RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Trudy MIAN:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Tr. Mat. Inst. Steklova, 2019, Volume 304, Pages 252–256 (Mi tm3970)  

Singular Sets of Extremal Controls in Optimal Control Problems

M. S. Nikol'skii

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: Some optimal control problems are considered with an integral functional (to be minimized), fixed motion time of the controlled object, and free right endpoint. In these problems, the set of degeneracy points of the Pontryagin maximum principle (singular set) for the extremal control is studied. For a wide class of linear control systems, sufficient conditions are obtained under which the singular set is either empty or consists of a finite set of points. In addition, an example of a control system is constructed in which the singular set has a very general form.

DOI: https://doi.org/10.4213/tm3970

Full text: PDF file (144 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Proceedings of the Steklov Institute of Mathematics, 2019, 304, 236–240

Bibliographic databases:

UDC: 517.977
Received: September 28, 2018
Revised: October 24, 2018
Accepted: December 24, 2018

Citation: M. S. Nikol'skii, “Singular Sets of Extremal Controls in Optimal Control Problems”, Optimal control and differential equations, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin, Tr. Mat. Inst. Steklova, 304, Steklov Math. Inst. RAS, Moscow, 2019, 252–256; Proc. Steklov Inst. Math., 304 (2019), 236–240

Citation in format AMSBIB
\Bibitem{Nik19}
\by M.~S.~Nikol'skii
\paper Singular Sets of Extremal Controls in Optimal Control Problems
\inbook Optimal control and differential equations
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Lev Semenovich Pontryagin
\serial Tr. Mat. Inst. Steklova
\yr 2019
\vol 304
\pages 252--256
\publ Steklov Math. Inst. RAS
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3970}
\crossref{https://doi.org/10.4213/tm3970}
\elib{http://elibrary.ru/item.asp?id=37461011}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2019
\vol 304
\pages 236--240
\crossref{https://doi.org/10.1134/S0081543819010164}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000470695400016}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85066784752}


Linking options:
  • http://mi.mathnet.ru/eng/tm3970
  • https://doi.org/10.4213/tm3970
  • http://mi.mathnet.ru/eng/tm/v304/p252

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
    Number of views:
    This page:72
    References:10
    First page:8

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019