An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers
The objective of this paper is to study a pursuit differential game with finite or countably number of pursuers and one evader. The game is described by differential equations in <inline-formula> <math display="inline"> <semantics> <msub> <mi>l</mi> <...
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doaj-f41521e620f1407ea5757de457d075a92020-11-25T01:23:30ZengMDPI AGMathematics2227-73902019-09-017984210.3390/math7090842math7090842An Optimal Pursuit Differential Game Problem with One Evader and Many PursuersIdris Ahmed0Poom Kumam1Gafurjan Ibragimov2Jewaidu Rilwan3Wiyada Kumam4KMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandKMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandInstitute for Mathematical Research and Department of Mathematics, Faculty of Science (FS), Universiti Putra Malaysia, Selangor, Serdang 43400, MalaysiaKMUTTFixed Point Research Laboratory, Room SCL 802 Fixed Point Laboratory, KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Science Laboratory Building, Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, ThailandProgram in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Thanyaburi, Pathumthani 12110, ThailandThe objective of this paper is to study a pursuit differential game with finite or countably number of pursuers and one evader. The game is described by differential equations in <inline-formula> <math display="inline"> <semantics> <msub> <mi>l</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula>-space, and integral constraints are imposed on the control function of the players. The duration of the game is fixed and the payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. However, we discuss the condition for finding the value of the game and construct the optimal strategies of the players which ensure the completion of the game. An important fact to note is that we relaxed the usual conditions on the energy resources of the players. Finally, some examples are provided to illustrate our result.https://www.mdpi.com/2227-7390/7/9/842pursuitcontrol functionsintegral constraintsstrategiesvalue of the game |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Idris Ahmed Poom Kumam Gafurjan Ibragimov Jewaidu Rilwan Wiyada Kumam |
spellingShingle |
Idris Ahmed Poom Kumam Gafurjan Ibragimov Jewaidu Rilwan Wiyada Kumam An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers Mathematics pursuit control functions integral constraints strategies value of the game |
author_facet |
Idris Ahmed Poom Kumam Gafurjan Ibragimov Jewaidu Rilwan Wiyada Kumam |
author_sort |
Idris Ahmed |
title |
An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers |
title_short |
An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers |
title_full |
An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers |
title_fullStr |
An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers |
title_full_unstemmed |
An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers |
title_sort |
optimal pursuit differential game problem with one evader and many pursuers |
publisher |
MDPI AG |
series |
Mathematics |
issn |
2227-7390 |
publishDate |
2019-09-01 |
description |
The objective of this paper is to study a pursuit differential game with finite or countably number of pursuers and one evader. The game is described by differential equations in <inline-formula> <math display="inline"> <semantics> <msub> <mi>l</mi> <mn>2</mn> </msub> </semantics> </math> </inline-formula>-space, and integral constraints are imposed on the control function of the players. The duration of the game is fixed and the payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. However, we discuss the condition for finding the value of the game and construct the optimal strategies of the players which ensure the completion of the game. An important fact to note is that we relaxed the usual conditions on the energy resources of the players. Finally, some examples are provided to illustrate our result. |
topic |
pursuit control functions integral constraints strategies value of the game |
url |
https://www.mdpi.com/2227-7390/7/9/842 |
work_keys_str_mv |
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