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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 3, Pages 58–75 (Mi timm1085)  

This article is cited in 2 scientific papers (total in 2 papers)

On the numerical solution of a minmax control problem with a positional functional

M. I. Gomoyunova, D. V. Kornevab, N. Yu. Lukoyanovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Yeltsin Ural Federal University

Abstract: We consider a minmax feedback control problem for a linear dynamic system with a positional quality criterion, which is the norm of the set of deviations of the motion from given target points at given times. The problem is formalized as a positional differential game. A numerical method is given for finding an approximate value of the game and constructing an optimal (minmax and maxmin) control law. The method is based on the recursive construction of upper convex (concave) hulls of auxiliary program functions. In addition, we use the “pixel” approximation of the domains of convexified functions and the approximate construction of the upper convex hull of a function as the lower envelope of a finite set of support hyperplanes of its subgraph.

Keywords: optimal control, differential games, numerical methods.

Full text: PDF file (325 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 291, suppl. 1, 77–95

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: 23.04.2014

Citation: M. I. Gomoyunov, D. V. Kornev, N. Yu. Lukoyanov, “On the numerical solution of a minmax control problem with a positional functional”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 3, 2014, 58–75; Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 77–95

Citation in format AMSBIB
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\paper On the numerical solution of a~minmax control problem with a~positional functional
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 3
\pages 58--75
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3364417}
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 291
\issue , suppl. 1
\pages 77--95
\crossref{https://doi.org/10.1134/S0081543815090060}
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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. M. I. Gomoyunov, “Lineino-vypuklye zadachi optimizatsii garantii pri zapazdyvanii v upravlenii”, Izv. IMI UdGU, 2015, no. 1(45), 37–105  mathnet  elib
    2. D. V. Kornev, “Chislennye metody resheniya differentsialnykh igr s neterminalnoi platoi”, Izv. IMI UdGU, 2016, no. 2(48), 82–151  mathnet  elib
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