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On a Linear Differential Game of Pursuit with Integral Constraints in ℓ 2

Author

Listed:
  • Ibroximjon Zaynabiddinov

    (Faculty of Physics-Mathematics, Andizhan State University, Andizhan 170100, Uzbekistan)

  • Marks Ruziboev

    (School of Engineering, Central Asian University, Tashkent 111221, Uzbekistan)

  • Gafurjan Ibragimov

    (V.I. Romanovskiy Institute of Mathematics, Uzbek Academy of Sciences, Tashkent 100174, Uzbekistan
    Department of Applied Mathematics, Tashkent State University of Economics, Tashkent 100006, Uzbekistan)

  • Tiziana Ciano

    (Department of Economics and Political Sciences, University of Aosta Valley, 11100 Aosta, Italy)

Abstract

In this paper, we study the stability, controllability, and differential game of pursuit for an infinite system of linear ODEs in ℓ 2 . The system we consider has a special right-hand side, which is not diagonal and serves as a toy model for controllable system of infinitely many interacting points. We impose integral constraints on the control parameters. We obtain criteria for stability and null controllability of the system. Further, we construct a strategy for the pursuer that guarantees completion of the pursuit problem for the differential game. To prove controllability we use the so called Gramian operators.

Suggested Citation

  • Ibroximjon Zaynabiddinov & Marks Ruziboev & Gafurjan Ibragimov & Tiziana Ciano, 2024. "On a Linear Differential Game of Pursuit with Integral Constraints in ℓ 2," Mathematics, MDPI, vol. 12(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:2:p:195-:d:1314563
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