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

 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
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} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3951623} \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}