Abstract:
In this paper, we study the well-known problem of Isaacs called the "Lifeline" game when movements of players occur by acceleration vectors, that is, by inertia in Euclidean space. To solve this problem, we investigate the dynamics of the attainability domain of an evader through finding solvability conditions of the pursuit-evasion problems in favor of a pursuer or an evader. Here a pursuit problem is solved by a parallel pursuit strategy. To solve an evasion problem, we propose a strategy for the evader and show that the evasion is possible from given initial positions of players. Note that this work develops and continues studies of Isaacs, Petrosjan, Pshenichnii, Azamov, and others performed for the case of players' movements without inertia.
Citation:
Bahrom T. Samatov, Ulmasjon B. Soyibboev, “Differential game with a lifeline for the inertial movements of players”, Ural Math. J., 7:2 (2021), 94–109
\Bibitem{SamSoy21}
\by Bahrom~T.~Samatov, Ulmasjon~B.~Soyibboev
\paper Differential game with a lifeline for the inertial movements of players
\jour Ural Math. J.
\yr 2021
\vol 7
\issue 2
\pages 94--109
\mathnet{http://mi.mathnet.ru/umj152}
\crossref{https://doi.org/10.15826/umj.2021.2.007}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=MR4358916}
\elib{https://elibrary.ru/item.asp?id=47556644}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85125074969}
Linking options:
https://www.mathnet.ru/eng/umj152
https://www.mathnet.ru/eng/umj/v7/i2/p94
This publication is cited in the following 7 articles:
Bahrom Samatov, Ulmasjon Soyibboev, IUTAM Bookseries, 40, Proceedings of the IUTAM Symposium on Optimal Guidance and Control for Autonomous Systems 2023, 2024, 165
Mohisanam Turgunboeva, “DIFFERENTIAL l-CATCH AND l-ESCAPE GAMES IN THE CASE OF NON-STATIONARY GEOMETRIC CONSTRAINTS ON CONTROLS”, VOGUMFT, 2024, no. 1(4), 256
Shuai Li, Chen Wang, Guangming Xie, “Optimal Strategies for Pursuit-Evasion Differential Games of Players With Damped Double Integrator Dynamics”, IEEE Trans. Automat. Contr., 69:8 (2024), 5278
Abdulla Azamov, Bahrom Samatov, Ulmasjon Soyibboev, “The Game with a “Life-Line” for Simple Harmonic Motions of Objects”, Int. Game Theory Rev., 26:04 (2024)
B. T. Samatov, U. B. Soyibboev, “Differential game with “lifeline” for Pontryagin's control example”, Izv. IMI UdGU, 61 (2023), 94–113
Bahrom Samatov, Gafurjan Ibragimov, Bahodirjon Juraev, Massimiliano Ferrara, “On the Lifeline Game of the Inertial Players with Integral and Geometric Constraints”, Mathematics, 11:19 (2023), 4209
Bahrom Samatov, Mohisanam Turgunboeva, “DIFFERENTIAL L-CAPTURE AND EVASION GAMES WITH INERTIAL PLAYERS UNDER GEOMETRIC CONSTRAINTS ON CONTROLS”, VOGUMFT, 2023, no. 2(3), 202
Citation in format AMSBIB
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