Abstract:  A novel sliding mode control technique based on the approximation of the first-order derivative of the Lyapunov function is presented for the combined control of the flexible multi-body satellites. And in this proposed control scheme, 〖JP+1〗a learning control structure is used to deal with the chattering. The stability of the closed-loop system is proved by the Lyapunov theory. The theoretical analysis further shows that the closed-loop system trajectory reaches the sliding mode surface in a finite time and the system output can asymptotically converge to zero on the sliding mode surface. Additionally, the controller has better robustness to the external disturbances, only the control input matrix information is given, and no other priori information on the upper and/or the lower bounds of the unknown system parameters and uncertain system dynamics is required for the controller design. At last, compared with the numerical simulation of the controller in the existing literatures, the results demonstrate the effectiveness and practicality of this novel chattering-free approach.

Key words: Flexible multi-body satellites, Sliding mode control, Attitude control, Recursive learning control