Adaptive double-saturated control for hovering over an asteroid

Hovering over an irregular-shaped asteroid is particularly challenging due to the large gravitational uncertainties and various external disturbances. An adaptive control scheme considering commanded acceleration and its change-rate saturation for hovering is developed in this paper. Taking full advantage of terminal sliding-mode control theory, first, we convert the double-saturated control problem to a new equivalent system by introducing a special bounded function, in which just control input saturation needs to be considered. Then, a continuous finite-time saturated controller is designed for the new system with the assistance of an constructed auxiliary subsystem. Additionally, an adaptive law is devised for the controller to avoid the requirement of the unknown upper bounds of the disturbances, rendering the control scheme especially suitable to asteroid hovering missions. The finite-time stability of the whole closed-loop system is proved via Lyapunov analysis. Numerical simulation studies are carried out, and the results demonstrate the design features and the desired performance.