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Fundam. Prikl. Mat., 1998, Volume 4, Issue 3, Pages 905–926 (Mi fpm332)  

This article is cited in 10 scientific papers (total in 11 papers)

Research Papers Dedicated to the Memory of A. N. Tikhonov

On the structure of the solution of a perturbed optimal-time control problem

A. R. Danilina, A. M. Il'inb

a Urals State Pedagogical University
b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: Smooth geometric restriction on control is considered, at which the limit problem has a solution with discotinuous control but the perturbed problem has continuous control. It is proved that in this case the solution is decomposed in an asymptotical series, the gauge functions of which depend on a small parameter in a complicate way.

Full text: PDF file (732 kB)

Bibliographic databases:
UDC: 517.977
Received: 01.05.1997

Citation: A. R. Danilin, A. M. Il'in, “On the structure of the solution of a perturbed optimal-time control problem”, Fundam. Prikl. Mat., 4:3 (1998), 905–926

Citation in format AMSBIB
\Bibitem{DanIli98}
\by A.~R.~Danilin, A.~M.~Il'in
\paper On the~structure of the~solution of a~perturbed optimal-time control problem
\jour Fundam. Prikl. Mat.
\yr 1998
\vol 4
\issue 3
\pages 905--926
\mathnet{http://mi.mathnet.ru/fpm332}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1800042}
\zmath{https://zbmath.org/?q=an:0967.49001}


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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. V. M. Babich, L. A. Kalyakin, M. D. Ramazanov, N. Kh. Rozov, “Arlen Mikhailovich Il'in (on the occasion of the 70th anniversary)”, Proc. Steklov Inst. Math. (Suppl.), 2003no. , suppl. 1, S1–S7  mathnet  mathscinet  zmath  elib
    2. Danilin, AR, “Asymptotic behavior of the solution to the Cauchy problem for a Hamilton-Jacoby equation depending on a small parameter”, Doklady Mathematics, 73:2 (2006), 214  crossref  mathscinet  zmath  isi  elib
    3. M. G. Dmitriev, G. A. Kurina, “Singular perturbations in control problems”, Autom. Remote Control, 67:1 (2006), 1–43  mathnet  crossref  mathscinet  zmath  elib  elib
    4. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a singular perturbation linear problem”, Proc. Steklov Inst. Math. (Suppl.), 271, suppl. 1 (2010), S53–S65  mathnet  crossref  isi  elib
    5. A. R. Danilin, O. O. Kovrizhnykh, “O zavisimosti zadachi bystrodeistviya dlya lineinoi sistemy ot dvukh malykh parametrov”, Vestnik ChelGU, 2011, no. 14, 46–60  mathnet
    6. “Arlen Mikhailovich Ilin (k vosmidesyatiletiyu so dnya rozhdeniya)”, Ufimsk. matem. zhurn., 4:2 (2012), 3–12  mathnet  mathscinet
    7. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotic representation of a solution to a singular perturbation linear time-optimal problem”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 22–35  mathnet  crossref  isi  elib
    8. A. R. Danilin, O. O. Kovrizhnykh, “Asymptotics of the optimal time in a time-optimal problem with two small parameters”, Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 46–53  mathnet  crossref  mathscinet  isi  elib
    9. A. R. Danilin, O. O. Kovrizhnykh, “Asimptotika optimalnogo vremeni v odnoi zadache o bystrodeistvii s malym parametrom”, Tr. IMM UrO RAN, 21, no. 1, 2015, 71–80  mathnet  mathscinet  elib
    10. A. R. Danilin, O. O. Kovrizhnykh, “Asimptotika resheniya odnoi singulyarno vozmuschennoi zadachi o bystrodeistvii”, Tr. IMM UrO RAN, 23, no. 2, 2017, 67–76  mathnet  crossref  elib
    11. A. R. Danilin, O. O. Kovrizhnykh, “Ob odnoi singulyarno vozmuschennoi zadache bystrodeistviya s dvumya malymi parametrami”, Tr. IMM UrO RAN, 24, no. 2, 2018, 76–92  mathnet  crossref  elib
  • Фундаментальная и прикладная математика
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