RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Zametki, 2018, Volume 103, Issue 2, Pages 163–171 (Mi mz11657)  

On Balder's Existence Theorem for Infinite-Horizon Optimal Control Problems

K. O. Besov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: Balder's well-known existence theorem (1983) for infinite-horizon optimal control problems is extended to the case in which the integral functional is understood as an improper integral. Simultaneously, the condition of strong uniform integrability (over all admissible controls and trajectories) of the positive part $\max\{f_0,0\}$ of the utility function (integrand) $f_0$ is relaxed to the requirement that the integrals of $f_0$ over intervals $[T,T']$ be uniformly bounded above by a function $\omega(T,T')$ such that $\omega(T,T')\to 0$ as $T,T'\to\infty$. This requirement was proposed by A.V. Dmitruk and N.V. Kuz'kina (2005); however, the proof in the present paper does not follow their scheme, but is instead derived in a rather simple way from the auxiliary results of Balder himself. An illustrative example is also given.

Keywords: optimal control, existence theorem, infinite horizon.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.4213/mzm11657

Full text: PDF file (507 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Mathematical Notes, 2018, 103:2, 167–174

Bibliographic databases:

Document Type: Article
UDC: 517.977.57
Received: 30.04.2017

Citation: K. O. Besov, “On Balder's Existence Theorem for Infinite-Horizon Optimal Control Problems”, Mat. Zametki, 103:2 (2018), 163–171; Math. Notes, 103:2 (2018), 167–174

Citation in format AMSBIB
\Bibitem{Bes18}
\by K.~O.~Besov
\paper On Balder's Existence Theorem for Infinite-Horizon Optimal Control Problems
\jour Mat. Zametki
\yr 2018
\vol 103
\issue 2
\pages 163--171
\mathnet{http://mi.mathnet.ru/mz11657}
\crossref{https://doi.org/10.4213/mzm11657}
\elib{http://elibrary.ru/item.asp?id=32428085}
\transl
\jour Math. Notes
\yr 2018
\vol 103
\issue 2
\pages 167--174
\crossref{https://doi.org/10.1134/S0001434618010182}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000427616800018}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85043794662}


Linking options:
  • http://mi.mathnet.ru/eng/mz11657
  • https://doi.org/10.4213/mzm11657
  • http://mi.mathnet.ru/eng/mz/v103/i2/p163

    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
  • Математические заметки Mathematical Notes
    Number of views:
    This page:146
    References:10
    First page:8

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2018