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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2012, Volume 277, Pages 192–198 (Mi tm3393)  
This article is cited in 3 scientific papers (total in 3 papers)

On the time-optimal problem for three- and four-dimensional control systems

M. S. Nikol'skii

Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
Full-text PDF (139 kB) Citations (3)
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Abstract: The paper is devoted to the time-optimal problem for three- and four-dimensional nonlinear control systems with one-dimensional control. We obtain sufficient conditions for a time-optimal control to be equivalent (in the Lebesgue sense) to a piecewise constant control that is also optimal, has a finite number of discontinuity points, and takes only extreme values. Such optimal controls are called bang-bang solutions and are of considerable interest in control theory and its applications.
Funding agency Grant number
Russian Foundation for Basic Research 09-01-00633
09-01-00378
11-01-12112-ofi-m
This work was supported by the Russian Foundation for Basic Research, project nos. 09-01-00633, 09-01-00378, and 11-01-12112-ofi-m-2011.
Received in December 2011
English version:
Proceedings of the Steklov Institute of Mathematics, 2012, Volume 277, Pages 184–190
DOI: https://doi.org/10.1134/S008154381204013X
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: M. S. Nikol'skii, “On the time-optimal problem for three- and four-dimensional control systems”, Mathematical control theory and differential equations, Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko, Trudy Mat. Inst. Steklova, 277, MAIK Nauka/Interperiodica, Moscow, 2012, 192–198; Proc. Steklov Inst. Math., 277 (2012), 184–190
Citation in format AMSBIB
\Bibitem{Nik12}
\by M.~S.~Nikol'skii
\paper On the time-optimal problem for three- and four-dimensional control systems
\inbook Mathematical control theory and differential equations
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko
\serial Trudy Mat. Inst. Steklova
\yr 2012
\vol 277
\pages 192--198
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3393}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3052272}
\elib{https://elibrary.ru/item.asp?id=17759406}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2012
\vol 277
\pages 184--190
\crossref{https://doi.org/10.1134/S008154381204013X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000309232900013}
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    • This publication is cited in the following 3 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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