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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2016, Volume 22, Number 2, Pages 277–291
DOI: https://doi.org/10.21538/0134-4889-2016-22-2-277-291
(Mi timm1313)
 

This article is cited in 4 scientific papers (total in 4 papers)

Theorems on the separability of αα-sets in Euclidean space

V. N. Ushakov, A. A. Uspenskii

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Full-text PDF (297 kB) Citations (4)
References:
Abstract: We study αα-sets in Euclidean space Rn. The notion of α-set is introduced as a generalization of a convex closed set in Rn. This notion appeared in the study of reachable sets and integral funnels of nonlinear control systems in Euclidean spaces. Reachable sets of nonlinear dynamic systems are usually nonconvex, and the degree of their nonconvexity is different in different systems. This circumstance prompted the introduction of a classification of sets in Rn according to the degree of their nonconvexity. Such a classification stems from control theory and is presented here as the notion of α-set in Rn.
Keywords: α-set, convex set in Rn, convex hull in Rn, α-hyperplane, α-separability, Bouligand cone, normal cone.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00486_а
Ural Branch of the Russian Academy of Sciences 15-16-1-13
Received: 10.12.2015
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, Volume 299, Issue 1, Pages 231–245
DOI: https://doi.org/10.1134/S0081543817090255
Bibliographic databases:
Document Type: Article
UDC: 517.972.87
Language: Russian
Citation: V. N. Ushakov, A. A. Uspenskii, “Theorems on the separability of α-sets in Euclidean space”, Trudy Inst. Mat. i Mekh. UrO RAN, 22, no. 2, 2016, 277–291; Proc. Steklov Inst. Math. (Suppl.), 299, suppl. 1 (2017), 231–245
Citation in format AMSBIB
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\paper Theorems on the separability of $\alpha$-sets in Euclidean space
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\pages 277--291
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  • https://www.mathnet.ru/eng/timm/v22/i2/p277
  • This publication is cited in the following 4 articles:
    1. V. N. Ushakov, A. A. Ershov, “O sootnoshenii mezhdu α-mnozhestvami i slabo vypuklymi mnozhestvami”, Tr. IMM UrO RAN, 30, no. 4, 2024, 276–285  mathnet  crossref  elib
    2. O. A. Kuvshinov, “O geometrii ovala Kassini, ego mere nevypuklosti i ε-sloe”, Izv. IMI UdGU, 60 (2022), 34–57  mathnet  crossref  mathscinet
    3. V. N. Ushakov, A. A. Ershov, “On Guaranteed Estimates of the Area of Convex Subsets of Compact Sets on the Plane”, Autom Remote Control, 82:11 (2021), 1976  crossref
    4. Vladimir Ushakov, Aleksandr Ershov, Maksim Pershakov, Communications in Computer and Information Science, 1090, Mathematical Optimization Theory and Operations Research, 2019, 329  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Trudy Instituta Matematiki i Mekhaniki UrO RAN
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