Simple motion evasion differential game of multiple pursuers and single evader with integral constraints on control function

The term “Differential games” is applied to a group of problems in applied mathematics that share certain characteristics related to the modelling of conflict. Differential games are games in which the position of the players develops continuously in time. In a basic differential game, there are two actors (a pursuer and an evader) with conflicting goal. The pursuer wishes is to catch the evader, while the evader’s mission is to prevent this capture. The main steps in studying evasion games are to: 1) construct a strategy for the evader, 2) show admissibility of this strategy, 3) show that evasion is possible.For the main result, we consider evasion differential game of multiple pursuers and single evader with integral constraints in the plane R2. The game is described by simple equations. Different from constraints on control functions of other works, here, each component of the control functions of players are subjected to integral constraint. We say that evasion is possible if the state of the evader does not coincide with that of any pursuer. To construct a strategy of the evader we use controls of the pursuers with time lag. We obtained a sufficient condition of evasion from many pursuers. At the end of this thesis we provide an illustrative example.

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