scholarly journals PURSUIT AND EVASION DIFFERENTIAL GAMES IN HILBERT SPACE

2010 ◽  
Vol 12 (03) ◽  
pp. 239-251 ◽  
Author(s):  
GAFURJAN I. IBRAGIMOV ◽  
RISMAN MAT HASIM
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
System Of Differential Equations ◽  
Pursuit Problem ◽  
Pursuit And Evasion ◽  
Evasion Problem ◽  
Total Resource

We consider pursuit and evasion differential game problems described by an infinite system of differential equations with countably many Pursuers in Hilbert space. Integral constraints are imposed on the controls of players. In this paper an attempt has been made to solve an evasion problem under the condition that the total resource of the Pursuers is less then that of the Evader and a pursuit problem when the total resource of the Pursuers greater than that of the Evader. The strategy of the Evader is constructed.

scholarly journals Differential Games for an Infinite 2-Systems of Differential Equations

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1467
Author(s):  
Muminjon Tukhtasinov ◽  
Gafurjan Ibragimov ◽  
Sarvinoz Kuchkarova ◽  
Risman Mat Hasim
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Differential Games ◽  
Differential Game ◽  
Infinite System ◽  
The State ◽  
Geometric Constraints ◽  
Control Parameters ◽  
Systems Of Differential Equations ◽  
Pursuit And Evasion

A pursuit differential game described by an infinite system of 2-systems is studied in Hilbert space l2. Geometric constraints are imposed on control parameters of pursuer and evader. The purpose of pursuer is to bring the state of the system to the origin of the Hilbert space l2 and the evader tries to prevent this. Differential game is completed if the state of the system reaches the origin of l2. The problem is to find a guaranteed pursuit and evasion times. We give an equation for the guaranteed pursuit time and propose an explicit strategy for the pursuer. Additionally, a guaranteed evasion time is found.

scholarly journals Differential Game of Optimal Pursuit for an Infinite System of Differential Equations

2017 ◽  
Vol 42 (1) ◽  
pp. 391-403 ◽  
Author(s):  
Gafurjan Ibragimov ◽  
Idham Arif Alias ◽  
Usman Waziri ◽  
Abbas Badakaya Ja’afaru
Keyword(s):  
Differential Equations ◽  
Differential Game ◽  
Infinite System ◽  
System Of Differential Equations ◽  
Optimal Pursuit

Pursuit and Evasion Games for an Infinite System of Differential Equations

2021 ◽  
Author(s):  
Gafurjan Ibragimov ◽  
Massimiliano Ferrara ◽  
Idham Arif Alias ◽  
Mehdi Salimi ◽  
Nurzeehan Ismail
Keyword(s):  
Differential Equations ◽  
Infinite System ◽  
System Of Differential Equations ◽  
Pursuit And Evasion

scholarly journals DIFFERENTIAL GAME WITH A LIFELINE FOR THE INERTIAL MOVEMENTS OF PLAYERS

2021 ◽  
Vol 7 (2) ◽  
pp. 94
Author(s):  
Bahrom T. Samatov ◽  
Ulmasjon B. Soyibboev
Keyword(s):  
Euclidean Space ◽  
Differential Game ◽  
Pursuit Problem ◽  
Solvability Conditions ◽  
Pursuit Evasion ◽  
Attainability Domain ◽  
Evasion Problem ◽  
Pursuit Strategy

In this paper, we study the well-known problem of Isaacs called the "Life line" 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.

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