Differential games with many pursuers and integral constraints on controls of players

Control and differential game problems, with dynamics described by parabolic and hyperbolic partial differential equations attract the attention of many researchers. Some of these problems can be reduced to the one described by infinite systems of ordinary differential equations by using the decompo...

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Main Author:	Ali Allahabi, Fateh Abdo
Format:	Thesis
Language:	English English
Published:	2011
Subjects:	Differential games
Online Access:	http://psasir.upm.edu.my/id/eprint/25929/1/FS%202011%2062R.pdf
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id	my-upm-ir.25929
record_format	uketd_dc
spelling	my-upm-ir.259292022-01-26T05:13:02Z Differential games with many pursuers and integral constraints on controls of players 2011-11 Ali Allahabi, Fateh Abdo Control and differential game problems, with dynamics described by parabolic and hyperbolic partial differential equations attract the attention of many researchers. Some of these problems can be reduced to the one described by infinite systems of ordinary differential equations by using the decomposition method. The main purpose of this thesis is to study the differential game problems described by an infinite system of 2-systems of second order differential equations, and it is extension to multi-player pursuit-evasion differential game problems, with various constraints, on control functions of players. The existence and uniqueness theorem in the space C(0, T; l2 r ) is proved. Built on this, an optimal control for the control system described by an infinite system of differential equations with integral constraint is presented. The optimal control result is extended to study a pursuit differential game problem with the integral constrains on the controls of players. The goal of the Pursuer is to force the system and its velocity to the origin on the spaces l2 r+1 and l2r respectively, and the Evader exactly tries to avoid this. In addition to this, a theorem on pursuit with mixed constraints is proved, where Pursuers control is subjected to integral constraint and geometric constraint is imposed on Evaders control. Moreover, we established the sufficient conditions for which evasion is possible in the game considered, with geometric constraints on the control of players. Furthermore, control of the Evader is constructed in an explicit form. Finally, a pursuit-evasion game with m Pursuer and one Evader are studied. In the pursuit game we present sufficient condition for which the Pursuers can bring the state of the system and its velocity into the origin for a finite time. For the evasion game we state and prove a theorem for which evasion is possible from any initial position Differential games 2011-11 Thesis http://psasir.upm.edu.my/id/eprint/25929/ http://psasir.upm.edu.my/id/eprint/25929/1/FS%202011%2062R.pdf application/pdf en public doctoral Universiti Putra Malaysia Differential games Faculty of Science English
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English English
topic	Differential games
spellingShingle	Differential games Ali Allahabi, Fateh Abdo Differential games with many pursuers and integral constraints on controls of players
description	Control and differential game problems, with dynamics described by parabolic and hyperbolic partial differential equations attract the attention of many researchers. Some of these problems can be reduced to the one described by infinite systems of ordinary differential equations by using the decomposition method. The main purpose of this thesis is to study the differential game problems described by an infinite system of 2-systems of second order differential equations, and it is extension to multi-player pursuit-evasion differential game problems, with various constraints, on control functions of players. The existence and uniqueness theorem in the space C(0, T; l2 r ) is proved. Built on this, an optimal control for the control system described by an infinite system of differential equations with integral constraint is presented. The optimal control result is extended to study a pursuit differential game problem with the integral constrains on the controls of players. The goal of the Pursuer is to force the system and its velocity to the origin on the spaces l2 r+1 and l2r respectively, and the Evader exactly tries to avoid this. In addition to this, a theorem on pursuit with mixed constraints is proved, where Pursuers control is subjected to integral constraint and geometric constraint is imposed on Evaders control. Moreover, we established the sufficient conditions for which evasion is possible in the game considered, with geometric constraints on the control of players. Furthermore, control of the Evader is constructed in an explicit form. Finally, a pursuit-evasion game with m Pursuer and one Evader are studied. In the pursuit game we present sufficient condition for which the Pursuers can bring the state of the system and its velocity into the origin for a finite time. For the evasion game we state and prove a theorem for which evasion is possible from any initial position
format	Thesis
qualification_level	Doctorate
author	Ali Allahabi, Fateh Abdo
author_facet	Ali Allahabi, Fateh Abdo
author_sort	Ali Allahabi, Fateh Abdo
title	Differential games with many pursuers and integral constraints on controls of players
title_short	Differential games with many pursuers and integral constraints on controls of players
title_full	Differential games with many pursuers and integral constraints on controls of players
title_fullStr	Differential games with many pursuers and integral constraints on controls of players
title_full_unstemmed	Differential games with many pursuers and integral constraints on controls of players
title_sort	differential games with many pursuers and integral constraints on controls of players
granting_institution	Universiti Putra Malaysia
granting_department	Faculty of Science
publishDate	2011
url	http://psasir.upm.edu.my/id/eprint/25929/1/FS%202011%2062R.pdf
_version_	1747811534149517312

Differential games with many pursuers and integral constraints on controls of players

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