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Sbornik: Mathematics, 2020, Volume 211, Issue 6, Pages 750–785
DOI: https://doi.org/10.1070/SM9234 (Mi sm9234) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Local infimum and a family of maximum principles in optimal control

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

a V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow, Russia
b Faculty of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow, Russia
c Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow, Russia
d Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz, Russia
English version PDF (683 kB) Citations (10)
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DOI: https://doi.org/10.1070/SM9234
Abstract: The notion of a local infimum for the optimal control problem, which generalizes the notion of an optimal trajectory, is introduced. For a local infimum the existence theorem is proved and necessary conditions in the form of a family of ‘maximum principles’ are derived. The meaningfulness of the necessary conditions, which generalize and strengthen Pontryagin's maximum principle, is illustrated by examples.
Bibliography: 9 titles.
Keywords: local infimum, optimal trajectory, maximum principle, sliding regime.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00649-a
This work was supported by the Russian Foundation for Basic Research (grant no. 17-01-00649-a).
Received: 16.02.2019 and 31.01.2020
Russian version:
Matematicheskii Sbornik, 2020, Volume 211, Number 6, Pages 3–39
DOI: https://doi.org/10.4213/sm9234
Bibliographic databases:
Document Type: Article
UDC: 517.977.52
MSC: Primary 35B50; Secondary 49J20, 49J40
Language: English
Original paper language: Russian
Citation: E. R. Avakov, G. G. Magaril-Il'yaev, “Local infimum and a family of maximum principles in optimal control”, Mat. Sb., 211:6 (2020), 3–39; Sb. Math., 211:6 (2020), 750–785
Citation in format AMSBIB
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:55
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