Selected pursuit and evasion differential game problems in Hilbert space

This thesis deals with the solution of some pursuit and evasion differential game problems described by some models in Hilbert space. The models arise from the solution of pursuit and evasion game problems described by some partial differential equations. Three different type of models are considere...

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Main Author:	Ja'afaru, Abbas Badakaya
Format:	Thesis
Language:	English
Published:	2012
Subjects:	Hilbert space
Online Access:	http://psasir.upm.edu.my/id/eprint/66797/1/FS%202012%2092%20IR.pdf
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spelling	my-upm-ir.667972019-02-01T00:25:41Z Selected pursuit and evasion differential game problems in Hilbert space 2012-05 Ja'afaru, Abbas Badakaya This thesis deals with the solution of some pursuit and evasion differential game problems described by some models in Hilbert space. The models arise from the solution of pursuit and evasion game problems described by some partial differential equations. Three different type of models are considered, where for each model, we solve pursuit and evasion problem with some forms of constraints on controls of the players. The first model is the infinite system of first order differential equations z˙k(t) + kz(t) = −uk(t) + vk(t), zk(0) = zk0, k = 1, 2, . . . , where zk, uk, vk, zk0 2 R1, z0 = (z10, z20, . . . ) 2 l2 r+1, u = (u1, u2, . . . ) is the control parameter of the pursuer, v = (v1, v2, . . . ) is that of the evader and 1, 2, . . . is a bounded sequence of negative numbers. For this model, we present solution of optimal pursuit problem, where the controls of the players are subjected to integral constraints. Secondly, we consider z˙k(t) + k(t)zk(t) = −uk(t) + vk(t), zk(0) = zk0, k = 1, 2, . . . , where z0 = (z10, z20, . . . ) 2 l2, k(t), k = 1, 2, . . . , are bounded, non-negative continuous functions such that k(0) = 0, k = 1, 2, . . . , on the interval [0, T] and all other parameters are defined as in the first model. In this case, we solve pursuit and evasion problems with integral, geometric, and mix constraints on control functions of the players. The third model is given by z¨k(t) + kz(t) = −uk(t) + vk(t), zk(0) = zk0, z˙k(0) = zk1, k = 1, 2, . . . , where zk, uk, vk 2 R1, k = 1, 2, . . . , z0 = (z10, z20, . . . ) 2 l2 r+1, z1 = (z11, z21, . . . ) 2 l2 r , u = (u1, u2, . . . ) is the control parameter of the pursuer and v = (v1, v2, . . . ) is the control parameter of the evader. Conditions for the solvability of pursuit and evasion problems described by this model are obtained. Furthermore, we also study control problems related to each of the three models. In the case of first and third models, necessary and sufficient conditions for which the state of the systems can be transfered to the origin are presented. Sufficient conditions are given for the control problem described by the second model for the cases of geometric and integral constraints on the control functions. Hilbert space 2012-05 Thesis http://psasir.upm.edu.my/id/eprint/66797/ http://psasir.upm.edu.my/id/eprint/66797/1/FS%202012%2092%20IR.pdf text en public doctoral Universiti Putra Malaysia Hilbert space
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Hilbert space
spellingShingle	Hilbert space Ja'afaru, Abbas Badakaya Selected pursuit and evasion differential game problems in Hilbert space
description	This thesis deals with the solution of some pursuit and evasion differential game problems described by some models in Hilbert space. The models arise from the solution of pursuit and evasion game problems described by some partial differential equations. Three different type of models are considered, where for each model, we solve pursuit and evasion problem with some forms of constraints on controls of the players. The first model is the infinite system of first order differential equations z˙k(t) + kz(t) = −uk(t) + vk(t), zk(0) = zk0, k = 1, 2, . . . , where zk, uk, vk, zk0 2 R1, z0 = (z10, z20, . . . ) 2 l2 r+1, u = (u1, u2, . . . ) is the control parameter of the pursuer, v = (v1, v2, . . . ) is that of the evader and 1, 2, . . . is a bounded sequence of negative numbers. For this model, we present solution of optimal pursuit problem, where the controls of the players are subjected to integral constraints. Secondly, we consider z˙k(t) + k(t)zk(t) = −uk(t) + vk(t), zk(0) = zk0, k = 1, 2, . . . , where z0 = (z10, z20, . . . ) 2 l2, k(t), k = 1, 2, . . . , are bounded, non-negative continuous functions such that k(0) = 0, k = 1, 2, . . . , on the interval [0, T] and all other parameters are defined as in the first model. In this case, we solve pursuit and evasion problems with integral, geometric, and mix constraints on control functions of the players. The third model is given by z¨k(t) + kz(t) = −uk(t) + vk(t), zk(0) = zk0, z˙k(0) = zk1, k = 1, 2, . . . , where zk, uk, vk 2 R1, k = 1, 2, . . . , z0 = (z10, z20, . . . ) 2 l2 r+1, z1 = (z11, z21, . . . ) 2 l2 r , u = (u1, u2, . . . ) is the control parameter of the pursuer and v = (v1, v2, . . . ) is the control parameter of the evader. Conditions for the solvability of pursuit and evasion problems described by this model are obtained. Furthermore, we also study control problems related to each of the three models. In the case of first and third models, necessary and sufficient conditions for which the state of the systems can be transfered to the origin are presented. Sufficient conditions are given for the control problem described by the second model for the cases of geometric and integral constraints on the control functions.
format	Thesis
qualification_level	Doctorate
author	Ja'afaru, Abbas Badakaya
author_facet	Ja'afaru, Abbas Badakaya
author_sort	Ja'afaru, Abbas Badakaya
title	Selected pursuit and evasion differential game problems in Hilbert space
title_short	Selected pursuit and evasion differential game problems in Hilbert space
title_full	Selected pursuit and evasion differential game problems in Hilbert space
title_fullStr	Selected pursuit and evasion differential game problems in Hilbert space
title_full_unstemmed	Selected pursuit and evasion differential game problems in Hilbert space
title_sort	selected pursuit and evasion differential game problems in hilbert space
granting_institution	Universiti Putra Malaysia
publishDate	2012
url	http://psasir.upm.edu.my/id/eprint/66797/1/FS%202012%2092%20IR.pdf
_version_	1747812408277073920

Selected pursuit and evasion differential game problems in Hilbert space

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