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Mat. Sb., 2017, Volume 208, Number 5, Pages 3–37 (Mi msb8721)  

This article is cited in 1 scientific paper (total in 1 paper)

Relaxation and controllability in optimal control problems

E. R. Avakovab, G. G. Magaril-Il'yaevbcd

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow
b Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
d Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz

Abstract: The paper is concerned with the relationships between necessary minimum conditions in an optimal control problem, minimum conditions in the corresponding relaxed problem and sufficient conditions for local controllability of the system. The results obtained are applied to a fairly general optimal control problem.
Bibliography: 7 titles.

Keywords: optimal control, Pontryagin maximum principle, controllability, regularity, relaxation, mix of controls.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00456-а
14-01-00744-а
This research was carried out with the financial support of the Russian Foundation for Basic Research (grant nos. 14-01-00456-a and 14-01-00744-a).


DOI: https://doi.org/10.4213/sm8721

Full text: PDF file (846 kB)
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References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2017, 208:5, 585–619

Bibliographic databases:

Document Type: Article
UDC: 517.977.52
MSC: 49J27, 49J15
Received: 21.04.2016 and 03.02.2017

Citation: E. R. Avakov, G. G. Magaril-Il'yaev, “Relaxation and controllability in optimal control problems”, Mat. Sb., 208:5 (2017), 3–37; Sb. Math., 208:5 (2017), 585–619

Citation in format AMSBIB
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\paper Relaxation and controllability in optimal control problems
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\pages 3--37
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\pages 585--619
\crossref{https://doi.org/10.1070/SM8721}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85025076792}


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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. E. R. Avakov, G. G. Magaril-Il'yaev, “Controllability and second-order necessary conditions for optimality”, Sb. Math., 210:1 (2019), 1–23  mathnet  crossref  crossref  adsnasa  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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