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Trudy Inst. Mat. i Mekh. UrO RAN, 2014, Volume 20, Number 1, Pages 68–82 (Mi timm1030)  

This article is cited in 4 scientific papers (total in 4 papers)

On the stability of a procedure for solving a minimax control problem for a positional functional

M. I. Gomoyunova, N. Yu. Lukoyanovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University named after the First President of Russia B. N. Yeltsin

Abstract: We consider a minimax feedback control problem for a linear dynamic system with a positional quality criterion, which is the norm of the family of deviations of the motion from given target points at given times. The problem is formalized as a positional differential game. A procedure for calculating the value of the game based on the backward construction of upper convex hulls of auxiliary program functions is studied. We also study a method of generating a minimax control law based on this procedure and on the extremal shift principle. The stability of the proposed resolving constructions with respect to computational and informational noises is proved.

Keywords: optimal control, differential games, stability.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2015, 288, suppl. 1, 54–69

Bibliographic databases:

Document Type: Article
UDC: 517.977
Received: 26.09.2013

Citation: M. I. Gomoyunov, N. Yu. Lukoyanov, “On the stability of a procedure for solving a minimax control problem for a positional functional”, Trudy Inst. Mat. i Mekh. UrO RAN, 20, no. 1, 2014, 68–82; Proc. Steklov Inst. Math. (Suppl.), 288, suppl. 1 (2015), 54–69

Citation in format AMSBIB
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\paper On the stability of a~procedure for solving a~minimax control problem for a~positional functional
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2014
\vol 20
\issue 1
\pages 68--82
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2015
\vol 288
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\pages 54--69
\crossref{https://doi.org/10.1134/S0081543815020078}
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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, D. V. Kornev, N. Yu. Lukoyanov, “On the numerical solution of a minmax control problem with a positional functional”, Proc. Steklov Inst. Math. (Suppl.), 291, suppl. 1 (2015), 77–95  mathnet  crossref  mathscinet  isi  elib
    2. D. V. Kornev, N. Yu. Lukoyanov, “On a minimax control problem for a positional functional under geometric and integral constraints on control actions”, Proc. Steklov Inst. Math. (Suppl.), 293, suppl. 1 (2016), 85–100  mathnet  crossref  mathscinet  isi  elib
    3. M. I. Gomoyunov, “Lineino-vypuklye zadachi optimizatsii garantii pri zapazdyvanii v upravlenii”, Izv. IMI UdGU, 2015, no. 1(45), 37–105  mathnet  elib
    4. 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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