On ‘-Catch Problem in Differential Games with Inertial Players and Non-Stationary Geometric Constraints on Controls

In this paper, we consider the ‘-catch problems in a differential game of one pursuer and one evader in Rn. The movements of the players are carried out by the same type of differential equations. Non-stationary geometric constraints are imposed on the control functions of the players. We say that the ‘-catch is completed if the state of the pursuer approaches that of the evader at ‘ distance. To solve the problems, the pursuer’s strategy, which is represented as a generalization of the Π-strategy, plays a crucial role. We derive the necessary and sufficient conditions for the completion of the differential game. This work continues and extends the contributions of Isaacs, Petrosyan, Pshenichnyi, the authors of this article, and other researchers