Elements of analytical solutions constructor in a class of time-optimal control problems with the break of curvature of a target set

DOI10.20310/2686-9667-2020-25-132-370-386OpenAlexW3125273400MaRDI QIDQ5012436

A. A. Uspenskii, Pavel Dmitrievich Lebedev

Publication date: 24 November 2021

Published in: Russian Universities Reports. Mathematics (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/vtamu205

zbMATH Keywords

diffeomorphismHamilton-Jacobi equationvelocitytransversalitybisectorminimax solutionoptimal result functionsingular set

Mathematics Subject Classification ID

Numerical analysis (65-XX) Calculus of variations and optimal control; optimization (49-XX)

Cites Work

• Calculation formulas for nonsmooth singularities of the optimal result function in a time-optimal problem
• On the set of limit values of local diffeomorphisms in wavefront evolution
• 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
• Connectedness and solarity in problems of best and near-best approximation
• Viscosity Solutions of Hamilton-Jacobi Equations
• Directional differentiability of the distance function
• 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
• Alpha-sets in finite dimensional Euclidean spaces and their properties
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