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

  • Gafurjan Ibragimov
  • Idham Arif AliasEmail author
  • Usman Waziri
  • Abbas Badakaya Ja’afaru
Article

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.

Keywords

Differential game Infinite system Pursuer Evader Hilbert space Integral constraint Optimal strategy 

Mathematics Subject Classification

Primary 91A23 Secondary 49N75 

Notes

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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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2017

Authors and Affiliations

  1. 1.Department of Mathematics, Institute for Mathematical ResearchUniversiti Putra MalaysiaSerdangMalaysia
  2. 2.Department of MathematicsUniversiti Putra MalaysiaSerdangMalaysia
  3. 3.Department of MathematicsBayero University KanoKanoNigeria

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