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Mathematics of the USSR-Sbornik, 1992, Volume 72, Issue 1, Pages 29–45
DOI: https://doi.org/10.1070/SM1992v072n01ABEH002137 (Mi sm1273) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Symplectic geometry and conditions necessary conditions for optimality

A. A. Agrachev, R. V. Gamkrelidze
English version PDF (941 kB) Citations (9)
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DOI: https://doi.org/10.1070/SM1992v072n01ABEH002137
Abstract: With the help of a symplectic technique the concept of a field of extremals in the classical calculus of variations is generalized to optimal control problems. This enables us to get new optimality conditions that are equally suitable for regular, bang-bang, and singular extremals. Special attention is given to systems of the form $\dot x=f_0(x)+uf_1(x)$ with a scalar control. New pointwise conditions for optimality and sufficient conditions for local controllability are obtained as a consequence of the general theory.
Received: 05.03.1990
Russian version:
Matematicheskii Sbornik, 1991, Volume 182, Number 1, Pages 36–54
Bibliographic databases:
Document Type: Article
UDC: 517.97
MSC: 49K15, 58F05
Language: English
Original paper language: Russian
Citation: A. A. Agrachev, R. V. Gamkrelidze, “Symplectic geometry and conditions necessary conditions for optimality”, Mat. Sb., 182:1 (1991), 36–54; Math. USSR-Sb., 72:1 (1992), 29–45
Citation in format AMSBIB
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\yr 1991
\vol 182
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\pages 36--54
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\transl
\jour Math. USSR-Sb.
\yr 1992
\vol 72
\issue 1
\pages 29--45
\crossref{https://doi.org/10.1070/SM1992v072n01ABEH002137}
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  • https://doi.org/10.1070/SM1992v072n01ABEH002137
  • https://www.mathnet.ru/eng/sm/v182/i1/p36
    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Математический сборник - 1991 Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:648
    Russian version PDF:164
    English version PDF:10
    References:63
    First page:4
     
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