Evasion from many pursuers in simple motion differential game with integral constraints.

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

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

Linear evasion differential game of one evader and several pursuers with integral constraints

AbstractAn evasion differential game of one evader and many pursuers is studied. The dynamics of state variables $$x_1,\ldots , x_m$$ x 1 , … , x m are described by linear differential equations. The control functions of players are subjected to integral constraints. If $$x_i(t) \ne 0$$ x i ( t ) ≠ 0 for all $$i \in \{1,\ldots ,m\}$$ i ∈ { 1 , … , m } and $$t \ge 0$$ t ≥ 0 , then we say that evasion is possible. It is assumed that the total energy of pursuers doesn't exceed the energy of evader. We construct an evasion strategy and prove that for any positive integer m evasion is possible

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

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

Differential LG - Game of Many Participant Players

In this article, we have considered a simple motion differential game of   pursuers and one evader in. Here controls of the pursuers are subjected to linear constraints which is the generalization of both integral and geometrical constraints, and control of the evader is subjected to a geometrical constraint. To solve a pursuit problem, the attainability domain of each pursuer has been constructed and therefore, necessary and sufficient conditions have been obtained by intersection of them