On a Linear Differential Game of Pursuit with Integral Constraints in ℓ2
Ibroximjon ZaynabiddinovFaculty of Physics-Mathematics, Andizhan State University, Andizhan 170100, UzbekistanMarks RuziboevGafurjan IbragimovDepartment of Applied Mathematics, Tashkent State University of Economics, Tashkent 100006, UzbekistanTiziana CianoDepartment of Economics and Political Sciences, University of Aosta Valley, 11100 Aosta, Italy
Ochiq kirishOltin
Litsenziya: cc-by
ABI
Annotatsiya
In this paper, we study the stability, controllability, and differential game of pursuit for an infinite system of linear ODEs in ℓ2. 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.
Hali tarjima qilinmagan