A Differential Game Problem of Many Pursuers and One Evader in the Hilbert Space $$\ell_2$$

2020 ◽  
Author(s):  
Jewaidu Rilwan ◽  
Poom Kumam ◽  
Gafurjan Ibragimov ◽  
Abbas Ja’afaru Badakaya ◽  
Idris Ahmed
Keyword(s):  
Hilbert Space ◽  
Differential Game ◽  
Game Problem

scholarly journals On pursuit-evasion differential game problem in a Hilbert space

2020 ◽  
Vol 5 (6) ◽  
pp. 7467-7479
Author(s):  
Jamilu Adamu ◽  
◽  
Kanikar Muangchoo ◽  
Abbas Ja’afaru Badakaya ◽  
Jewaidu Rilwan ◽  
...  
Keyword(s):  
Hilbert Space ◽  
Differential Game ◽  
Game Problem ◽  
Pursuit Evasion

scholarly journals A Purusit Differential Game Problem on a Closed Convex Subset of a Hilbert Space

2020 ◽  
pp. 115-119
Author(s):  
Abbas Ja'afaru Badakaya ◽  
Bilyaminu Muhammad
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Finite Number ◽  
Differential Game ◽  
Convex Subset ◽  
Game Problem ◽  
Nonempty Closed Convex Subset ◽  
First Order ◽  
Control Functions ◽  
And Control

We study a pursuit differential game problem with finite number of pursuers and one evader on a nonempty closed convex subset of the Hilbert space l2. Players move according to certain first order ordinary differential equations and control functions of the pursuers and evader are subject to integral constraints. Pursuers win the game if the geometric positions of a pursuer and the evader coincide. We formulated and prove theorems that are concern with conditions that ensure win for the pursuers. Consequently, wining strategies of the pursuers are constructed. Furthermore, illustrative example is given to demonstrate the result.

scholarly journals Game value for a pursuit-evasion differential game problem in a Hilbert space

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Abbas Ja'afaru Badakaya ◽  
Aminu Sulaiman Halliru ◽  
Jamilu Adamu
Keyword(s):  
Hilbert Space ◽  
Differential Game ◽  
Game Problem ◽  
Pursuit Evasion ◽  
Game Value

scholarly journals Simple motion pursuit differential game problem of many players with integral and geometric constraints on controls function.

2021 ◽  
pp. 12-16
Author(s):  
Jamilu Adamu ◽  
B. M. Abdulhamid ◽  
D. T. Gbande ◽  
A. S. Halliru
Keyword(s):  
Hilbert Space ◽  
Differential Game ◽  
Admissible Control ◽  
Sufficient Conditions ◽  
Game Problem ◽  
Geometric Constraints ◽  
Simple Motion ◽  
Control Functions

We study a simple motion pursuit differential game of many pursuers and one evader in a Hilbert space $l_{2}$. The control functions of the pursuers and evader are subject to integral and geometric constraints respectively. Duration of the game is denoted by positive number $\theta $. Pursuit is said to be completed if there exist strategies $u_{j}$ of the pursuers $P_{j}$ such that for any admissible control $v(\cdot)$ of the evader $E$ the inequality $\|y(\tau)-x_{j}(\tau)\|\leq l_{j}$ is satisfied for some $ j\in \{1,2, \dots\}$ and some time $\tau$. In this paper, sufficient conditions for completion of pursuit were obtained. Consequently strategies of the pursuers that ensure completion of pursuit are constructed.

A GUARANTEED PURSUIT TIME IN A DIFFERENTIAL GAME IN HILBERT SPACE

2019 ◽  
Vol 38 ◽  
pp. 43-54
Author(s):  
Gafurjan Ibragimov ◽  
Usman Waziri ◽  
Idham Arif Alias ◽  
Zarina Bibi Ibrahim
Keyword(s):  
Hilbert Space ◽  
Differential Game

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.

Solving the Problem of UAV Air Combat Game Based on Differential Variational Inequality and D-Gap Function

2014 ◽  
Vol 1042 ◽  
pp. 172-177
Author(s):  
Guang Yan Xu ◽  
Ping Li ◽  
Biao Zhou
Keyword(s):  
Optimal Control ◽  
Variational Inequality ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Differential Game ◽  
Numerical Solutions ◽  
Game Problem ◽  
Gap Function ◽  
Differential Variational Inequality ◽  
Air Combat

The strategy of unmanned aerial vehicle air combat can be described as a differential game problem. The analytical solutions for the general differential game problem are usually difficult to obtain. In most cases, we can only get its numerical solutions. In this paper, a Nash differential game problem is converted to the corresponding differential variational inequality problem, and then converted into optimal control problem via D-gap function. The nonlinear continuous optimal control problem is obtained, which is easy to get numerical solutions. Compared with other conversion methods, the specific solving process of this method is more simple, so it has certain validity and feasibility.

scholarly journals A zero sum differential game in a Hilbert space

2003 ◽  
Vol 283 (1) ◽  
pp. 167-179
Author(s):  
Mrinal K. Ghosh ◽  
A.K. Nandakumaran ◽  
K.S. Mallikarjuna Rao
Keyword(s):  
Hilbert Space ◽  
Differential Game ◽  
Zero Sum

scholarly journals An evasion differential game problem on the plane

2019 ◽  
Vol 11 (2) ◽  
pp. 229
Author(s):  
A.J. Badakaya ◽  
M.A. Umar
Keyword(s):  
Differential Game ◽  
Game Problem
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