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Mat. Sb., 2020, Volume 211, Number 6, Pages 3–39 (Mi msb9234)  

This article is cited in 5 scientific papers (total in 5 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

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).

* Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/sm9234

Full text: PDF file (726 kB)
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English version:
Sbornik: Mathematics, 2020, 211:6, 750–785

Bibliographic databases:

UDC: 517.977.52
MSC: Primary 35B50; Secondary 49J20, 49J40
Received: 16.02.2019 and 31.01.2020

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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\paper Local infimum and a~family of maximum principles in optimal control
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. R. Avakov, G. G. Magaril-Il'yaev, “Gamkrelidze Convexification and Bogolyubov's Theorem”, Math. Notes, 107:4 (2020), 539–551  mathnet  crossref  crossref  isi  elib
    2. E. Avakov, G. Magaril-Il'Yaev, “Local controllability and a family of maximum principles for a free time optimal control problem”, SIAM J. Control Optim., 58:6 (2020), 3212–3236  crossref  mathscinet  zmath  isi
    3. E. R. Avakov, G. G. Magaril-Il'yaev, “Implicit Function. Controllability and Perturbation of Optimal Control Problems”, Math. Notes, 109:4 (2021), 503–516  mathnet  crossref  crossref  isi
    4. E. R. Avakov, G. G. Magaril-Il'yaev, “Local controllability and optimality”, Sb. Math., 212:7 (2021), 887–920  mathnet  crossref  crossref  isi
    5. E. R. Avakov, G. G. Magaril-Il'yaev, “A Note on the Classical Implicit Function Theorem”, Math. Notes, 110:6 (2021), 942–946  mathnet  crossref  crossref
  • Математический сборник Sbornik: Mathematics (from 1967)
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