Linear pursuit-and-evasion games with impulse evader control

Differential games with impulse control have been insufficiently studied. Among the known studies we should note [1], which generalizes the approach to N. I. Krasovskii's school to differential games. In this article we develop a new formulation in which the pursuer uses tin ordinary control while the evader uses an impulse control. This approach models dynamic system control that allows strong noise or failures producing discontinuous paths [2]. We also consider cases with different timing of the impulse noise and develop sufficiently constructive strategies for both the pursuer and the evader. Unlike games in epsilon-strategies, our game assumes that the pursuer has information only about the current evader control. Since the evader applies impulse control with certain intervals between impulses, these problems are solved using the approaches originally developed for epsilon-strategies. The present article is related to monograph [3].