Differential Games with Inertial Players Under the Langenhop Type Constraints on Controls

In this paper, we study the pursuit-evasion problem for inertial motions of players. Here, the players' controls are selected from the class of functions that satisfy of the Langenhope type integral inequalities. The physical interpretation of such constraints on controls is close to energy constraints, similar to integral constraints. To solve the pursuit problem, a parallel approach strategy (briefly, a Pi-strategy) is defined for the pursuer. To solve the evasion problem, the evader's control with delayed information about the pursuer's control is determined. New sufficient conditions for the finding solutions of the pursuit-evasion problem are obtained. This work is a development of the works of R. Isaacs, L.A. Petrosyan, B.N. Pshenichny, A.A. Azamov, N.N. Petrov and others, including the authors of this article.