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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2009, Volume 15, Number 4, Pages 290–301 (Mi timm444)  

This article is cited in 32 scientific papers (total in 32 papers)

On linear differential games with integral constraints

A. A. Chikrii, A. A. Belousov

Institute of Cybernetics NAS Ukraine
References:
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.
Received: 29.04.2009
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, Volume 269, Issue 1, Pages S69–S80
DOI: https://doi.org/10.1134/S0081543810060076
Bibliographic databases:
Document Type: Article
UDC: 518.9
Language: Russian
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
\Bibitem{ChiBel09}
\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
\mathnet{http://mi.mathnet.ru/timm444}
\elib{https://elibrary.ru/item.asp?id=12952773}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 269
\issue , suppl. 1
\pages S69--S80
\crossref{https://doi.org/10.1134/S0081543810060076}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962408500}
Linking options:
  • https://www.mathnet.ru/eng/timm444
  • https://www.mathnet.ru/eng/timm/v15/i4/p290
  • This publication is cited in the following 32 articles:
    1. I.V. Kal'chuk, Y.V. Pryvalov, “ON SOME OPTIMIZATION PROPERTIES OF THE GAUSS–WEIERSTRASS OPERATOR”, KCA, 2025, 149  crossref
    2. G. I. Ibragimov, X. Sh. Qo'shaqov, A. A. Muxammadjonov, “Optimal Pursuit Differential Game Problem for an Infinite System of Binary Differential Equations”, Lobachevskii J Math, 45:3 (2024), 1131  crossref
    3. A.M. Shutovskyi, “ON SOME ASYMPTOTIC PROPERTIES OF SOLUTIONS OF TRIHARMONIC EQUATIONS”, KCA, 2024, 152  crossref
    4. Greta Chikrii, “Linear Discrete Game Under Quadratic Constraints on Controls”, Cybernetics and Computer Technologies, 2024, no. 2, 5  crossref
    5. A. M. Shutovskyi, “Some Asymptotic Properties of Solutions to Triharmonic Equations”, Cybern Syst Anal, 60:3 (2024), 472  crossref
    6. A. Yu. Mishchuk, A. M. Shutovskyi, “Optimization Properties of Generalized Chebyshev–Poisson Integrals”, Cybern Syst Anal, 60:4 (2024), 613  crossref
    7. A.Yu. Mishchuk, A.M. Shutovskyi, “ON THE OPTIMIZATION PROPERTIES OF GENERALIZED CHEBYSHEV–POISSON INTEGRALS”, KCA, 2024, 117  crossref
    8. R.V. Tovkach, V.M. Medvid, “A NECESSARY CONDITION FOR THE CONVERGENCE OF THE FOURIER TRANSFORM”, KCA, 2024, 146  crossref
    9. E.T. Karimov, N.E. Tokmagambetov, D.A. Usmonov, “INVERSE-INITIAL PROBLEM FOR TIME-DEGENERATE PDE INVOLVING THE BI-ORDINAL HILFER DERIVATIVE”, KCA, 2024, 133  crossref
    10. R. V. Tovkach, V. M. Medvid, “A Necessary Condition for the Convergence of the Fourier Transform”, Cybern Syst Anal, 2024  crossref
    11. A. M. Shutovskyi, V. V. Pryt, “Optimization Characteristics of the Operator with Delta-Like Kernel for Quasi-Smooth Functions”, Cybern Syst Anal, 2024  crossref
    12. A.M. Shutovskyi, V.V. Pryt, “OPTIMIZATION CHARACTERISTICS OF AN OPERATOR WITH DELTA-SHAPED KERNEL FOR QUASI-SMOOTH FUNCTIONS”, KCA, 2024, 125  crossref
    13. A. M. Shutovskyi, “Some Representations of Triharmonic Functions”, Cybern Syst Anal, 2024  crossref
    14. A.M. Shutovskyi, “SOME REPRESENTATIONS OF TRIHARMONIC FUNCTIONS”, KCA, 2024, 169  crossref
    15. 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
    16. G. M. Abdualimova, N. A. Mamadaliev, M. Tukhtasinov, “Sufficient solvability conditions for the problem of pursuit under an impulse action”, Comput. Math. Math. Phys., 63:7 (2023), 1166–1175  mathnet  mathnet  crossref  crossref
    17. Gafurjan Ibragimov, Yusra Salleh, Idham Arif Alias, Bruno Antonio Pansera, Massimiliano Ferrara, “Evasion from Several Pursuers in the Game with Coordinate-wise Integral Constraints”, Dyn Games Appl, 13:3 (2023), 819  crossref
    18. N. A. Mamadaliev, B. Kh. Khayitkulov, “Complete solution of a class of differential pursuit games with integral constraint and impulse control”, Russian Math. (Iz. VUZ), 66:3 (2022), 22–29  mathnet  crossref  crossref
    19. E. M. Mukhsinov, “About one differential game of neutral type with integral restrictions in Hilbert space”, Ufa Math. J., 14:3 (2022), 86–96  mathnet  crossref  mathscinet
    20. B. T. Samatov, N. T. Umaraliyeva, S. I. Uralova, “Differential Games with the Langenhop Type Constrains on Controls”, Lobachevskii J Math, 42:12 (2021), 2942  crossref
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