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Izv. Akad. Nauk SSSR Ser. Mat., 1984, Volume 48, Issue 4, Pages 854–864 (Mi izv1494)  

This article is cited in 3 scientific papers (total in 3 papers)

Riemann integrability of an optimal control in linear time-optimal problems

D. B. Silin


Abstract: A linear time-optimal problem is considered. It is shown that the set of initial states for which a three-dimensional time-optimal problem at the origin, with constant coefficients, has no solution in the class of Riemann integrable controls can fill up a given ball to an arbitrary extent. For a large class of multidimensional systems it is shown that this set does not contain isolated points. Sufficient conditions for the existence of a Riemann integrable control are studied for problems with variable coefficients.
Bibliography: 8 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1985, 25:1, 183–192

Bibliographic databases:

UDC: 517.977.55
MSC: Primary 49A10; Secondary 52A99
Received: 24.12.1981

Citation: D. B. Silin, “Riemann integrability of an optimal control in linear time-optimal problems”, Izv. Akad. Nauk SSSR Ser. Mat., 48:4 (1984), 854–864; Math. USSR-Izv., 25:1 (1985), 183–192

Citation in format AMSBIB
\Bibitem{Sil84}
\by D.~B.~Silin
\paper Riemann integrability of an optimal control in linear time-optimal problems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1984
\vol 48
\issue 4
\pages 854--864
\mathnet{http://mi.mathnet.ru/izv1494}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=755960}
\zmath{https://zbmath.org/?q=an:0588.49002}
\transl
\jour Math. USSR-Izv.
\yr 1985
\vol 25
\issue 1
\pages 183--192
\crossref{https://doi.org/10.1070/IM1985v025n01ABEH001275}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. D. B. Silin, “Time-optimal linear problems with controls discontinuous on a set of positive measure”, Math. USSR-Sb., 57:1 (1987), 277–291  mathnet  crossref  mathscinet  zmath
    2. M. I. Zelikin, “Neregulyarnost optimalnogo upravleniya v regulyarnykh ekstremalnykh zadachakh”, Fundament. i prikl. matem., 1:2 (1995), 399–408  mathnet  mathscinet  zmath
    3. A. A. Azamov, “On Pontryagin's First Direct Method in Pursuit Problems”, Math. Notes, 90:2 (2011), 157–161  mathnet  crossref  crossref  mathscinet  isi
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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