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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2010, Volume 271, Pages 40–58 (Mi tm3232)  
This article is cited in 3 scientific papers (total in 3 papers)

Optimal synthesis in an infinite-dimensional space

V. F. Borisov, M. I. Zelikina, L. A. Manitab

a Faculty of Mechanics and Mathematics, Moscow State University, Moscow, Russia
b Moscow State Institute of Electronics and Mathematics (Technical University), Moscow, Russia
Full-text PDF (277 kB) Citations (3)
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Abstract: For a class of optimal control problems and Hamiltonian systems generated by these problems in the space l2, we prove the existence of extremals with a countable number of switchings on a finite time interval. The optimal synthesis that we construct in the space l2 forms a fiber bundle with piecewise smooth two-dimensional fibers consisting of extremals with a countable number of switchings over an infinite-dimensional basis of singular extremals.
Received in November 2009
English version:
Proceedings of the Steklov Institute of Mathematics, 2010, Volume 271, Pages 34–52
DOI: https://doi.org/10.1134/S008154381004005X
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: V. F. Borisov, M. I. Zelikin, L. A. Manita, “Optimal synthesis in an infinite-dimensional space”, Differential equations and topology. II, Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin, Trudy Mat. Inst. Steklova, 271, MAIK Nauka/Interperiodica, Moscow, 2010, 40–58; Proc. Steklov Inst. Math., 271 (2010), 34–52
Citation in format AMSBIB
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\paper Optimal synthesis in an infinite-dimensional space
\inbook Differential equations and topology.~II
\bookinfo Collected papers. In commemoration of the centenary of the birth of Academician Lev Semenovich Pontryagin
\serial Trudy Mat. Inst. Steklova
\yr 2010
\vol 271
\pages 40--58
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
\yr 2010
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\pages 34--52
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Linking options:
  • https://www.mathnet.ru/eng/tm3232
  • https://www.mathnet.ru/eng/tm/v271/p40
    • This publication is cited in the following 3 articles:
    1. Manita L., Ronzhina M., Computer Simulations in Physics and Beyond (Csp2017), Journal of Physics Conference Series, 955, IOP Publishing Ltd, 2018  crossref  isi  scopus
    2. L. A. Manita, M. I. Ronzhina, “Optimal synthesis in the control problem of an $n$-link inverted pendulum with a moving base”, Journal of Mathematical Sciences, 221:1 (2017), 137–153  mathnet  crossref
    3. M. I. Zelikin, “Fractal theory of Saturn's ring”, Proc. Steklov Inst. Math., 291 (2015), 87–101  mathnet  crossref  crossref  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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