Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 495, Pages 100–106
DOI: https://doi.org/10.31857/S268695432006017X (Mi danma142) 		 
This article is cited in 2 scientific papers (total in 2 papers)

CONTROL PROCESSES

Estimation of the growth of the degree of nonconvexity of reachable sets in terms of $\alpha$-sets

V. N. Ushakov, A. A. Ershov

N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russian Federation
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DOI: https://doi.org/10.31857/S268695432006017X
Abstract: We study the properties of $\alpha$-sets, which are a generalization of convex sets. The relationship between $\alpha$-sets and weakly convex sets is established in the sense of Vial and Efimov–Stechkin. An estimate of the growth over time of the nonconvexity measure $\alpha$ of reachable sets is obtained for one class of control systems in a two-dimensional state space.
Keywords: generalized convex set, $\alpha$-set, weakly convex set, reachable set, control system.
Funding agency Grant number
Russian Foundation for Basic Research 18–01–00221 А
This work was supported by the Russian Foundation for Basic Research, project no. 18-01-00221 A.
Received: 04.09.2020
Revised: 23.09.2020
Accepted: 24.09.2020
English version:
Doklady Mathematics, 2020, Volume 102, Issue 3, Pages 532–537
DOI: https://doi.org/10.1134/S1064562420060198
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: V. N. Ushakov, A. A. Ershov, “Estimation of the growth of the degree of nonconvexity of reachable sets in terms of $\alpha$-sets”, Dokl. RAN. Math. Inf. Proc. Upr., 495 (2020), 100–106; Dokl. Math., 102:3 (2020), 532–537
Citation in format AMSBIB
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\by V.~N.~Ushakov, A.~A.~Ershov
\paper Estimation of the growth of the degree of nonconvexity of reachable sets in terms of $\alpha$-sets
\jour Dokl. RAN. Math. Inf. Proc. Upr.
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\pages 100--106
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\zmath{https://zbmath.org/?q=an:1481.52001}
\elib{https://elibrary.ru/item.asp?id=44367212}
\transl
\jour Dokl. Math.
\yr 2020
\vol 102
\issue 3
\pages 532--537
\crossref{https://doi.org/10.1134/S1064562420060198}
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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