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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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    References listed on IDEAS

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    1. Gafurjan I. Ibragimov & Mehdi Salimi, 2009. "Pursuit-Evasion Differential Game with Many Inertial Players," Mathematical Problems in Engineering, Hindawi, vol. 2009, pages 1-15, September.
    2. Ibragimov, Gafurjan I. & Salimi, Mehdi & Amini, Massoud, 2012. "Evasion from many pursuers in simple motion differential game with integral constraints," European Journal of Operational Research, Elsevier, vol. 218(2), pages 505-511.
    3. Abbas Badakaya Ja'afaru & Gafurjan Ibragimov, 2012. "On Some Pursuit and Evasion Differential Game Problems for an Infinite Number of First-Order Differential Equations," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, July.
    4. Gafurjan Ibragimov & Nu'man Satimov, 2012. "A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, November.
    5. Idris Ahmed & Poom Kumam & Gafurjan Ibragimov & Jewaidu Rilwan & Wiyada Kumam, 2019. "An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers," Mathematics, MDPI, vol. 7(9), pages 1-11, September.
    6. Abbas Badakaya Ja′afaru & Gafurjan Ibragimov, 2012. "On Some Pursuit and Evasion Differential Game Problems for an Infinite Number of First‐Order Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    7. Gafurjan Ibragimov & Nu′man Satimov, 2012. "A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    8. Massimiliano Ferrara & Gafurjan Ibragimov & Vincenzo Scalzo, 2017. "Differential Games and Discrete Dynamics in Applied Sciences," Discrete Dynamics in Nature and Society, Hindawi, vol. 2017, pages 1-3, January.
    9. 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.
    10. Atamurat Kuchkarov & Gafurjan Ibragimov & Massimiliano Ferrara, 2016. "Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-8, August.
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