Stabilization of the radial equilibrium of a tethered satellite with respect to out-of-plane initial perturbations

We investigate the stabilization of the radial equilibrium of a tethered satellite by tension control, if both in-plane and out-of-plane deviations from the vertical position are taken into account. While in-plane perturbations can be eliminated in finite time, the length rate change of the tether acts as parametric control on the out-of-plane deviations. Therefore the control becomes less effective, if the perturbation decreases. In order to improve the convergence we investigate the optimal control problem assuming no costs for the applied tension force but restricting the control force to a finite interval. For tether cconfigurations close to the vertical target position this approach yields a solution with singular control, which leads to a faster decay of the deviations. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)