Optimal orbit transfers by linear and nonlinear programming for the stochastic optimization of the apogee maneuver of three-axis stabilized geostationary satellites

A method for the stochastic optimization of the injection from the transfer orbit and for the deterministic optimization of the positioning after the apogee maneuver for three-axis stabilized geostationary satellites is described. The nonlinear programming problem of the apogee impulse parameter optimization is done by a gradient-free method. During the optimization, error cases in the range of + or - 3 sigma of the apogee impulse and all operational constraints and satellite hardware limitations are taken into account. The positioning task is formulated as a linear programming problem which is solved by the SIMPLEX scheme. For the final optimization of the impulse times the gradient-free method is used again. An approach for the limitation of the number of impulses to a reasonable figure is outlined. Finally, numerical examples for the stochastic and deterministic optimization, respectively, are discussed.