Differential games of many players for infinite system of differential equations - Kazimirova, Ruzakhon Yunus Kizi (2024)
This thesis focuses on studying evasion and pursuit differential games involving multiple pursuers and a single evader for infinite systems of differential equations in the Hilbert space l2. Three problems are examined in this thesis. In the first problem, an evasion differential game with multiple pursuers and one evader is considered, described by an infinite system of binary differential equations in two cases. Solutions are presented for the evasion problem with negative coefficients in the first case and nonnegative coefficients in the second case, under the geometric constraints imposed on the players’ controls. The goal of the pursuers is to bring the state of at least one controlled system to the origin of l2, while the evader aims to prevent this. A sufficient condition for evasion is obtained for any initial state of the players, and an evasion strategy for the evader is constructed. The second problem involves a multiple-pursuer and single-evader evasion differential game with integral constraints for an infinite system of two-block differential equations. For this problem, it is shown that if the evader’s control resource is greater than or equal to the combined resources of the pursuers, evasion is possible from any initial position in the infinite system. Both the first and second problems are approached by reducing the game in Hilbert space l2 to an equivalent differential game in finite-dimensional Euclidean space. An explicit evasion strategy is proposed, guaranteeing successful evasion. The third problem addresses a pursuit differential game involving multiple pursuers and one evader, described by an infinite system of second-order differential equations, where the players’ control functions are subject to integral constraints. To solve this problem, the case of one pursuer and one evader is first examined, and this result is subsequently applied to obtain the main result of the problem. Additionally, a condition in terms of the players’ energies is derived, providing a sufficient condition for successful pursuit. Strategies for the pursuers are constructed to ensure the capture of the evader.