Station-keeping for a translunar communication station

A translunar communication station is to be kept close to a nominal unstable periodic ‘Halo’ orbit, visible at all times from Earth. The analytically computed nominal orbit is not perfect, requiring an average control acceleration of about 10^?6 g's for tight control. An adjustable quadratic combination of position deviation and control acceleration is minimized to provide an (adjustable) control law with period feedback gains and a periodic bias. The average control acceleration can be reduced to less than 10^?8 g's with an error settling time of less than 21/2 months. The resulting limiting motion provides, in turn, an improved nominal, permitting the same low control cost with much tighter control, corresponding to settling times of the order of one day.