A satellite control problem

A numerical approach is described for calculating the optimal policy in the stochastic control problem of keeping a satellite close to a fixed point in space when it is subject to random forces. The random forces are modelled by Brownian Motion. A policy is evaluated in terms of its long run expected average cost. The running costs consist of a charge for fuel used plus a charge of x sub 1 squared per unit of time when the satellite is x sub 1 units away from the target. The space is one-dimensional. The method used is to apply backward induction to a bounded discrete space, discrete time version of the problem. Incidentally a solution is presented for the deterministic version of the problem where there are no random forces.