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Fixed-Time Pursuit–Evasion Differential Game with Grönwall Constraints in Hilbert Space l 2

Author

Listed:
  • Gafurjan Ibragimov

    (Romanovskii Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent 100174, Uzbekistan
    Department of Natural Subjects, University of Public Safety of the Republic of Uzbekistan, Tashkent 100109, Uzbekistan)

  • Saidakbar Gulomov

    (Department of Applied Mathematics and Mechanics, Andijan State University, Universitet Street-129, Andijan 170100, Uzbekistan
    Department of Physics and Mathematics, Kokand University Andijan Branch, Bobur Shox Street-2b, Andijan 170619, Uzbekistan)

  • Bruno Antonio Pansera

    (Department of Law, Economics and Human Sciences & Decisions_Lab, University Mediterranea of Reggio Calabria, Via dell’Universitá 25, I-89124 Reggio Calabria, Italy)

Abstract

This paper studies a pursuit–evasion differential game in the Hilbert space l 2 involving countably many pursuers and one evader. The players follow simple motion dynamics, while their control functions are subject to Grönwall-type constraints. The value of the game λ is defined as the infimum of the distances between the evader and the pursuers at a given terminal time θ . The pursuers aim to minimize this distance λ by the end of the game, while the evader aims to keep it as large as possible. Optimal strategies for the pursuers are constructed via the method of fictitious pursuers, and an explicit evasion strategy is derived. As a result, the optimal strategies of both sides and the value of the game are obtained.

Suggested Citation

  • Gafurjan Ibragimov & Saidakbar Gulomov & Bruno Antonio Pansera, 2026. "Fixed-Time Pursuit–Evasion Differential Game with Grönwall Constraints in Hilbert Space l 2," Games, MDPI, vol. 17(4), pages 1-15, July.
    • Handle: RePEc:gam:jgames:v:17:y:2026:i:4:p:35-:d:1982157
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