Linear discrete pursuit game with phase constraints

• Main Authors: Raxmanov, Asqar, Ibragimov, Gafurjan
• Format: Article
• Language: English
• Published: Hindawi Publishing Corporation 2014
• Online Access: http://psasir.upm.edu.my/id/eprint/34384/1/Linear%20Discrete%20Pursuit%20Game%20with%20Phase%20Constraints.pdf; http://psasir.upm.edu.my/id/eprint/34384/; http://www.hindawi.com/journals/tswj/2014/435103/abs/

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.