scholarly journals Simple Motion Pursuit and Evasion Differential Games with Many Pursuers on Manifolds with Euclidean Metric

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Atamurat Kuchkarov ◽  
Gafurjan Ibragimov ◽  
Massimiliano Ferrara
Keyword(s):  
Euclidean Space ◽  
Differential Games ◽  
Differential Game ◽  
Finite Time ◽  
The State ◽  
Simple Motion ◽  
Euclidean Metric ◽  
Pursuit Game ◽  
Pursuit And Evasion ◽  
Evasion Game

We consider pursuit and evasion differential games of a group ofmpursuers and one evader on manifolds with Euclidean metric. The motions of all players are simple, and maximal speeds of all players are equal. If the state of a pursuer coincides with that of the evader at some time, we say that pursuit is completed. We establish that each of the differential games (pursuit or evasion) is equivalent to a differential game ofmgroups of countably many pursuers and one group of countably many evaders in Euclidean space. All the players in any of these groups are controlled by one controlled parameter. We find a condition under which pursuit can be completed, and if this condition is not satisfied, then evasion is possible. We construct strategies for the pursuers in pursuit game which ensure completion the game for a finite time and give a formula for this time. In the case of evasion game, we construct a strategy for the evader.

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 A Simplified Pursuit-evasion Game with Reinforcement Learning

2021 ◽  
Vol 65 (2) ◽  
pp. 160-166
Author(s):  
Gabor Paczolay ◽  
Istvan Harmati
Keyword(s):  
Linear Programming ◽  
Reinforcement Learning ◽  
Programming Problem ◽  
Collision Avoidance ◽  
Linear Programming Problem ◽  
The State ◽  
State Information ◽  
Pursuit Evasion ◽  
Pursuit And Evasion ◽  
Evasion Game

In this paper we visit the problem of pursuit and evasion and specifically, the collision avoidance during the problem. Two distinct tasks are visited: the first is a scenario when the agents can communicate with each other online, meanwhile in the second scenario they have to only rely on the state information and the knowledge about other agents' actions. We propose a method combining the already existing Minimax-Q and Nash-Q algorithms to provide a solution that can better take the enemy as well as friendly agents' actions into consideration. This combination is a simple weighting of the two algorithms with the Minimax-Q algorithm being based on a linear programming problem.

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 PURSUIT-EVASION DIFFERENTIAL GAMES WITH THE GRÖNWALL TYPE CONSTRAINTS ON CONTROLS

2020 ◽  
Vol 6 (2) ◽  
pp. 95
Author(s):  
Bahrom T. Samatov ◽  
Gafurjan Ibragimov ◽  
Iroda V. Khodjibayeva
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Optimal Strategy ◽  
Optimal Strategies ◽  
The State ◽  
Differential Constraints ◽  
Quality Problem ◽  
Pursuit Evasion ◽  
Optimal Pursuit ◽  
Pursuit Strategy

A simple pursuit-evasion differential game of one pursuer and one evader is studied. The players' controls are subject to differential constraints in the form of the integral Grönwall inequality. The pursuit is considered completed if the state of the pursuer coincides with the state of the evader. The main goal of this work is to construct optimal strategies for the players and find the optimal pursuit time. A parallel approach strategy for Grönwall-type constraints is constructed and it is proved that it is the optimal strategy of the pursuer. In addition, the optimal strategy of the evader is constructed and the optimal pursuit time is obtained. The concept of a parallel pursuit strategy (\(\Pi\)-strategy for short) was introduced and used to solve the quality problem for "life-line" games by L.A.Petrosjan. This work develops and expands the works of Isaacs, Petrosjan, Pshenichnyi, and other researchers, including the authors.

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.

scholarly journals Finite-Time Boundedness for a Class of Delayed Markovian Jumping Neural Networks with Partly Unknown Transition Probabilities

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Li Liang
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Transition Probabilities ◽  
The State ◽  
Time Interval ◽  
Finite Time Interval ◽  
Markovian Jumping ◽  
Stochastic Boundedness ◽  
Partly Unknown Transition Probabilities ◽  
Finite Time Boundedness

This paper is concerned with the problem of finite-time boundedness for a class of delayed Markovian jumping neural networks with partly unknown transition probabilities. By introducing the appropriate stochastic Lyapunov-Krasovskii functional and the concept of stochastically finite-time stochastic boundedness for Markovian jumping neural networks, a new method is proposed to guarantee that the state trajectory remains in a bounded region of the state space over a prespecified finite-time interval. Finally, numerical examples are given to illustrate the effectiveness and reduced conservativeness of the proposed results.

DETERMINISTIC DIFFERENTIAL GAMES UNDER PROBABILITY KNOWLEDGE OF INITIAL CONDITION

2008 ◽  
Vol 10 (01) ◽  
pp. 1-16 ◽  
Author(s):  
P. CARDALIAGUET ◽  
M. QUINCAMPOIX
Keyword(s):  
Differential Games ◽  
Differential Game ◽  
Random Distribution ◽  
Uniqueness Result ◽  
Initial Condition ◽  
Initial State ◽  
Lack Of Information ◽  
In The Beginning ◽  
Zero Sum ◽  
Future Work

We study a zero-sum differential game where the players have only an unperfect information on the state of the system. In the beginning of the game only a random distribution on the initial state is available. The main result of the paper is the existence of the value obtained through an uniqueness result for Hamilton-Jacobi-Isaacs equations stated on the space of measure in ℝn. This result is the first step for future work on differential games with lack of information.

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