This paper proposes an adaptive super-twisting control (ASTC) for the deployment of space-tethered systems with the consideration of uncertainty of external and internal disturbances with unknown boundaries. The main advantage of the ASTC scheme is that it can deal with the unknown bounds of uncertainties and disturbances. The proposed control law consists of two adaptive control gains that ensure the establishment, in a finite time, of a real second-order sliding mode. This, in turn, guarantees a convergence to a small domain and without overestimating the control gains. The stability of the control law is demonstrated theoretically. Compared with the sliding mode control algorithm with power reaching law, the newly proposed adaptive super-twisting control method performs better in the settling time, the maximum in-plane angle, and angular velocity control and suppressing oscillations. Numerical simulations are presented to validate the effectiveness and robustness of the proposed ASTC scheme.
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