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Izvestiya: Mathematics, 2001, Volume 65, Issue 3, Pages 617–640
DOI: https://doi.org/10.1070/IM2001v065n03ABEH000343 (Mi im343) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Properties of the set of admissible “state-control” pairs for first-order evolution control systems

A. A. Tolstonogov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences
English version PDF (281 kB) Citations (9)
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DOI: https://doi.org/10.1070/IM2001v065n03ABEH000343
Abstract: We consider a control system described by a non-linear first-order evolution equation on an evolution triple of Banach spaces (a “Gelfand triple”) with a mixed multivalued control constraint whose values are non-convex closed sets in the control space. Besides the original system, we consider systems with the following control constraints: the constraint whose values are the closed convex hulls of the values of the original constraint, and the constraint whose values are the extreme points of the convexified constraint that belong to the original one. We study topological properties of the sets of admissible “state-control” pairs for the same system with various constraints and consider the relations between them. An example of a non-linear parabolic control system is worked out in detail.
Received: 11.07.2000
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2001, Volume 65, Issue 3, Pages 201–224
DOI: https://doi.org/10.4213/im343
Bibliographic databases:
MSC: 34A60, 49J30, 93C25
Language: English
Original paper language: Russian
Citation: A. A. Tolstonogov, “Properties of the set of admissible “state-control” pairs for first-order evolution control systems”, Izv. RAN. Ser. Mat., 65:3 (2001), 201–224; Izv. Math., 65:3 (2001), 617–640
Citation in format AMSBIB
\Bibitem{Tol01}
\by A.~A.~Tolstonogov
\paper Properties of the set of admissible ``state-control'' pairs for first-order evolution control systems
\jour Izv. RAN. Ser. Mat.
\yr 2001
\vol 65
\issue 3
\pages 201--224
\mathnet{http://mi.mathnet.ru/im343}
\crossref{https://doi.org/10.4213/im343}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1853373}
\zmath{https://zbmath.org/?q=an:1001.49003}
\elib{https://elibrary.ru/item.asp?id=14151135}
\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 3
\pages 617--640
\crossref{https://doi.org/10.1070/IM2001v065n03ABEH000343}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746836653}
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  • https://doi.org/10.1070/IM2001v065n03ABEH000343
  • https://www.mathnet.ru/eng/im/v65/i3/p201
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:551
    Russian version PDF:216
    English version PDF:26
    References:76
    First page:1
     
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