Continuous-time model predictive control of under-actuated spacecraft with bounded control torques

The stabilization problem of rigid spacecraft is essential for space explorations and operations. This paper studies the model predictive stabilization problem of a class of underactuated rigid spacecrafts with two bounded control torques. A novel model predictive control (MPC) algorithm is designed by making use of the homogeneity of the system dynamics. In addition, a local homogeneous Lyapunov function is constructed based on which the approach to designing the terminal set and other parameters are developed. Finally, the conditions for ensuring algorithm feasibility and closed-loop stability are provided. We show that under the given conditions, the designed MPC algorithm is feasible, and the closed-loop system is asymptotically stable. Simulation and comparison studies verify that the developed results are effective and valid, and the designed controller fulfills the constraint satisfaction and achieves much faster convergence rate in comparison with conventional continuous time-varying controllers.