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

Ibroximjon Zaynabiddinov, Marks Ruziboev, Gafurjan Ibragimov and Tiziana Ciano ()
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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
Tiziana Ciano: Department of Economics and Political Sciences, University of Aosta Valley, 11100 Aosta, Italy

Mathematics, 2024, vol. 12, issue 2, 1-11

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.

Keywords: differential equations in Hilbert spaces; mild solutions; null control problem; optimal control; pursuit problem; linear operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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