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Avtomatika i Telemekhanika, 2005, Issue 6, Pages 59–73 (Mi at1385)  
This article is cited in 18 scientific papers (total in 18 papers)

Deterministic Systems

Regularization of cheap periodic control problems

E. N. Smetannikovaa, V. A. Sobolevb

a S. P. Korolyov Samara State Aerospace University
b Samara State University
Full-text PDF (234 kB) Citations (18)
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Abstract: A regularization method for cheap periodic control problems is designed. The periodic problem for singularly perturbed Riccati matrix differential equations is reduced to an extended system of singularly perturbed initial problems. This system admits the application of a geometric approach based on the use of integral manifolds and, consequently, dimensional reduction. The solution is asymptotically expanded in fractional powers of a small parameter. An example on control of periodic oscillations of a mechanical system is given.
Presented by the member of Editorial Board: B. T. Polyak

Received: 26.06.2003
English version:
Automation and Remote Control, 2005, Volume 66, Issue 6, Pages 903–916
DOI: https://doi.org/10.1007/s10513-005-0134-x
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: E. N. Smetannikova, V. A. Sobolev, “Regularization of cheap periodic control problems”, Avtomat. i Telemekh., 2005, no. 6, 59–73; Autom. Remote Control, 66:6 (2005), 903–916
Citation in format AMSBIB
\Bibitem{SmeSob05}
\by E.~N.~Smetannikova, V.~A.~Sobolev
\paper Regularization of cheap periodic control problems
\jour Avtomat. i Telemekh.
\yr 2005
\issue 6
\pages 59--73
\mathnet{http://mi.mathnet.ru/at1385}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2157574}
\zmath{https://zbmath.org/?q=an:1108.49029}
\transl
\jour Autom. Remote Control
\yr 2005
\vol 66
\issue 6
\pages 903--916
\crossref{https://doi.org/10.1007/s10513-005-0134-x}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-21644435274}
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  • https://www.mathnet.ru/eng/at/y2005/i6/p59
    • This publication is cited in the following 18 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:37
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