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Contemporary Mathematics. Fundamental Directions, 2006, Volume 19, Pages 5–44 (Mi cmfd64)  

This article is cited in 3 scientific papers (total in 3 papers)

Kelley Condition and Structure of Lagrange Manifold in a Neighborhood of a First-Order Singular Extremal

V. F. Borisov
Full-text PDF (511 kB) Citations (3)
References:
Abstract: The paper considers optimal control problems linearly depending on the scalar control parameter in which there exist first-order singular extremals. The author proves a theorem on the structure of a generic Lagrange manifold (field of extremals) in a neighborhood of first-order singular extremals. As a consequence of this theorem, the author proves the optimality of singular extremals and nonsingular extremals in problems with fixed endpoints on small intervals of time. As an illustration, the paper presents constructions of Lagrange manifolds for the general linear-quadratic control problem with completely integrable linear system of differential constraints and for a certain problem of mathematical economics, a two-factor economic growth model with production function of the Cobb–Douglas type.
English version:
Journal of Mathematical Sciences, 2008, Volume 151, Issue 6, Pages 3431–3472
DOI: https://doi.org/10.1007/s10958-008-9046-y
Bibliographic databases:
UDC: 517.977
Language: Russian
Citation: V. F. Borisov, “Kelley Condition and Structure of Lagrange Manifold in a Neighborhood of a First-Order Singular Extremal”, Optimal control, CMFD, 19, PFUR, M., 2006, 5–44; Journal of Mathematical Sciences, 151:6 (2008), 3431–3472
Citation in format AMSBIB
\Bibitem{Bor06}
\by V.~F.~Borisov
\paper Kelley Condition and Structure of Lagrange Manifold in a~Neighborhood of a~First-Order Singular Extremal
\inbook Optimal control
\serial CMFD
\yr 2006
\vol 19
\pages 5--44
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd64}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336472}
\zmath{https://zbmath.org/?q=an:1219.49037}
\elib{https://elibrary.ru/item.asp?id=13583920}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 151
\issue 6
\pages 3431--3472
\crossref{https://doi.org/10.1007/s10958-008-9046-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-49649083747}
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  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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