On a Linear Differential Game of Pursuit with Integral Constraints in <i>ℓ</i>²

Abstract

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.

Keywords

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