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Izv. RAN. Ser. Mat., 2001, Volume 65, Issue 3, Pages 201–224 (Mi izv343)  

This article is cited in 6 scientific papers (total in 6 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

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.

DOI: https://doi.org/10.4213/im343

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English version:
Izvestiya: Mathematics, 2001, 65:3, 617–640

Bibliographic databases:

MSC: 34A60, 49J30, 93C25
Received: 11.07.2000

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
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\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
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\crossref{https://doi.org/10.4213/im343}
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\zmath{https://zbmath.org/?q=an:1001.49003}
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\transl
\jour Izv. Math.
\yr 2001
\vol 65
\issue 3
\pages 617--640
\crossref{https://doi.org/10.1070/IM2001v065n03ABEH000343}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33746836653}


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  • https://doi.org/10.4213/im343
  • http://mi.mathnet.ru/eng/izv/v65/i3/p201

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. A. A. Tolstonogov, “On solutions of an evolution control system depending on parameters”, Sb. Math., 194:9 (2003), 1383–1409  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. A. A. Tolstonogov, “Properties of attainable sets of evolution inclusions and control systems of subdifferential type”, Siberian Math. J., 45:4 (2004), 763–784  mathnet  crossref  mathscinet  zmath  isi  elib
    3. A. A. Tolstonogov, “Relaxation in control systems of subdifferential type”, Izv. Math., 70:1 (2006), 121–152  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    4. A. A. Tolstonogov, “Control systems of subdifferential type depending on a parameter”, Izv. Math., 72:5 (2008), 985–1022  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. S.A. Timoshin, A.A. Tolstonogov, “Existence and properties of solutions of a control system with hysteresis effect”, Nonlinear Analysis: Theory, Methods & Applications, 2011  crossref  mathscinet  zmath  isi  scopus
    6. A. A. Tolstonogov, “Properties of Solutions of a Control System with Hysteresis”, J Math Sci, 2014  crossref  mathscinet  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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