No abstract

We consider pursuit-evasion differential game of countable number inertial players in Hilbert space with integral constraints on the control functions of players. Duration of the game is fixed. The payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. The pursuers try to minimize the functional, and the evader tries to maximize it. In this paper, we find the value of the game and construct optimal strategies of the players.

We study a differential game of optimal approach of finite or countable number of pursuers with one evader in the Hilbert space l2. On control functions of the players integral constraints are imposed. Such constraints arise in modeling the constraint on energy. The duration of the game θ is fixed. The payoff functional is the greatest lower bound of distances between the pursuers and evader when the game is terminated. The pursuers try to minimize the payoff functional, and the evader tries to maximize it. In this paper, we find formula for the value of the game and construct explicitly optimal strategies of the players. Important point to note is that the energy resource of any pursuer needs not be greater than that of the evader.

We study a two dimensional evasion differential game with several pursuers and one evader with integral constraints on control functions of players. Assuming that the total resource of the pursuers does not exceed that of the evader, we solve the game by presenting explicit strategy for the evader which guarantees evasion.

We study a simple motion pursuit differential game of many pursuers and many evaders on a nonempty convex subset of R n. In process of the game, all players must not leave the given set. Control functions of players are subjected to integral constraints. Pursuit is said to be completed if the position of each evader y j , j ∈ {1, 2, ...k}, coincides with the position of a pursuer x i , i ∈ {1, ..., m}, at some time t j , that is, x i t j y j t j. We show that if the total resource of the pursuers is greater than that of the evaders, then pursuit can be completed. Moreover, we construct strategies for the pursuers. According to these strategies, we define a finite number of time intervals θ i−1 , θ i and on each interval only one of the pursuers pursues an evader, and other pursuers do not move. We derive inequalities for the resources of these pursuer and evader and, moreover, show that the total resource of the pursuers remains greater than that of the evaders.