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Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, Issue 3, Pages 79–87 (Mi vuu391)  

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

MATHEMATICS

Optimal control under $L_p$-compact constraints on the disturbance

D. A. Serkovab

a Institute of Mathematics and Mechanics named after N. N. Krasovskii, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi, 16, Yekaterinburg, 620219, Russia
b Ural Federal University named after the first President of Russia B. N. Yeltsin, ul. Mira, 19, Yekaterinburg, 620002, 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 disturbances as functions of time are subject to functional constraints belonging to a given family of constraints. The actions of control are formed by the strategies with full memory.
It is demonstrated, that optimal guaranteed result in this problem is equal to the value of the lower game. For the effectiveness of implemented control algorithm additional conditions on the system and appropriate ways of constructing an optimal strategy are specified.

Keywords: optimal guarantee, strategy with full memory, lower game.

Full text: PDF file (241 kB)
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Document Type: Article
UDC: 517.952+517.977
MSC: 93C15, 49N30, 49N35
Received: 30.08.2013

Citation: D. A. Serkov, “Optimal control under $L_p$-compact constraints on the disturbance”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 2013, no. 3, 79–87

Citation in format AMSBIB
\Bibitem{Ser13}
\by D.~A.~Serkov
\paper Optimal control under $L_p$-compact constraints on the disturbance
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2013
\issue 3
\pages 79--87
\mathnet{http://mi.mathnet.ru/vuu391}


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    This publication is cited in the following articles:
    1. D. A. Serkov, “On the unimprovability of full-memory strategies in problems of guaranteed result optimization”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 157–172  mathnet  crossref  mathscinet  isi  elib
  • Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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