A satellite control problem
Abstract
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 onedimensional. 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.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 December 1977
 Bibcode:
 1977STIN...7821194C
 Keywords:

 Brownian Movements;
 Satellite Attitude Control;
 Stochastic Processes;
 Cost Analysis;
 Fuel Consumption;
 Mathematical Models;
 Probability Distribution Functions;
 Launch Vehicles and Space Vehicles