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On pursuit and evasion game problems with Gr $$\ddot{\text {o}}$$ o ¨ nwall-type constraints

Author

Listed:
  • Jewaidu Rilwan

    (Bayero University Kano)

  • Massimiliano Ferrara

    (Bocconi University
    University “Mediterranea” of Reggio Calabria)

  • Abbas Ja’afaru Badakaya

    (Bayero University Kano)

  • Bruno Antonio Pansera

    (University “Mediterranea” of Reggio Calabria)

Abstract

We study a fixed duration pursuit-evasion differential game problem of one pursuer and one evader with Grönwall-type constraints (recently introduced in the work of Samatov et al. (Ural Math J 6:95–107, 2020b)) imposed on all players’ control functions. The players’ dynamics are governed by a generalized dynamic equation. The payoff is the greatest lower bound of the distances between the evader and the pursuers when the game is terminated. The pursuers’ goal, which contradicts that of the evader, is to minimize the payoff. We obtained sufficient conditions for completion of pursuit and evasion as well. To this end, players’ attainability domain and optimal strategies are constructed.

Suggested Citation

  • Jewaidu Rilwan & Massimiliano Ferrara & Abbas Ja’afaru Badakaya & Bruno Antonio Pansera, 2023. "On pursuit and evasion game problems with Gr $$\ddot{\text {o}}$$ o ¨ nwall-type constraints," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(6), pages 5551-5562, December.
    • Handle: RePEc:spr:qualqt:v:57:y:2023:i:6:d:10.1007_s11135-023-01616-9
    DOI: 10.1007/s11135-023-01616-9
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