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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 840925, 5 pages
Research Article

Linear Discrete Pursuit Game Problem with Total Constraints

1Institute of Mathematics of Uzbekistan, 29 Dorman yuli Street, 100125 Tashkent, Uzbekistan
2Institute for Mathematical Research and Department of Mathematics, Faculty of Science (FS), Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 8 March 2013; Revised 28 May 2013; Accepted 28 May 2013

Academic Editor: Valery Y. Glizer

Copyright © 2013 Atamurat Kuchkarov et al. 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 study a linear discrete pursuit game problem of one pursuer and one evader. Control vectors of the players are subjected to total constraints which are discrete analogs of the integral constraints. By definition pursuit can be completed in the game if there exists a strategy of the pursuer such that for any control of the evader the state of system reaches the origin at some time. We obtain sufficient conditions of completion of the game from any initial position of the state space. Strategy of the pursuer is defined as a function of the current state of system and value of control parameter of the evader.