On the Lifeline Game of the Inertial Players with Integral and Geometric Constraints

Bahrom Samatov, Gafurjan Ibragimov, Bahodirjon Juraev and Massimiliano Ferrara ()
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Bahrom Samatov: Department of Mathematics, Namangan State University, Namangan 116019, Uzbekistan
Gafurjan Ibragimov: V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, Tashkent 100174, Uzbekistan
Bahodirjon Juraev: Faculty of Physics-Mathematics, Andijan State University, Andijon 170100, Uzbekistan
Massimiliano Ferrara: Department of Law, Economics and Human Sciences, University Mediterranea of Reggio Calabria, 89124 Reggio Calabria, Italy

Mathematics, 2023, vol. 11, issue 19, 1-13

Abstract: In this paper, we consider a pursuit–evasion game of inertial players, where the pursuer’s control is subject to integral constraint and the evader’s control is subject to geometric constraint. In the pursuit problem, the main tool is the strategy of parallel pursuit. Sufficient conditions are obtained for the solvability of pursuit–evasion problems. Additionally, the main lemma describing the monotonicity of an attainability domain of the evader is proved, and an explicit analytical formula for this domain is given. One of the main results of the paper is the solution of the Isaacs lifeline game for a special case.

Keywords: differential game; integral constraint; geometric constraint; pursuer; evader; strategy; guaranteed capture time; attainability domain; lifeline game (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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