Sequential decisions in the control of a spaceship

Abstract

Abstract : Imagine a spaceship travelling towards a certain planet with predetermined speed, in a direction which will bring it close to the target after a known period of time. Observations on the position of the target, relative to the present course, are made continuously and lead to a gradually improving prediction of the eventual miss distance. On the other hand, the fuel available in the spaceship for making minor changes in the direction of motion, is gradually losing its effectiveness. This is because the final change of position caused by a small velocity imposed perpendicular to the present motion, is roughly proportional to the remaining time. Thus we have a control problem which is essentially one of compromise between the extremes of using the fuel early and perhaps in the wrongway, because of poor information; or waiting too long for more precise information, so that the fuel becomes ineffective.