Construction of scattering curves in one class of time-optimal control problems with leaps of a target set boundary curvature

DOI10.35634/2226-3594-2020-55-07zbMath1458.35130OpenAlexW3040098216MaRDI QIDQ5151945

A. A. Uspenskii, Pavel Dmitrievich Lebedev

Publication date: 17 February 2021

Published in: Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/iimi393

zbMATH Keywords

curvaturetime-optimal problemsingular settangentdispersing linepseudo vertex

Mathematics Subject Classification ID

Symmetries, equivariance on manifolds (58K70) Wave front sets in context of PDEs (35A18) Viscosity solutions to PDEs (35D40) Hamilton-Jacobi equations (35F21) Initial-boundary value problems for linear first-order PDEs (35F16)

Related Items (3)

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 ⋮ On the structure of the singular set of solutions in one class of 3D time-optimal control problems ⋮ Analytic-numerical approach to construction of minimax solution to the Hamilton-Jacobi equation in three-dimensional space

Cites Work

• Construction of a minimax solution for an eikonal-type equation
• Construction of the optimal outcome function for a time-optimal problem on the basis of a symmetry set
• Construction of the solvability set in differential games with simple motion and nonconvex terminal set
• Centre symmetry sets of families of plane curves
• On the topology of wave fronts in spaces of low dimension
• 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 a solution to a velocity problem in the case of violation of the smoothness of the curvature of the target set boundary
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