Sequential decisions in the control of a space-ship (terminal cost proportional to magnitude of miss distance)

Abstract

This is an extension of the paper [1] by Bather and Chernoff, where approximations are obtained to the solution of a sequential control problem involving the decision of when to use fuel to alter course during a space-ship's approach to a target. It is desired to come as close as possible to the target. If fuel is used too early, it may be used incorrectly due to imprecise information about the location of the target; however if the fuel is used too late it may be ineffective in reducing the miss distance.