On the Lifeline Game of the Inertial Players with Integral and Geometric Constraints
Bahrom SamatovDepartment of Mathematics, Namangan State University, Namangan 116019, UzbekistanGafurjan IbragimovDepartment of General and Exact Subjects, Tashkent State University of Economics, Tashkent 100006, UzbekistanBahodirjon JuraevFaculty of Physics-Mathematics, Andijan State University, Andijon 170100, UzbekistanМассимилиано ФеррараDepartment of Law, Economics and Human Sciences, University Mediterranea of Reggio Calabria, 89124 Reggio Calabria, Italy
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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.
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