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 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 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 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 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 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

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.

scholarly journals Two-Stage Pursuit Strategy for Incomplete-Information Impulsive Space Pursuit-Evasion Mission Using Reinforcement Learning

Aerospace ◽  
2021 ◽  
Vol 8 (10) ◽  
pp. 299
Author(s):  
Bin Yang ◽  
Pengxuan Liu ◽  
Jinglang Feng ◽  
Shuang Li
Keyword(s):  
Reinforcement Learning ◽  
Incomplete Information ◽  
Trajectory Optimization ◽  
Game Problem ◽  
Gradient Algorithm ◽  
Two Stage ◽  
Pursuit Evasion ◽  
Evasion Game ◽  
Close Distance ◽  
Pursuit Strategy

This paper presents a novel and robust two-stage pursuit strategy for the incomplete-information impulsive space pursuit-evasion missions considering the J2 perturbation. The strategy firstly models the impulsive pursuit-evasion game problem into a far-distance rendezvous stage and a close-distance game stage according to the perception range of the evader. For the far-distance rendezvous stage, it is transformed into a rendezvous trajectory optimization problem and a new objective function is proposed to obtain the pursuit trajectory with the optimal terminal pursuit capability. For the close-distance game stage, a closed-loop pursuit approach is proposed using one of the reinforcement learning algorithms, i.e., the deep deterministic policy gradient algorithm, to solve and update the pursuit trajectory for the incomplete-information impulsive pursuit-evasion missions. The feasibility of this novel strategy and its robustness to different initial states of the pursuer and evader and to the evasion strategies are demonstrated for the sun-synchronous orbit pursuit-evasion game scenarios. The results of the Monte Carlo tests show that the successful pursuit ratio of the proposed method is over 91% for all the given scenarios.

Hybrid Method Based on Artificial Potential Field and Differential Game Theory for the UAV Path Planing

2014 ◽  
Vol 687-691 ◽  
pp. 260-264
Author(s):  
Feng Tian ◽  
Ji Feng Zou ◽  
Tong Zhang
Keyword(s):  
Game Theory ◽  
Differential Game ◽  
Potential Field ◽  
Artificial Potential Field ◽  
Complex Environment ◽  
Pursuit Evasion ◽  
Differential Game Theory ◽  
Evasion Game ◽  
Simulation Results ◽  
Dynamic Path

In this paper, a method of the UAV path planing in the complex environment by using artificial potential field and differential game theory is introduced. This article studies the pursuit evasion game of the dynamic path planing for the UAV. The fly zone of either the pursuer or the evader is divided into two categories, namely the obstacle areas and the obstacle-free areas. So we can use the artificial potential field in the obstacle areas,and we use differential game theory in the obstacle-free areas for the UAV. This method can apply to pursuit-evasion game in the complex environment for the UAV path planing.Not only the UAV can avoid obstacles but also they can find the best capture path.Finally,the simulation results verify its correctness and validity .

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