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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 1, Pages 49–58 (Mi vuu363)  

This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

On necessary boundary conditions for strongly optimal control in infinite horizon control problems

D. V. Khlopin

Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, Russia

Abstract: In the paper we consider the infinite horizon control problems in the free end case. We obtain the necessary conditions of strong optimality. The method of the proof actually follows the classic paper by Halkin, and the boundary condition for infinity that we construct in our paper is a stronger variety of the Seierstad condition. The complete system of relations of the maximum principle that was obtained in the paper allows us to write the expression for the adjoint variable in the form of improper integral that depends only on the developing trajectory. S. M. Aseev, A. V. Kryazhimskii, and V. M. Veliov obtained the similar condition as a necessary condition for certain classes of control problems. As we note in our paper, the obtained conditions of strong optimality lead us to a redefined system of relations for sufficiently broad class of control problems. An example is considered.

Keywords: control problem, strong optimal control, infinite horizon problem, necessary conditions of optimality, transversality condition for infinity, Pontryagin maximum principle.

Full text: PDF file (198 kB)
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UDC: 517.977.5
MSC: 49K15, 49J45, 37N40
Received: 11.02.2013

Citation: D. V. Khlopin, “On necessary boundary conditions for strongly optimal control in infinite horizon control problems”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 1, 49–58

Citation in format AMSBIB
\Bibitem{Khl13}
\by D.~V.~Khlopin
\paper On necessary boundary conditions for strongly optimal control in infinite horizon control problems
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 1
\pages 49--58
\mathnet{http://mi.mathnet.ru/vuu363}


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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. Dmitrii V. Khlopin, “Neobkhodimye usloviya ravnovesiya na beskonechnom promezhutke”, MTIP, 5:2 (2013), 105–136  mathnet
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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