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 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

scholarly journals Application of a fixed point theorem on infinite cartesian product to an infinite system of differential equations

2021 ◽  
Vol 37 (2) ◽  
pp. 259-263
Author(s):  
MARCEL-ADRIAN ŞERBAN
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Differential Equations ◽  
Point Theorem ◽  
Infinite System ◽  
Cartesian Product ◽  
System Of Differential Equations ◽  
Abstract Result ◽  
Infinite Dimensional ◽  
Contraction Theorem

"In the paper Operators on infinite dimensional cartesian product, (Analele Univ. Vest Timişoara, Mat. Inform., 48 (2010), 253–263), by I. A. Rus and M. A. Şerban, the authors give a generalization of the Fibre contraction theorem on infinite dimensional cartesian product. In this paper we give an application of this abstract result to an infinite system of differential equations. "

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