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Discrete Dynamics in Nature and Society
Volume 2016, Article ID 1289456, 6 pages
Research Article

Linear Pursuit Differential Game under Phase Constraint on the State of Evader

1Department of Informatics, Tashkent University of Information Technologies, TUIT, Amir Temur Str. 108, 100202 Tashkent, Uzbekistan
2Department of Mathematics & Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
3Department of Law and Economics, University Mediterranea of Reggio Calabria, Reggio Calabria, Italy
4ICRIOS, Bocconi University, Milan, Italy

Received 22 June 2016; Accepted 14 September 2016

Academic Editor: Rigoberto Medina

Copyright © 2016 Askar Rakhmanov 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 consider a linear pursuit differential game of one pursuer and one evader. Controls of the pursuer and evader are subjected to integral and geometric constraints, respectively. In addition, phase constraint is imposed on the state of evader, whereas pursuer moves throughout the space. We say that pursuit is completed, if inclusion is satisfied at some , where and are states of pursuer and evader, respectively, and is terminal set. Conditions of completion of pursuit in the game from all initial points of players are obtained. Strategy of the pursuer is constructed so that the phase vector of the pursuer first is brought to a given set, and then pursuit is completed.