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

Asqar Raxmonov and Gafurjan I. Ibragimov

Abstract and Applied Analysis, 2014, vol. 2014, 1-6

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.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:674651

DOI: 10.1155/2014/674651

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