On Reachability Under Uncertainty

The paperstud=W the problem of reachability for linear systems in the presence of uncertain input dputA bances that may also be interpreted as the action of an a ersary in a game-theoretic setting. It emphasizes thed i#erences between reachabilityund# open-loop and closedW# op control. The situation when observations arrive at given isolated instances of time, lead s to problems of anticipative (maxmin) or nonanticipative (minmax) piecewise open-loop control with corrections. As the number of correctionstend to infinity, one comes in both cases to a nonanticipative feedS ck control strategy that ensures reachability undS uncertainty and may be found through a solution of the forward Hamilton-JacobiBellman -Isaacs equation. The basic relations ared erived through the investigation of superpositions of value functions for appropriate sequential maxmin or minmax problems of control. Introduction Recentd evelopments in real-time automation have promoted new interest in the reachability pro..