Continuous Feedback in Some Differential Games
Abstract
Two control systems with disturbances are considered. The first one is two-dimensional, and its target set is an arc. The second of the two conflict control systems is scalar. Its target set consists of two points. In the first system, no program control or Caratheodory strategy guarantees the evasion, but there exists a a discontinuous feedback control that does. In the second system, evasion can be guaranteed by continuous strategies but not by program controls; the best possible distance for the evader is given by a discontinuous strategy and also by a multivalued upper semicontinuous strategy. In particular, this shows the difference between the case of nonconvex target set considered in this paper and the linear-convex case.