On a fixed duration pursuit differential game with geometric and integral constraints

In this paper we investigate a differential game in which countably many dynamical objects pursue a single one. All the players perform simple motions. The duration of the game is fixed. The controls of a group of pursuers are subject to integral constraints, and the controls of the other pursuers and the evader are subject to geometric constraints. The payoff of the game is the distance between the evader and the closest pursuer when the game is terminated. We construct optimal strategies for players and find the value of the game

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

An evasion differential game problem on the plane

Evasion differential game problem with many pursuers and one evader is studied on the plane. The control functions of the players are subject to integral constraints on each coordinates. Sufficient conditions for evasion to be proposed from many pursuers are obtained. Moreover, evader’s strategy is constructed and illustrative example is given.Keywords: evasion, integral constraint, strategies

Pursuit game problem of an infinite system of differential equations with geometric and integral constraints

The present paper considers a pursuit game problem of an infinite system of 1st-order differential equations in the space l 2. In the game, the player's control functions satisfy both geometric and integral constraints. The pursuer's action is to force the state of the system to coincides with another state for a finite time and the evader's action is to retrieve this. In each case, we obtain a condition for the completion of the game for which the pursuer's strategy is explicitly constructed. In addition, we study a control problem

Differential game with many pursuers when controls are subjected to coordinate-wise integral constraints

In this paper, we study a differential game of many pursuers and one evader in R2. The motions of all players are simple. An integral constraint is imposed on each coordinate of the control functions of players. We say that pursuit is completed if the state of a pursuer coincides with that of the evader at some time. The pursuers try to complete the pursuit, and the evader tries to avoid this. Sufficient conditions for completion of the differential game were obtained. The strategies of the pursuers are constructed based on the current values of control parameter of the evader. Also an illustrative example is provided