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Tr. Mat. Inst. Steklova, 2012, Volume 277, Pages 144–151 (Mi tm3380)  

This article is cited in 5 scientific papers (total in 5 papers)

Nonlinear positional differential game in the class of mixed strategies

A. A. Krasovskiia, A. N. Krasovskiib

a International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria
b Ural State Agricultural Academy, Yekaterinburg, Russia

Abstract: The feedback control problem is considered for a nonlinear dynamic system under lack of information on disturbances. The problem on minmax-maxmin of the guaranteed result for a given positional quality index is formalized as an antagonistic two-player differential game in the framework of the concept developed in the Sverdlovsk (now Yekaterinburg) school on the theory of differential games. The problem is solved in the class of mixed strategies. The existence of the value of the game and a saddle point is established. The solution to the problem is based on the application of appropriate leader models, the method of extremal shift to the accompanying points and the method of upper convex hulls. The results of the study are applied to a realistic control model. The simulation outputs are presented.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2012, 277, 137–143

Bibliographic databases:

UDC: 517.977+517.978
Received in January 2012

Citation: A. A. Krasovskii, A. N. Krasovskii, “Nonlinear positional differential game in the class of mixed strategies”, Mathematical control theory and differential equations, Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko, Tr. Mat. Inst. Steklova, 277, MAIK Nauka/Interperiodica, Moscow, 2012, 144–151; Proc. Steklov Inst. Math., 277 (2012), 137–143

Citation in format AMSBIB
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\paper Nonlinear positional differential game in the class of mixed strategies
\inbook Mathematical control theory and differential equations
\bookinfo Collected papers. In commemoration of the 90th anniversary of Academician Evgenii Frolovich Mishchenko
\serial Tr. Mat. Inst. Steklova
\yr 2012
\vol 277
\pages 144--151
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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\jour Proc. Steklov Inst. Math.
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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. V. Kornev, N. Yu. Lukoyanov, “O chislennom reshenii differentsialnykh igr s neterminalnoi platoi v klassakh smeshannykh strategii”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 2013, no. 3, 34–48  mathnet
    2. D. V. Kornev, “Chislennye metody resheniya differentsialnykh igr s neterminalnoi platoi”, Izv. IMI UdGU, 2016, no. 2(48), 82–151  mathnet  elib
    3. M. I. Gomoyunov, A. R. Plaksin, “Finite-dimensional approximations of neutral-type conflict-controlled systems”, IFAC PAPERSONLINE, 50:1 (2017), 5109–5114  crossref  isi  scopus
    4. M. I. Gomoyunov, A. R. Plaksin, “Finite-dimensional approximations of neutral-type conflict-controlled systems”, Izv. Inst. Mat. Inform., 2017, no. 1, 111–122  mathnet  crossref  mathscinet  zmath  isi  elib
    5. Yu. Averboukh, “Extremal shift rule for continuous-time zero-sum Markov games”, Dyn. Games Appl., 7:1 (2017), 1–20  crossref  mathscinet  zmath  isi  scopus
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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