Robust station-keeping for Halo orbits via auxiliary-controller-independent Lyapunov-based model predictive control

This paper develops an enhanced robust Lyapunov-based model predictive control (LMPC) scheme for station-keeping of Halo orbits with consideration of bounded uncertainties and control constraints. This method integrates the idea of robust control Lyapunov function (RCLF) into nonlinear MPC to robustly stabilize the tracking error within the explicitly characterized stability region. Specifically, the RCLF dissipation condition is firstly derived to analyze the stabilizability of the system with undefined feedback control. This property allows to construct the control-law-independent robust controllable domain, inside which admissible control exists to stabilize the spacecraft under bounded uncertainties. Subsequently, a sampling-based search strategy is developed to estimate the robust controllable domain, thereby deriving two contraction constraints. By incorporating the two constraints, the enhanced LMPC can be formulated independently of specific auxiliary control laws, whose stability region is explicitly characterized and extended. It brings appealing advantages that alleviate hard-to-avoid conservatism in traditional methods, thus improving tracking performances. Theoretically, within the stability region, robust stability and recursive feasibility can be well guaranteed. Numerical simulations demonstrate that the enhanced LMPC can eventually stabilize spacecraft to Halo orbit under bounded uncertainties and control constraints. Compared with traditional methods, the proposed controller achieves a 3–5 times scale of stability region, and tracking errors are reduced by about 50%.