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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, Issue 2, Pages 74–83 (Mi vuu323)  

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

MATHEMATICS

Optimal guarantee under the disturbances of Caratheodory type

D. A. Serkov

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

Abstract: The problem of the optimization of a guaranteed result for the control system, described by an ordinary differential equation, and a continuous payoff functional, is considered. At every moment the values of the control and of the disturbance are in the given compact sets. The actions of the disturbance are assumed to be generated by an unknown function of the Caratheodory type, i.e. by the function continuous with respect to the spatial variable for every value of time variable and measurable with respect to the time variable for every value of spatial one. The actions of control are formed by the strategies with full memory.
It is demonstrated, that for a class of control systems the optimal guaranteed result in this problem is equal to the value of the lower game, i.e. to the value of the optimal guaranteed result in the class of quasi-strategies. The optimal strategy with full memory, that allows numerical implementation, is provided. An illustrative nonlinear example is given.

Keywords: optimal guarantee, disturbance of Caratheodory type, strategy with full memory, lower game.

Full text: PDF file (207 kB)
References: PDF file   HTML file
UDC: 517.952+517.977
MSC: 93C15, 49N30, 49N35
Received: 12.03.2012

Citation: D. A. Serkov, “Optimal guarantee under the disturbances of Caratheodory type”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2012, no. 2, 74–83

Citation in format AMSBIB
\Bibitem{Ser12}
\by D.~A.~Serkov
\paper Optimal guarantee under the disturbances of Caratheodory type
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2012
\issue 2
\pages 74--83
\mathnet{http://mi.mathnet.ru/vuu323}


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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. D. A. Serkov, “Minimizatsiya riska pri funktsionalnykh ogranicheniyakh na dinamicheskuyu pomekhu”, Izv. IMI UdGU, 2014, no. 2(44), 3–95  mathnet
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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