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.

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

scholarly journals Linear evasion differential game of one evader and several pursuers with integral constraints

2021 ◽  
Author(s):  
Gafurjan Ibragimov ◽  
Massimiliano Ferrara ◽  
Marks Ruziboev ◽  
Bruno Antonio Pansera
Keyword(s):  
Positive Integer ◽  
Differential Equations ◽  
Total Energy ◽  
Differential Game ◽  
Linear Differential Equations ◽  
State Variables ◽  
Integral Constraints ◽  
Control Functions ◽  
Evasion Strategy ◽  
Linear Differential

AbstractAn evasion differential game of one evader and many pursuers is studied. The dynamics of state variables $$x_1,\ldots , x_m$$ x 1 , … , x m are described by linear differential equations. The control functions of players are subjected to integral constraints. If $$x_i(t) \ne 0$$ x i ( t ) ≠ 0 for all $$i \in \{1,\ldots ,m\}$$ i ∈ { 1 , … , m } and $$t \ge 0$$ t ≥ 0 , then we say that evasion is possible. It is assumed that the total energy of pursuers doesn’t exceed the energy of evader. We construct an evasion strategy and prove that for any positive integer m evasion is possible.

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 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 Evasion from many pursuers in simple motion differential game with integral constraints

2012 ◽  
Vol 218 (2) ◽  
pp. 505-511 ◽  
Author(s):  
Gafurjan I. Ibragimov ◽  
Mehdi Salimi ◽  
Massoud Amini
Keyword(s):  
Differential Game ◽  
Simple Motion ◽  
Integral Constraints

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.

The Power of Public Positions

2018 ◽  
Author(s):  
Thomas Sinclair
Keyword(s):  
Detailed Analysis ◽  
Political Authority ◽  
The State ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
State Institutions ◽  
State Of Nature ◽  
Necessary And Sufficient

The Kantian account of political authority holds that the state is a necessary and sufficient condition of our freedom. We cannot be free outside the state, Kantians argue, because any attempt to have the “acquired rights” necessary for our freedom implicates us in objectionable relations of dependence on private judgment. Only in the state can this problem be overcome. But it is not clear how mere institutions could make the necessary difference, and contemporary Kantians have not offered compelling explanations. A detailed analysis is presented of the problems Kantians identify with the state of nature and the objections they face in claiming that the state overcomes them. A response is sketched on behalf of Kantians. The key idea is that under state institutions, a person can make claims of acquired right without presupposing that she is by nature exceptional in her capacity to bind others.

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.

State Feedback Robust H∞ Control for Generalized Discrete System and Simulation

2013 ◽  
Vol 467 ◽  
pp. 621-626
Author(s):  
Chen Fang ◽  
Jiang Hong Shi ◽  
Kun Yu Li ◽  
Zheng Wang
Keyword(s):  
Discrete System ◽  
State Feedback ◽  
Closed Loop ◽  
The State ◽  
Linear Matrix ◽  
Sufficient Condition ◽  
Matrix Inequalities ◽  
Parameter Uncertainties ◽  
Robust Controller ◽  
Closed Loop Systems

For a class of uncertain generalized discrete linear system with norm-bounded parameter uncertainties, the state feedback robust control problem is studied. One sufficient condition for the solvability of the problem and the state feedback robust controller are obtained in terms of linear matrix inequalities. The designed controller guarantees that the closed-loop systems is regular, causal, stable and satisfies a prescribed norm bounded constraint for all admissible uncertain parameters under some conditions. The result of the normal discrete system can be regarded as a particular form of our conclusion. A simulation example is given to demonstrate the effectiveness of the proposed method.

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