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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2021, Volume 315, Pages 261–270
DOI: https://doi.org/10.4213/tm4219 (Mi tm4219) 		 
This article is cited in 5 scientific papers (total in 5 papers)

On Estimating the Degree of Nonconvexity of Reachable Sets of Control Systems

V. N. Ushakov, A. A. Ershov, A. R. Matviychuk

N.N. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
Full-text PDF (225 kB) Citations (5)
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DOI: https://doi.org/10.4213/tm4219
Abstract: We study the properties of reachable sets of control systems that are linear in control. For the reachable sets of a certain class of such systems, we estimate the growth of their degree of nonconvexity $\alpha $ over time. As an auxiliary result, we establish a relationship between $\alpha $-sets and weakly convex sets in the sense of Vial.
Keywords: Generalized convex set, $\alpha $-set, weakly convex set, reachable set, control system.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2021-1383
The work was performed as part of research conducted in the Ural Mathematical Center with the financial support of the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-02-2021-1383).
Received: February 20, 2021
Revised: March 10, 2021
Accepted: July 13, 2021
English version:
Proceedings of the Steklov Institute of Mathematics, 2021, Volume 315, Pages 247–256
DOI: https://doi.org/10.1134/S0081543821050199
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: V. N. Ushakov, A. A. Ershov, A. R. Matviychuk, “On Estimating the Degree of Nonconvexity of Reachable Sets of Control Systems”, Optimal Control and Differential Games, Collected papers, Trudy Mat. Inst. Steklova, 315, Steklov Math. Inst., Moscow, 2021, 261–270; Proc. Steklov Inst. Math., 315 (2021), 247–256
Citation in format AMSBIB
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\by V.~N.~Ushakov, A.~A.~Ershov, A.~R.~Matviychuk
\paper On Estimating the Degree of Nonconvexity of Reachable Sets of Control Systems
\inbook Optimal Control and Differential Games
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2021
\vol 315
\pages 261--270
\publ Steklov Math. Inst.
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm4219}
\crossref{https://doi.org/10.4213/tm4219}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2021
\vol 315
\pages 247--256
\crossref{https://doi.org/10.1134/S0081543821050199}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000745120000019}
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  • https://doi.org/10.4213/tm4219
  • https://www.mathnet.ru/eng/tm/v315/p261
    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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