About non-stationary problem of simple pursuit in the class of impulse strategies

The problem of simple pursuit in the class of impulse strategies of pursuers is considered. The goal of pursuers is evader's capture, the goal of evader is to prevent the meeting. The geometrical constraints on controls of players are strictly convex compact set with a smooth boundary. The basis of this work is based on the basic ideas of the method of resolving functions. We formulate an analogue of Pshenichnyi's theorem allowing to obtain sufficient conditions for solving the problem. Cases of impulse controls of pursuers and the cases of impulse controls of evaders are considered separately. In each case the sufficient conditions for a winning strategy are obtained. The results of solving the problem with impulse controls of pursuers are illustrated on an example.