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

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  • Asqar Raxmonov
  • Gafurjan I. Ibragimov

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.

Suggested Citation

  • Asqar Raxmonov & Gafurjan I. Ibragimov, 2014. "An Approach for Solving Discrete Game Problems with Total Constraints on Controls," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, April.
    • Handle: RePEc:hin:jnlaaa:674651
    DOI: 10.1155/2014/674651
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    Cited by:

    1. Askar Rakhmanov & Gafurjan Ibragimov & Massimiliano Ferrara, 2016. "Linear Pursuit Differential Game under Phase Constraint on the State of Evader," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-6, October.

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