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Journal of Applied Mathematics
Volume 2012, Article ID 748096, 10 pages
Research Article

Simple Motion Evasion Differential Game of Many Pursuers and One Evader with Integral Constraints on Control Functions of Players

INSPEM and Department of Mathematics, UPM, 43400 Serdang, Malaysia

Received 7 May 2012; Revised 15 September 2012; Accepted 15 September 2012

Academic Editor: Alexander Timokha

Copyright © 2012 Gafurjan Ibragimov and Yusra Salleh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider an evasion differential game of many pursuers and one evader with integral constraints in the plane. The game is described by simple equations. Each component of the control functions of players is subjected to integral constraint. Evasion is said to be possible if the state of the evader does not coincide with that of any pursuer. Strategy of the evader is constructed based on controls of the pursuers with lag. A sufficient condition of evasion from many pursuers is obtained and an illustrative example is provided.