Avoiding the origin: A finite-fuel stochastic control problem

Abstract

We consider a model for the control of a satellite--fuel is expended in a linear fashion to move a satellite following a diffusion--the aim being to keep the satellite above a critical level. Under suitable assumptions on the drift and diffusion coefficients, it is shown that the probability of the satellite falling below the critical level is minimized by a policy that moves the satellite a certain distance above the critical level and then imposes a reflecting boundary at this higher level until the fuel is exhausted.