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 Ural Math. J., 2020, Volume 6, Issue 2, Pages 95–107 (Mi umj130)

Pursuit-evasion differential games with Grönwall-type constraints on controls

Bahrom T. Samatova, Gafurjan Ibragimovb, Iroda V. Khodjibayevac

a Namangam State University
b Universiti Putra Malaysia
c Namangan Engineering and Technology Institute, Namangan

Abstract: A simple pursuit-evasion differential game of one pursuer and one evader is studied. The players' controls are subject to differential constraints in the form of the integral Grönwall inequality. The pursuit is considered completed if the state of the pursuer coincides with the state of the evader. The main goal of this work is to construct optimal strategies for the players and find the optimal pursuit time. A parallel approach strategy for Grönwall-type constraints is constructed and it is proved that it is the optimal strategy of the pursuer. In addition, the optimal strategy of the evader is constructed and the optimal pursuit time is obtained. The concept of a parallel pursuit strategy ($\Pi$-strategy for short) was introduced and used to solve the quality problem for “life-line” games by L.A. Petrosjan. This work develops and expands the works of Isaacs, Petrosjan, Pshenichnyi, and other researchers, including the authors.

Keywords: differential game, Grönwall's inequality, geometric constraint, pursuit, evasion, optimal strategy, domain of attainability, life-line

 Funding Agency Grant Number Ministry of Education of Malaysia 01-01-17-1921FR National University Uzbekistan FR-GS-33 The present research was partially supported by the National Fundamental Research Grant Scheme FRGS of Malaysia (Project No. 01-01-17-1921FR) and by the National Fundamental Research Grant Scheme of the National University Uzbekistan (Project No. FR-GS-33).

DOI: https://doi.org/10.15826/umj.2020.2.010

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Citation: Bahrom T. Samatov, Gafurjan Ibragimov, Iroda V. Khodjibayeva, “Pursuit-evasion differential games with Grönwall-type constraints on controls”, Ural Math. J., 6:2 (2020), 95–107

Citation in format AMSBIB
\Bibitem{SamIbrKho20} \by Bahrom~T.~Samatov, Gafurjan~Ibragimov, Iroda~V.~Khodjibayeva \paper Pursuit-evasion differential games with Gr\"{o}nwall-type constraints on controls \jour Ural Math. J. \yr 2020 \vol 6 \issue 2 \pages 95--107 \mathnet{http://mi.mathnet.ru/umj130} \crossref{https://doi.org/10.15826/umj.2020.2.010} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=MR4194018} \elib{https://elibrary.ru/item.asp?id=44611154} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85099543327}