The focus of this study is on the development of a robust controller with a simple gain adaptation for satellite formation control. The complete nonlinear dynamics of the motion of the follower satellite relative to the leader satellite is considered and the rigorous proof for the stability of the controlled formation system is given in the presence of unknown external disturbances and unknown mass of the follower satellite. Although the controller design is based on the concept of sliding mode control, the proposed control strategy is free from chattering and guarantees a finite-time convergence of the controlled system to the target area. Furthermore, a simple adaptive law to automatically update the control gain is suggested that does not require a priori knowledge of the uncertainties of the system. In addition, to guarantee the robustness from the beginning and to improve the transient performance, a new sliding surface is also constructed. Numerical simulations are carried out to demonstrate the effectiveness of the proposed adaptive controller to maintain a desired formation configuration by compensating for the initial offset errors and external disturbance effects including gravitational perturbations and atmospheric drag.
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