Evasion differential game from many pursuers of one evader whose control set is a sector

From mathematical point of view, game involves a number of players, a set of strategies for each player, and analysis of the game outcome which conclude either victory or defeat for each player involved. A common type of game is often called the pursuit-evasion game. Pursuit-evasion game is one of t...

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Main Author:	Syed Mafdzot, Sharifah Anisah
Format:	Thesis
Language:	English
Published:	2016
Subjects:	Differential games Game theory Control theory
Online Access:	http://psasir.upm.edu.my/id/eprint/75497/1/FS%202016%2025%20-%20IR.pdf
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spelling	my-upm-ir.754972019-11-26T01:55:05Z Evasion differential game from many pursuers of one evader whose control set is a sector 2016-02 Syed Mafdzot, Sharifah Anisah From mathematical point of view, game involves a number of players, a set of strategies for each player, and analysis of the game outcome which conclude either victory or defeat for each player involved. A common type of game is often called the pursuit-evasion game. Pursuit-evasion game is one of the widely studied game theory where it involves players of two opposite sides, which are pursuer and evader. The pursuer’s goal is to capture the evader while oppositely, the evader is to avoid being captured. Strategy to be constructed for players depend on the purpose of the game. It can be solved as an evasion problem for the evader. In this case, strategy for evader will be constructed and behavior of the pursuer is assumed to be any. On the other hand, the game could also be a pursuit problem and thus construction of the strategy is for the pursuer, with assumption that the evader can move freely. In this thesis, we study an evasion differential game of many pursuers x₁; : : : ;xm against one evader y in the plane R2. Movements of the players are described by simple differential equations. Control functions of players are subjected to geometric constraints where maximum speed of each pursuer is equal to 1, and maximum speed of the evader is a > 1. Control set of the evader is a sector S with radius a. We say that evasion is possible if xi(t) 6= y(t) for all t ≥ 0 and i = 1; : : : ;m. In other words, the evasion problem is solved when it is proved that the position of the evader never coincides with the position of each pursuer at all time. To achieve the solution, conditions of evasion that guarantee the evasion from any initial positions of players are to be found. We examine game with one pursuer by constructing the evader’s strategy, checking the admissibility, and estimating distances between the evader and pursuer for the possibility of evasion. Then we show that evasion game is solvable for the case of k pursuers. The motivation behind the study is to construct a new admissible strategy for the evasion to be possible in the evasion differential game of one evader versus many pursuers, which were studied in many works before. Differential games Game theory Control theory 2016-02 Thesis http://psasir.upm.edu.my/id/eprint/75497/ http://psasir.upm.edu.my/id/eprint/75497/1/FS%202016%2025%20-%20IR.pdf text en public masters Universiti Putra Malaysia Differential games Game theory Control theory
institution	Universiti Putra Malaysia
collection	PSAS Institutional Repository
language	English
topic	Differential games Game theory Control theory
spellingShingle	Differential games Game theory Control theory Syed Mafdzot, Sharifah Anisah Evasion differential game from many pursuers of one evader whose control set is a sector
description	From mathematical point of view, game involves a number of players, a set of strategies for each player, and analysis of the game outcome which conclude either victory or defeat for each player involved. A common type of game is often called the pursuit-evasion game. Pursuit-evasion game is one of the widely studied game theory where it involves players of two opposite sides, which are pursuer and evader. The pursuer’s goal is to capture the evader while oppositely, the evader is to avoid being captured. Strategy to be constructed for players depend on the purpose of the game. It can be solved as an evasion problem for the evader. In this case, strategy for evader will be constructed and behavior of the pursuer is assumed to be any. On the other hand, the game could also be a pursuit problem and thus construction of the strategy is for the pursuer, with assumption that the evader can move freely. In this thesis, we study an evasion differential game of many pursuers x₁; : : : ;xm against one evader y in the plane R2. Movements of the players are described by simple differential equations. Control functions of players are subjected to geometric constraints where maximum speed of each pursuer is equal to 1, and maximum speed of the evader is a > 1. Control set of the evader is a sector S with radius a. We say that evasion is possible if xi(t) 6= y(t) for all t ≥ 0 and i = 1; : : : ;m. In other words, the evasion problem is solved when it is proved that the position of the evader never coincides with the position of each pursuer at all time. To achieve the solution, conditions of evasion that guarantee the evasion from any initial positions of players are to be found. We examine game with one pursuer by constructing the evader’s strategy, checking the admissibility, and estimating distances between the evader and pursuer for the possibility of evasion. Then we show that evasion game is solvable for the case of k pursuers. The motivation behind the study is to construct a new admissible strategy for the evasion to be possible in the evasion differential game of one evader versus many pursuers, which were studied in many works before.
format	Thesis
qualification_level	Master's degree
author	Syed Mafdzot, Sharifah Anisah
author_facet	Syed Mafdzot, Sharifah Anisah
author_sort	Syed Mafdzot, Sharifah Anisah
title	Evasion differential game from many pursuers of one evader whose control set is a sector
title_short	Evasion differential game from many pursuers of one evader whose control set is a sector
title_full	Evasion differential game from many pursuers of one evader whose control set is a sector
title_fullStr	Evasion differential game from many pursuers of one evader whose control set is a sector
title_full_unstemmed	Evasion differential game from many pursuers of one evader whose control set is a sector
title_sort	evasion differential game from many pursuers of one evader whose control set is a sector
granting_institution	Universiti Putra Malaysia
publishDate	2016
url	http://psasir.upm.edu.my/id/eprint/75497/1/FS%202016%2025%20-%20IR.pdf
_version_	1747813058419359744

Evasion differential game from many pursuers of one evader whose control set is a sector

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