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

Author

Listed:
  • 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
    Department of General and Exact Subjects, Tashkent State University of Economics, Tashkent 100006, 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
    ICRIOS—The Invernizzi Centre for Research in Innovation, Organization, Strategy and Entrepreneurship, Department of Management and Technology, Bocconi University, 20100 Milano, Italy)

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.

Suggested Citation

  • Bahrom Samatov & Gafurjan Ibragimov & Bahodirjon Juraev & Massimiliano Ferrara, 2023. "On the Lifeline Game of the Inertial Players with Integral and Geometric Constraints," Mathematics, MDPI, vol. 11(19), pages 1-13, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:19:p:4209-:d:1255962
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    References listed on IDEAS

    as
    1. Gafurjan Ibragimov & Yusra Salleh, 2012. "Simple Motion Evasion Differential Game of Many Pursuers and One Evader with Integral Constraints on Control Functions of Players," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-10, October.
    2. Gafurjan Ibragimov & Massimiliano Ferrara & Marks Ruziboev & Bruno Antonio Pansera, 2021. "Linear evasion differential game of one evader and several pursuers with integral constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(3), pages 729-750, September.
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