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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 674651, 6 pages
http://dx.doi.org/10.1155/2014/674651
Research Article

An Approach for Solving Discrete Game Problems with Total Constraints on Controls

1Department of Informatics, Tashkent University of Information Technologies (TUIT), Amir Temur Street 108, 100202 Tashkent, Uzbekistan
2Institute for Mathematical Research and Department of Mathematics, Faculty of Science, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 12 November 2013; Revised 5 March 2014; Accepted 11 March 2014; Published 17 April 2014

Academic Editor: Valery Y. Glizer

Copyright © 2014 Asqar Raxmonov and Gafurjan I. Ibragimov. 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.

Abstract

We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Controls of the players satisfy total constraints. Terminal set is a subset of and it is assumed to have nonempty interior. Game is said to be completed if at some step . To construct the control of the pursuer, at each step , we use positions of the players from step 1 to step and the value of the control parameter of the evader at the step . We give sufficient conditions of completion of pursuit and construct the control for the pursuer in explicit form. This control forces the evader to expend some amount of his resources on a period consisting of finite steps. As a result, after several such periods the evader exhausted his energy and then pursuit will be completed.