikonal-type equation
• Analytical and numerical construction of the optimal outcome function for a class of time-optimal problems
• Topology of singularities of a stable real caustic germ of type $E_6$
• Identification of the singularity of the generalized solution of the Dirichlet problem for an eikonal type equation under the conditions of minimal smoothness of a boundary set
• Construction of scattering curves in one class of time-optimal control problems with leaps of a target set boundary curvature
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