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The Scientific World Journal - Volume 2014 2014, Article ID 435103, 5 pages -

Research Article

Department of Informatics, Tashkent University of Information Technologies, TUIT, Amir Temur Street 108, 100202 Tashkent, Uzbekistan

Institute for Mathematical Research & Department of Mathematics, FS, Universiti Putra Malaysia, 43400 Serdang, Selangor, Malaysia

Received 1 June 2014; Accepted 31 August 2014; Published 30 October 2014

Academic Editor: Seenith Sivasundaram

Copyright © 2014 Asqar Raxmanov and Gafurjan 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.


We consider a linear pursuit game of one pursuer and one evader whose motions are described by different-type linear discrete systems. Position of the evader satisfies phase constraints: , where is a subset of . We considered two cases: 1 controls of the players satisfy geometric constraints, and 2 controls of the players satisfy total constraints. Terminal set is a subset of and it is assumed to have a nonempty interior. Game is said to be completed if at some step ; thus, the evader has not the right to leave set . To construct the control of the pursuer, at each step , we use the value of the control parameter of the evader at the step . We obtain sufficient conditions of completion of pursuit from certain initial positions of the players in finite time interval and construct a control for the pursuer in explicit form.

Autor: Asqar Raxmanov and Gafurjan Ibragimov



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