ABSTRAKT

The pursuit problem for linear differential games with integral constraints on players controls is considered. The problem solution is based on the Chikrii resolving functions method. The construction of resolving function substantiating the rule of players parallel approach, namely Π-strategy for a pursuer is proposed. For the considered case the new Pontryagin sufficient conditions are obtained for the solvability of the pursuit problem. As an example two classes of games are adduced with each class being of a specific interest.