scholarly journals A simple motion differential game with different constraints on controls and under phase constraint on the state of the evader

2016 ◽  
Author(s):  
Askar Rakhmanov ◽  
Gafurjan Ibragimov
Keyword(s):  
Differential Game ◽  
The State ◽  
Phase Constraint ◽  
Simple Motion

scholarly journals Linear Pursuit Differential Game under Phase Constraint on the State of Evader

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Askar Rakhmanov ◽  
Gafurjan Ibragimov ◽  
Massimiliano Ferrara
Keyword(s):  
Differential Game ◽  
The State ◽  
Geometric Constraints ◽  
Phase Constraint ◽  
Phase Vector ◽  
Terminal Set

We consider a linear pursuit differential game of one pursuer and one evader. Controls of the pursuer and evader are subjected to integral and geometric constraints, respectively. In addition, phase constraint is imposed on the state of evader, whereas pursuer moves throughout the space. We say that pursuit is completed, if inclusiony(t1)-x(t1)∈Mis satisfied at somet1>0, wherex(t)andy(t)are states of pursuer and evader, respectively, andMis terminal set. Conditions of completion of pursuit in the game from all initial points of players are obtained. Strategy of the pursuer is constructed so that the phase vector of the pursuer first is brought to a given set, and then pursuit is completed.

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 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 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 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.

Observation of the State of a Differential Game

1985 ◽  
Vol 18 (2) ◽  
pp. 248-249
Author(s):  
Auloge Jean-Yves
Keyword(s):  
Differential Game ◽  
The State

Simple Motion Evasion Differential Game of Many Pursuers and Evaders with Integral Constraints

2017 ◽  
Vol 8 (2) ◽  
pp. 352-378 ◽  
Author(s):  
Gafurjan Ibragimov ◽  
Massimiliano Ferrara ◽  
Atamurat Kuchkarov ◽  
Bruno Antonio Pansera
Keyword(s):  
Differential Game ◽  
Simple Motion ◽  
Integral Constraints

THE VALUE FUNCTION OF A DIFFERENTIAL GAME WITH SIMPLE MOTIONS AND AN INTEGRO-TERMINAL COST

2018 ◽  
pp. 877-890
Author(s):  
Lyubov Gennad’evna Shagalova
Keyword(s):  
Differential Equation ◽  
State Space ◽  
Differential Game ◽  
Value Function ◽  
Piecewise Linear ◽  
The State ◽  
The Value Function

An antagonistic positional differential game of two persons is considered. The dynamics of the system is described by a differential equation with simple motions, and the payoff functional is integro-terminal. For the case when the terminal function and the Hamiltonian are piecewise linear, and the dimension of the state space is two, a finite algorithm for the exact construction of the value function is proposed.

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