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

Jewaidu Rilwan (), Massimiliano Ferrara (), Abbas Ja’afaru Badakaya () and Bruno Antonio Pansera ()
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Jewaidu Rilwan: Bayero University Kano
Massimiliano Ferrara: Bocconi University
Abbas Ja’afaru Badakaya: Bayero University Kano
Bruno Antonio Pansera: University “Mediterranea” of Reggio Calabria

Quality & Quantity: International Journal of Methodology, 2023, vol. 57, issue 6, No 28, 5562 pages

Abstract: 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.

Keywords: Gr $$\ddot{\text {o}}$$ o ¨ nwall’s inequality; Pursuit; Evasion; Optimal strategy; Attainability domain; 91A23; 91A10; 49N70; 49N90; 34H05 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11135-023-01616-9

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