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A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints

Author

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  • Gafurjan Ibragimov
  • Nu′man Satimov

Abstract

We study a simple motion pursuit differential game of many pursuers and many evaders on a nonempty convex subset of ℝn. In process of the game, all players must not leave the given set. Control functions of players are subjected to integral constraints. Pursuit is said to be completed if the position of each evader yj, j ∈ {1, 2, …k}, coincides with the position of a pursuer xi, i ∈ {1, …, m}, at some time tj, that is, xi(tj) = yj(tj). We show that if the total resource of the pursuers is greater than that of the evaders, then pursuit can be completed. Moreover, we construct strategies for the pursuers. According to these strategies, we define a finite number of time intervals [θi−1, θi] and on each interval only one of the pursuers pursues an evader, and other pursuers do not move. We derive inequalities for the resources of these pursuer and evader and, moreover, show that the total resource of the pursuers remains greater than that of the evaders.

Suggested Citation

  • Gafurjan Ibragimov & Nu′man Satimov, 2012. "A Multiplayer Pursuit Differential Game on a Closed Convex Set with Integral Constraints," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:460171
    DOI: 10.1155/2012/460171
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    Cited by:

    1. Jewaidu Rilwan & Massimiliano Ferrara & Abbas Ja’afaru Badakaya & Bruno Antonio Pansera, 2023. "On pursuit and evasion game problems with Gr $$\ddot{\text {o}}$$ o ¨ nwall-type constraints," Quality & Quantity: International Journal of Methodology, Springer, vol. 57(6), pages 5551-5562, December.
    2. Bara’atu Bashir Borodo & Ma’aruf Shehu Minjibir & Abbas Ja’afaru Badakaya, 2025. "Pursuit Differential Game Problem with Component-wise Constraints in $$l_\infty $$ l ∞," Journal of Optimization Theory and Applications, Springer, vol. 207(2), pages 1-15, November.
    3. Atamurat Kuchkarov & Gafurjan Ibragimov & Akmal Sotvoldiev, 2013. "Linear Discrete Pursuit Game Problem with Total Constraints," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    4. Gafurjan Ibragimov & Massimiliano Ferrara & Atamurat Kuchkarov & Bruno Antonio Pansera, 2018. "Simple Motion Evasion Differential Game of Many Pursuers and Evaders with Integral Constraints," Dynamic Games and Applications, Springer, vol. 8(2), pages 352-378, June.
    5. Idham Arif Alias & Gafurjan Ibragimov & Askar Rakhmanov, 2017. "Evasion Differential Game of Infinitely Many Evaders from Infinitely Many Pursuers in Hilbert Space," Dynamic Games and Applications, Springer, vol. 7(3), pages 347-359, September.
    6. Idris Ahmed & Poom Kumam & Gafurjan Ibragimov & Jewaidu Rilwan & Wiyada Kumam, 2019. "An Optimal Pursuit Differential Game Problem with One Evader and Many Pursuers," Mathematics, MDPI, vol. 7(9), pages 1-11, September.
    7. Asqar Raxmonov & Gafurjan I. Ibragimov, 2014. "An Approach for Solving Discrete Game Problems with Total Constraints on Controls," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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