Differential games problems described by system of infinite differential equations in Hilbert space

This thesis deals with the solutions of differential game problems described by some infinite systems of ordinary differential equations in Hilbert space. The infinite system arises from the solution of some control and differential game of problems described by some partial differential equation...

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Main Author:	Waziri, Usman
Format:	Thesis
Language:	English
Published:	2018
Subjects:	Hilbert space Differential equations
Online Access:	http://psasir.upm.edu.my/id/eprint/68710/1/FS%202018%2035%20-%20IR.pdf
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spelling	my-upm-ir.687102019-06-11T02:02:27Z Differential games problems described by system of infinite differential equations in Hilbert space 2018-01 Waziri, Usman This thesis deals with the solutions of differential game problems described by some infinite systems of ordinary differential equations in Hilbert space. The infinite system arises from the solution of some control and differential game of problems described by some partial differential equations. By using decomposition method, some of these problems can be reduced to the one described by some infinite system of ordinary differential equations. Therefore, this thesis focuses on different types of infinite systems using various approaches in Hilbert space. The first system is an infinite system of first order differential equations, and the second system is an infinite system of 2-systems of first order differential equations. For all the systems, we study the existence and uniqueness, and then we consider control and differential game problems with some forms of constraints on controls of the players. For the first system, we present solution of optimal pursuit problems with negative coefficients, where the controls of the players are subjected to integral constraints. Pursuer’s goal is to force the state of the system toward the origin and the evader tries to avoid this. Secondly, we extend the first system and introduce another state away from that of the initial state. In this game, pursuer attempts to bring the state of the system toward another the evader’s purpose is opposite where we study pursuit game problems with negative coefficients. Furthermore, the second game is improved with various constraints and the coefficients assumed to be any real numbers, the condition of completion of pursuit with geometric and integral constraints is proposed. For the second system, we solve pursuit differential game problem of 2-system of first-order that involves a generalization of all considered games with conjugate complex, the case of integral constraints. The main findings and contributions of this thesis is to study differential game described by infinite system of differential equations. For the first system, we propose an optimal pursuit time. For the second the third cases, we propose a new approach of completion of pursuit and for the second system, a guaranteed pursuit time is also proposed. Hilbert space Differential equations 2018-01 Thesis http://psasir.upm.edu.my/id/eprint/68710/ http://psasir.upm.edu.my/id/eprint/68710/1/FS%202018%2035%20-%20IR.pdf text en public doctoral Universiti Putra Malaysia Hilbert space Differential equations
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Hilbert space Differential equations
spellingShingle	Hilbert space Differential equations Waziri, Usman Differential games problems described by system of infinite differential equations in Hilbert space
description	This thesis deals with the solutions of differential game problems described by some infinite systems of ordinary differential equations in Hilbert space. The infinite system arises from the solution of some control and differential game of problems described by some partial differential equations. By using decomposition method, some of these problems can be reduced to the one described by some infinite system of ordinary differential equations. Therefore, this thesis focuses on different types of infinite systems using various approaches in Hilbert space. The first system is an infinite system of first order differential equations, and the second system is an infinite system of 2-systems of first order differential equations. For all the systems, we study the existence and uniqueness, and then we consider control and differential game problems with some forms of constraints on controls of the players. For the first system, we present solution of optimal pursuit problems with negative coefficients, where the controls of the players are subjected to integral constraints. Pursuer’s goal is to force the state of the system toward the origin and the evader tries to avoid this. Secondly, we extend the first system and introduce another state away from that of the initial state. In this game, pursuer attempts to bring the state of the system toward another the evader’s purpose is opposite where we study pursuit game problems with negative coefficients. Furthermore, the second game is improved with various constraints and the coefficients assumed to be any real numbers, the condition of completion of pursuit with geometric and integral constraints is proposed. For the second system, we solve pursuit differential game problem of 2-system of first-order that involves a generalization of all considered games with conjugate complex, the case of integral constraints. The main findings and contributions of this thesis is to study differential game described by infinite system of differential equations. For the first system, we propose an optimal pursuit time. For the second the third cases, we propose a new approach of completion of pursuit and for the second system, a guaranteed pursuit time is also proposed.
format	Thesis
qualification_level	Doctorate
author	Waziri, Usman
author_facet	Waziri, Usman
author_sort	Waziri, Usman
title	Differential games problems described by system of infinite differential equations in Hilbert space
title_short	Differential games problems described by system of infinite differential equations in Hilbert space
title_full	Differential games problems described by system of infinite differential equations in Hilbert space
title_fullStr	Differential games problems described by system of infinite differential equations in Hilbert space
title_full_unstemmed	Differential games problems described by system of infinite differential equations in Hilbert space
title_sort	differential games problems described by system of infinite differential equations in hilbert space
granting_institution	Universiti Putra Malaysia
publishDate	2018
url	http://psasir.upm.edu.my/id/eprint/68710/1/FS%202018%2035%20-%20IR.pdf
_version_	1747812621627686912

Differential games problems described by system of infinite differential equations in Hilbert space

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