Control of an underactuated rigid spacecraft via deterministic learning

In this paper, based on recently developed deterministic learning (DL) theory, we investigate the problem of stabilization for an underactuated rigid spacecraft with unknown system dynamics. Our objective is to learn the unknown underactuated system dynamics while tracking to a desired orbit and design the control law to achieve stabilization. Firstly, the system dynamic and kinematic equations are given, the kinematic equation is described by the (w, z) parametrization. Secondly, an adaptive neural network (NN) controller with the employed radial basis function (RBF) is designed to guarantee the stability of the underactuated rigid spacecraft system and the tracking performance. The unknown dynamics of underactuated rigid spacecraft system can be approximated by NN in a local region and the learned knowledge is stored in constant RBF networks. The accessorial variables γ₁ and γ₂ are imported in the designing course of the control laws via backstepping method. Thirdly, when repeating same or similar control tasks, the learned knowledge can be recalled and reused to achieve guaranteed stability with little effort. Finally, simulation studies are included to demonstrate the effectiveness of the proposed method.