Optimal Pursuit Game of Two Pursuers and One Evader with the Gronwall-Type Constraints on Controls

被引：1
|
作者：
Ibragimov, Gafurjan [1 ]
Yusupov, Ikrombek [2 ]
Ferrara, Massimiliano [3 ,4 ,5 ]
机构：
[1] Univ Digital Econ & Agrotechnol, Tashkent 100022, Uzbekistan
[2] Andijan State Univ, Dept Math, Andijan 170100, Uzbekistan
[3] Univ Mediterranea Reggio Calabria, Dept Law Econ & Human Sci, I-89125 Reggio Di Calabria, Italy
[4] Univ Mediterranea Reggio Calabria, Decis Lab, I-89125 Reggio Di Calabria, Italy
[5] Bocconi Univ, ICRIOS Invernizzi Ctr Res Innovat Org Strategy & E, Dept Management & Technol, I-20136 Milan, Italy
来源：
MATHEMATICS | 2023年 / 11卷 / 02期
关键词：
differential game; Gronwall constraints; pursuers; evader; optimal pursuit time; optimal strategy; DIFFERENTIAL GAME; EVASION GAMES;
D O I：
10.3390/math11020374
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We studied a simple motion differential game of two pursuers and one evader in R-2. The control functions of players are subjected to the Gronwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the game is considered complete. The pursuers attempt to complete the game as earlier as possible. The evader attempts to avoid being captured or delays the capture time. We found an equation for the optimal pursuit time and construct the optimal strategies of players.
引用
收藏
页数：10
相关论文
共 30 条
  • [21] π-STRATEGY FOR A DIFFERENTIAL GAME OF PURSUIT WITH INTEGRAL CONSTRAINTS OF A GENERALIZED TYPE
    Samatov, B. T.
    Horilov, M. A.
    Juraev, B. I.
    VESTNIK UDMURTSKOGO UNIVERSITETA-MATEMATIKA MEKHANIKA KOMPYUTERNYE NAUKI, 2023, 33 (02): : 293 - 311
  • [22] Optimal Evading Strategies for Two-Pursuer/One-Evader Problems
    Makkapati, Venkata Ramana
    Sun, Wei
    Tsiotras, Panagiotis
    JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, 2018, 41 (04) : 851 - 862
  • [23] Differential Game with Many Pursuers when Controls are Subjected to Coordinate-wise Integral Constraints
    Alias, Idham Arif
    Ibragimov, Gafurjan
    Kuchkarov, Atamurat
    Sotvoldiyev, Akmal
    MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES, 2016, 10 (02): : 195 - 207
  • [24] Multiple-Pursuer/One-Evader Pursuit-Evasion Game in Dynamic Flowfields
    Sun, Wei
    Tsiotras, Panagiotis
    Lolla, Tapovan
    Subramani, Deepak N.
    Lermusiaux, Pierre F. J.
    JOURNAL OF GUIDANCE CONTROL AND DYNAMICS, 2017, 40 (07) : 1627 - 1637
  • [25] MULTI PURSUER DIFFERENTIAL GAME OF OPTIMAL APPROACH WITH INTEGRAL CONSTRAINTS ON CONTROLS OF PLAYERS
    Ibragimov, Gafurjan
    Abd Rasid, Norshakila
    Kuchkarov, Atamurat
    Ismail, Fudziah
    TAIWANESE JOURNAL OF MATHEMATICS, 2015, 19 (03): : 963 - 976
  • [26] Discrete Pursuit Game when Controls are subjected to Geometric and Total Constraints
    Rakhmanov, Askar
    Akbarova, Marguba
    MALAYSIAN JOURNAL OF MATHEMATICAL SCIENCES, 2015, 9 (03): : 481 - 490
  • [27] Multi-Pursuer and One-Evader Evasion Differential Game with Integral Constraints for an Infinite System of Binary Differential Equations
    Kazimirova, Ruzakhon
    Ibragimov, Gafurjan
    Pansera, Bruno Antonio
    Ibragimov, Abdulla
    MATHEMATICS, 2024, 12 (08)
  • [28] Evasion Differential Game Of Two Evaders And One Pursuer With Integral Constraints
    Alias, Idham Arif
    Salleh, Yusra
    Azamov, Abdulla
    INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES AND STATISTICS 2013 (ICMSS2013), 2013, 1557 : 140 - 145
  • [29] A Differential Game Problem of Many Pursuers and One Evader in the Hilbert Space ℓ2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell_2$$\end{document}
    Jewaidu Rilwan
    Poom Kumam
    Gafurjan Ibragimov
    Abbas Ja’afaru Badakaya
    Idris Ahmed
    Differential Equations and Dynamical Systems, 2023, 31 (4) : 925 - 943
  • [30] On pursuit and evasion game problems with Gro¨\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ddot{\text {o}}$$\end{document}nwall-type constraints
    Jewaidu Rilwan
    Massimiliano Ferrara
    Abbas Ja’afaru Badakaya
    Bruno Antonio Pansera
    Quality & Quantity, 2023, 57 (6) : 5551 - 5562
123