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.

On two pursuit differential game problems with state and geometric constraints in a Hilbert space

2021 ◽  
Vol 65 (3) ◽  
pp. 5-16
Author(s):  
Abbas Ja’afaru Badakaya ◽  
Keyword(s):  
Differential Game ◽  
Convex Set ◽  
Sufficient Conditions ◽  
Nonempty Closed Convex Subset ◽  
Geometric Constraints ◽  
First Order ◽  
Control Functions ◽  
Closed Convex Set ◽  
The Given ◽  
First Order Differential Equations

This paper concerns with the study of two pursuit differential game problems of many pursuers and many evaders on a nonempty closed convex subset of R^n. Throughout the period of the games, players must stay within the given closed convex set. Players’ laws of motion are defined by certain first order differential equations. Control functions of the pursuers and evaders are subject to geometric constraints. Pursuit is said to be completed if the geometric position of each of the evader coincides with that of a pursuer. We proved two theorems each of which is solution to a problem. Sufficient conditions for the completion of pursuit are provided in each of the theorems. Moreover, we constructed strategies of the pursuers that ensure completion of pursuit.

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 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 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

SOLUTION OF SIMPLE PURSUIT-EVASION PROBLEM WHEN EVADER MOVES ON A GIVEN CURVE

2010 ◽  
Vol 12 (03) ◽  
pp. 223-238 ◽  
Author(s):  
ATAMURAT SH. KUCHKAROV
Keyword(s):  
Differential Game ◽  
Sufficient Conditions ◽  
Initial Position ◽  
Necessary And Sufficient Conditions ◽  
Phase Constraint ◽  
Simple Motion ◽  
Pursuit Evasion ◽  
Evasion Problem ◽  
Necessary And Sufficient

We investigate a simple motion pursuit-evasion differential game of one Pursuer and one Evader. Maximal speeds of the players are equal. The Evader moves along a given curve without self-intersection. There is no phase constraint for the Pursuer. Necessary and sufficient conditions to complete pursuit from both fixed initial position and all initial positions are obtained.

scholarly journals EVASION FROM ONE PURSUER IN A HILBERT SPACE

2012 ◽  
Vol 09 ◽  
pp. 529-536
Author(s):  
FATEH ALLAHABI ◽  
G.I. IBRAGIMOV
Keyword(s):  
Hilbert Space ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Differential Game ◽  
Hilbert Spaces ◽  
Second Order ◽  
Geometric Constraints ◽  
Infinite Systems

We study a differential game of one pursuer and one evader described by infinite systems of second order ordinary differential equations. Controls of players are subjected to geometric constraints. Differential game is considered in Hilbert spaces. We proved one theorem on evasion. Moreover, we constructed explicitly a control of the evader.

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 Pursuit-Evasion Differential Game with Many Inertial Players

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Gafurjan I. Ibragimov ◽  
Mehdi Salimi
Keyword(s):  
Hilbert Space ◽  
Lower Bound ◽  
Differential Game ◽  
Optimal Strategies ◽  
Countable Number ◽  
Integral Constraints ◽  
Pursuit Evasion ◽  
Value Of The Game ◽  
Control Functions

We consider pursuit-evasion differential game of countable number inertial players in Hilbert space with integral constraints on the control functions of players. Duration of the game is fixed. The payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. The pursuers try to minimize the functional, and the evader tries to maximize it. In this paper, we find the value of the game and construct optimal strategies of the players.

scholarly journals Simple Motion Evasion Differential Game of Many Pursuers and One Evader with Integral Constraints on Control Functions of Players

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Gafurjan Ibragimov ◽  
Yusra Salleh
Keyword(s):  
Differential Game ◽  
The State ◽  
Sufficient Condition ◽  
Integral Constraint ◽  
Simple Motion ◽  
Integral Constraints ◽  
Control Functions ◽  
Simple Equations

We consider an evasion differential game of many pursuers and one evader with integral constraints in the plane. The game is described by simple equations. Each component of the control functions of players is subjected to integral constraint. Evasion is said to be possible if the state of the evader does not coincide with that of any pursuer. Strategy of the evader is constructed based on controls of the pursuers with lag. A sufficient condition of evasion from many pursuers is obtained and an illustrative example is provided.

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
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