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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 4, Pages 290–301 (Mi timm444)  

This article is cited in 8 scientific papers (total in 8 papers)

On linear differential games with integral constraints

A. A. Chikrii, A. A. Belousov

Institute of Cybernetics NAS Ukraine

Abstract: Pursuit game problems for linear systems with integral constraints for controls are studied. The proposed scheme uses the ideas of the method of resolving functions. An analog of the Pontryagin condition is formulated, which makes it possible to establish sufficient conditions for the termination of the differential game in some guaranteed time by using the measurable choice theorem for constructing the pursuer's control. The obtained results are illustrated by typical examples of game situations: simple motion and Pontryagin's test case.

Keywords: differential game, pursuit game, integral constraint, set-valued mapping, resolving function.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 269, suppl. 1, S69–S80

Document Type: Article
UDC: 518.9
Received: 29.04.2009

Citation: A. A. Chikrii, A. A. Belousov, “On linear differential games with integral constraints”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 4, 2009, 290–301; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S69–S80

Citation in format AMSBIB
\by A.~A.~Chikrii, A.~A.~Belousov
\paper On linear differential games with integral constraints
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 4
\pages 290--301
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 269
\issue , suppl. 1
\pages S69--S80

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    This publication is cited in the following articles:
    1. B. T. Samatov, “On a pursuit-evasion problem under a linear change of the pursuer resource”, Siberian Adv. Math., 23:4 (2013), 294–302  mathnet  crossref  mathscinet  elib
    2. Ibragimov G., Satimov Nu'man, “A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints”, Abstract Appl. Anal., 2012, 460171  crossref  mathscinet  zmath  isi  elib  scopus
    3. Ibragimov G., Salleh Yu., “Simple Motion Evasion Differential Game of Many Pursuers and One Evader with Integral Constraints on Control Functions of Players”, J. Appl. Math., 2012, 748096  crossref  mathscinet  zmath  isi  scopus
    4. A. A. Chikrii, A. A. Belousov, “O lineinykh differentsialnykh igrakh s vypuklymi integralnymi ogranicheniyami”, Tr. IMM UrO RAN, 19, no. 4, 2013, 308–319  mathnet  mathscinet  elib
    5. Samatov B.T., “The Resolving Functions Method for the Pursuit Problem with Integral Constraints on Controls”, J. Automat. Inf. Sci., 45:8 (2013), 41–58  crossref  mathscinet  isi  elib  scopus
    6. Ibragimov G., Abd Rasid N., Kuchkarov A., Ismail F., “Multi Pursuer Differential Game of Optimal Approach With Integral Constraints on Controls of Players”, Taiwan. J. Math., 19:3 (2015), 963–976  crossref  mathscinet  zmath  isi  elib  scopus
    7. M. Tukhtasinov, “Lineinaya differentsialnaya igra presledovaniya s impulsnymi i integralno-ogranichennymi upravleniyami igrokov”, Tr. IMM UrO RAN, 22, no. 3, 2016, 273–282  mathnet  crossref  mathscinet  elib
    8. Alias I.A., Ibragimov G., Rakhmanov A., “Evasion Differential Game of Infinitely Many Evaders From Infinitely Many Pursuers in Hilbert Space”, Dyn. Games Appl., 7:3 (2017), 347–359  crossref  mathscinet  zmath  isi  scopus
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