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 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 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 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 Game of Optimal Pursuit for an Infinite System of Differential Equations

2017 ◽  
Vol 42 (1) ◽  
pp. 391-403 ◽  
Author(s):  
Gafurjan Ibragimov ◽  
Idham Arif Alias ◽  
Usman Waziri ◽  
Abbas Badakaya Ja’afaru
Keyword(s):  
Differential Equations ◽  
Differential Game ◽  
Infinite System ◽  
System Of Differential Equations ◽  
Optimal Pursuit

scholarly journals On time transformations for differential equations with state-dependent delay

2014 ◽  
Vol 12 (2) ◽  
Author(s):  
Alexander Rezounenko
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Asymptotic Properties ◽  
The State ◽  
Delay Systems ◽  
Constant Delay ◽  
Systems Of Differential Equations ◽  
State Dependent ◽  
State Dependent Delay ◽  
Time Transformations

AbstractSystems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state, i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.

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.

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.

Pursuit and Evasion Games for an Infinite System of Differential Equations

2021 ◽  
Author(s):  
Gafurjan Ibragimov ◽  
Massimiliano Ferrara ◽  
Idham Arif Alias ◽  
Mehdi Salimi ◽  
Nurzeehan Ismail
Keyword(s):  
Differential Equations ◽  
Infinite System ◽  
System Of Differential Equations ◽  
Pursuit And Evasion

scholarly journals Diffraction of Electromagnetic Waves on a Waveguide Joint

2018 ◽  
Vol 173 ◽  
pp. 02014 ◽  
Author(s):  
Mikhail Malykh ◽  
Leonid Sevastianov ◽  
Anastasiya Tyutyunnik ◽  
Nikolai Nikolaev
Keyword(s):  
Hilbert Space ◽  
Electromagnetic Field ◽  
Differential Equations ◽  
Helmholtz Equation ◽  
Computer Algebra ◽  
Electromagnetic Waves ◽  
Computer Algebra System ◽  
Infinite System ◽  
Hamiltonian Form ◽  
Helmholtz Equations

In general, the investigation of the electromagnetic field in an inhomogeneous waveguide doesn’t reduce to the study of two independent boundary value problems for the Helmholtz equation. We show how to rewrite the Helmholtz equations in the “Hamiltonian form” to express the connection between these two problems explicitly. The problem of finding monochromatic waves in an arbitrary waveguide is reduced to an infinite system of ordinary differential equations in a properly constructed Hilbert space. The calculations are performed in the computer algebra system Sage.

Infinite Systems of Differential Equations II

1979 ◽  
Vol 31 (3) ◽  
pp. 596-603 ◽  
Author(s):  
J. P. McClure ◽  
R. Wong
Keyword(s):  
Differential Equations ◽  
Infinite System ◽  
Nonlinear Differential Equations ◽  
Coefficient Matrix ◽  
Nonnegative Real Number ◽  
Initial Value ◽  
Infinite Systems ◽  
Systems Of Differential Equations ◽  
The Stability ◽  
Image Position

This paper is a continuation of earlier work [6], in which we studied the existence and the stability of solutions to the infinite system of nonlinear differential equations(1.1)i = 1, 2, …. Here s is a nonnegative real number, Rs = {t ∈ R: t ≧ s}, and denotes a sequence-valued function. Conditions on the coefficient matrix A(t) = [aij(t)] and the nonlinear perturbation were established which guarantee that for each initial value c= {ct} ∈ l1, the system (1.1) has a strongly continuous l1valued solution x(t) (i.e., each is continuous and converges uniformly on compact subsets of Rs). A theorem was also given which yields the exponential stability for the nonlinear system (1.1).

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