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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2014, Volume 20, Number 3, Pages 276–290 (Mi timm1100)  
This article is cited in 14 scientific papers (total in 14 papers)

Calculation formulas for nonsmooth singularities of the optimal result function in a time-optimal problem

A. A. Uspenskii

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
Full-text PDF (243 kB) Citations (14)
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Abstract: Analytical formulas are obtained for extremal points of a singular set in a class of time-optimal problems on a plane. It is proved that the formation of singularities depends directly on the geometry of the target set and on the differential properties of its boundary. Three typical cases are studied and conditions for the appearance of nonsmooth singularities are found. Examples are given.
Keywords: time-optimal problem, optimal result function, diffeomorphism, eikonal, symmetry set.
Received: 22.05.2014
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, Volume 291, Issue 1, Pages 239–254
DOI: https://doi.org/10.1134/S0081543815090163
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: A. A. Uspenskii, “Calculation formulas for nonsmooth singularities of the optimal result function in a time-optimal problem”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 276–290; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 239–254
Citation in format AMSBIB
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    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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