Nonlinear Robust Control for Satellite Formation Flying via Adaptive Second-Order Sliding Modes

This paper presents a robust adaptive control methodology based on the concept of second-order sliding modes for satellite formation control in the presence of unknown, but bounded uncertainties. By introducing two sliding variables to achieve the concept of second-order sliding modes, a robust controller is designed so that it forces the first sliding variable to converge to a desired error box in a finite time. Then, the second sliding variable is automatically bounded in a much smaller region by sliding mode control theory, thereby considerably improving the control accuracy. The proposed control scheme is of a smooth form and effectively alleviates chattering. An adaptive law that updates the control gain is also presented without a priori knowledge of the uncertainties. Numerical simulations, in which a desired formation configuration is required to be precisely maintained under uncertain mass and external disturbances, are carried out to validate the efficiency and the accuracy of the proposed robust adaptive control scheme developed herein.