Station-keeping of tethered satellite system around a halo orbit using nonlinear model predictive control

The nonlinear model predictive control (NMPC) method is employed to design the controller for the station-keeping mission around Halo orbits of dumbbell tethered satellites in the circular restricted three-body problem (CRTBP). First, the target Halo orbit is obtained using the perturbation method. The station-keeping control problem is translated into a tracking control problem by tracking a target point moving along the reference orbit. Then, the original system model is discretized by the fourth-order Ronge-Kutta method. The finite horizon optimal control problem is transformed into a nonlinear optimization problem and solved by nonlinear programming, which then provides the control input for the next control period. Finally, the numerical simulation results demonstrate that even in the case of large initial position deviation, the controller can still guarantee that the tethered satellite system move along the target orbit precisely with relatively small velocity increment.