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Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, Volume 33, Issue 1, Pages 103–118
DOI: https://doi.org/10.35634/vm230107 (Mi vuu838) 		 
This article is cited in 3 scientific papers (total in 3 papers)

MATHEMATICS

The method of resolving functions for solving a pursuit problem with integral constraints on player controls

N. A. Mamadalievab, Kh. Ya. Mustapokulovbc, G. M. Abdualimovad

a Institute of Mathematics named after V. I. Romanovsky of the Academy of Sciences of the Republic of Uzbekistan, ul. Universitetskaya, 9, Tashkent, 100174, Uzbekistan
b National University of Uzbekistan named after Mirzo Ulugbek, ul. Universitetskaya, 4, Tashkent, 100174, Uzbekistan
c Tashkent State Technical University named after I. Karimov, ul. Universitetskaya, 4, Tashkent, 100174, Uzbekistan
d Andijan State University, ul. Universitskaya, 129, Andijan, 170100, Uzbekistan
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DOI: https://doi.org/10.35634/vm230107
Abstract: In this paper, we study pursuit game problems described by a system of equations with a retarded argument under integral constraints on the players' controls. The proposed scheme uses the ideas of the method of resolving functions. Modifications of methods (i.e., the first and so-called third methods) [1,3,12] of pursuit are proposed in the case when integral constraints are imposed on the players' controls. Sufficient conditions are obtained for the possibility of completing the pursuit in a finite time.
Keywords: differential game, pursuit game, integral constraint, resolving function, conflict-controlled process, multivalued mapping, control, pursuer, evader.
Received: 12.09.2022
Accepted: 13.02.2023
Bibliographic databases:
Document Type: Article
UDC: 517.977
MSC: 35F46, 35K51, 35R12, 49N25, 93C20
Language: Russian
Citation: N. A. Mamadaliev, Kh. Ya. Mustapokulov, G. M. Abdualimova, “The method of resolving functions for solving a pursuit problem with integral constraints on player controls”, Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki, 33:1 (2023), 103–118
Citation in format AMSBIB
\Bibitem{MamMusAbd23}
\by N.~A.~Mamadaliev, Kh.~Ya.~Mustapokulov, G.~M.~Abdualimova
\paper The method of resolving functions for solving a pursuit problem with integral constraints on player controls
\jour Vestn. Udmurtsk. Univ. Mat. Mekh. Komp. Nauki
\yr 2023
\vol 33
\issue 1
\pages 103--118
\mathnet{http://mi.mathnet.ru/vuu838}
\crossref{https://doi.org/10.35634/vm230107}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4573571}
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  • https://www.mathnet.ru/eng/vuu838
  • https://www.mathnet.ru/eng/vuu/v33/i1/p103
    • This publication is cited in the following 3 articles:
    1. A. I. Machtakova, N. N. Petrov, “O dvukh zadachakh presledovaniya gruppy ubegayuschikh v differentsialnykh igrakh s drobnymi proizvodnymi”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 34:1 (2024), 65–79  mathnet  crossref
    2. Numanzhon A. Mamadaliev, Khamdam Ya. Mustapokulov, Mukhammadsodik M. Abdumannopov, “Differentsialnye igry presledovaniya neitralnogo tipa s integralnymi ogranicheniyami na upravleniya igrokov”, MTIP, 16:4 (2024), 45–68  mathnet
    3. Numanzhon Mamadaliev, Khamdam Mustapokulov, “Pursuit Problem for Differential-Difference Equations of Neutral Type”, J Math Sci, 277:3 (2023), 431  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Вестник Удмуртского университета. Математика. Механика. Компьютерные науки
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