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Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls

Author

Listed:
  • Gafurjan Ibragimov

    (Department of Digital Economics and Agrotechnologies, University of Digital Economics and Agrotechnologies, Tashkent 100022, Uzbekistan
    These authors contributed equally to this work.)

  • Ikrombek Yusupov

    (Department of Mathematics, Andijan State University, Andijan 170100, Uzbekistan
    These authors contributed equally to this work.)

  • Massimiliano Ferrara

    (Department of Law, Economics and Human Sciences and Decisions Lab, University Mediterranea of Reggio Calabria, 89125 Reggio Calabria, Italy
    ICRIOS—The Invernizzi Centre for Research in Innovation, Organization, Strategy and Entrepreneurship, Department of Management and Technology, Bocconi University, 20136 Milan, Italy
    These authors contributed equally to this work.)

Abstract

We studied a simple motion differential game of two pursuers and one evader in R 2 . The control functions of players are subjected to the Grönwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the game is considered complete. The pursuers attempt to complete the game as earlier as possible. The evader attempts to avoid being captured or delays the capture time. We found an equation for the optimal pursuit time and construct the optimal strategies of players.

Suggested Citation

  • Gafurjan Ibragimov & Ikrombek Yusupov & Massimiliano Ferrara, 2023. "Optimal Pursuit Game of Two Pursuers and One Evader with the Grönwall-Type Constraints on Controls," Mathematics, MDPI, vol. 11(2), pages 1-10, January.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:2:p:374-:d:1031567
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    References listed on IDEAS

    as
    1. Gafurjan Ibragimov & Massimiliano Ferrara & Marks Ruziboev & Bruno Antonio Pansera, 2021. "Linear evasion differential game of one evader and several pursuers with integral constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 729-750, September.
    2. Aleksandr I. Blagodatskikh & Nikolai N. Petrov, 2019. "Simultaneous Multiple Capture of Rigidly Coordinated Evaders," Dynamic Games and Applications, Springer, vol. 9(3), pages 594-613, September.
    3. Gafurjan Ibragimov & Massimiliano Ferrara & Atamurat Kuchkarov & Bruno Antonio Pansera, 2018. "Simple Motion Evasion Differential Game of Many Pursuers and Evaders with Integral Constraints," Dynamic Games and Applications, Springer, vol. 8(2), pages 352-378, June.
    4. Sergey Ganebny & Sergey Kumkov & Stéphane Ménec & Valerii Patsko, 2012. "Model Problem in a Line with Two Pursuers and One Evader," Dynamic Games and Applications, Springer, vol. 2(2), pages 228-257, June.
    Full references (including those not matched with items on IDEAS)

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