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Differential Game of Optimal Pursuit for an Infinite System of Differential Equations

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Abstract

We study an optimal pursuit differential game problem in the Hilbert space \(l_{r+1}^2\). The game is described by an infinite system of the first-order differential equations whose coefficients are negative. The control functions of players are subjected to integral constraints. If the state of the system coincides with the origin of the space \(l_{r+1}^2\), then game is considered completed. We obtain an equation to find the optimal pursuit time. Moreover, we construct the optimal strategies for players.

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Acknowledgements

The present research was partially supported by the National Fundamental Research Grant Scheme FRGS of Malaysia, 01-01-16-1840FR and 01-01-17-1921FR.

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Authors and Affiliations

  1. Department of Mathematics, Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia

    Gafurjan Ibragimov & Idham Arif Alias

  2. Department of Mathematics, Universiti Putra Malaysia, Serdang, Malaysia

    Usman Waziri

  3. Department of Mathematics, Bayero University Kano, Kano, Nigeria

    Abbas Badakaya Ja’afaru

Authors
  1. Gafurjan Ibragimov
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  2. Idham Arif Alias
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  3. Usman Waziri
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  4. Abbas Badakaya Ja’afaru
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Correspondence to Idham Arif Alias.

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Communicated by Anton Abdulbasah Kamil.

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Ibragimov, G., Alias, I.A., Waziri, U. et al. Differential Game of Optimal Pursuit for an Infinite System of Differential Equations. Bull. Malays. Math. Sci. Soc. 42, 391–403 (2019). https://doi.org/10.1007/s40840-017-0581-x

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  • DOI: https://doi.org/10.1007/s40840-017-0581-x

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