On a Linear Differential Game of Pursuit with Integral Constraints in ℓ2

被引：1

作者：

Zaynabiddinov, Ibroximjon ^{[1
]}

Ruziboev, Marks ^{[2
]}

Ibragimov, Gafurjan ^{[3
,4
]}

Ciano, Tiziana ^{[5
]}

机构：

[1] Andizhan State Univ, Fac Phys Math, Andizhan 170100, Uzbekistan

[2] Cent Asian Univ, Sch Engn, Tashkent 111221, Uzbekistan

[3] Uzbek Acad Sci, VI Romanovskiy Inst Math, Tashkent 100174, Uzbekistan

[4] Tashkent State Univ Econ, Dept Appl Math, Tashkent 100006, Uzbekistan

[5] Univ Aosta Valley, Dept Econ & Polit Sci, I-11100 Aosta, Italy

来源：

MATHEMATICS | 2024年 / 12卷 / 02期

关键词：

differential equations in Hilbert spaces; mild solutions; null control problem; optimal control; pursuit problem; linear operators; CONTROLLABILITY;

D O I：

10.3390/math12020195

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the stability, controllability, and differential game of pursuit for an infinite system of linear ODEs in & ell;(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.

引用

页数：11

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