Linear Differential Evasion Game with Locally Inertial Controls

Abstract

Linear differential evasion game with two players, the pursuer and the evader, is
considered. New classes of controls for both players are introduced, which called locally inertial
controls. In these classes the evasion problem from any initial position that does not belong to
the terminal set is solved. Effective sufficient conditions of evasion and algorithms for building
the evasion control are obtained. The results demonstrated on the well-known in the theory of
differential games example.