On control problem for infinite system of differential equations of second order

We study a control problem described by infinite system of differential equations of second order in the space 2 r 1l+. Control parameter is subjected to integral constraint. Our goal is to transfer the state of the system from a given initial position to the origin for finite time. We obtained necessary and sufficient conditions on the initial positions for which the problem can be solved

On game value for a pursuit‑evasion differential game with state and integral constraints

A pursuit-evasion differential game of countably many pursuers and one evader is investigated. Integral constraints are imposed on the control functions of the players. Duration of the game is fixed, and the payoff functional is the greater lower bound of distances between the pursuers and evader when the game is completed. The pursuers want to minimize, and the evader to maximize the payoff. In this paper, we find the value of the game and construct optimal strategies for the players