Robust Lunar Landing Trajectory Control Laws Using Neural ODEs with Reservoir Computing for Efficient Learning

This study proposes a novel approach that applies neural ordinary differential equations (ODEs) combined with an adaptive echo state network (ESN)-based reservoir computing framework to spacecraft trajectory control laws. The stability of the resulting closed-loop systems is investigated as a key metric for nonlinear control laws and demonstrated through numerical analysis. The proposed method does not fall within conventional classifications of implicit or explicit guidance, thereby overcoming their inherent limitations. Neural ODEs are deep learning frameworks that represent continuous dynamics, enabling the derivation of robust control laws that achieve mission objectives without reliance on reference trajectories. Control inputs are generated directly from the current trajectory state, allowing the spacecraft to satisfy prescribed boundary conditions. The control laws are further trained to maintain robustness against unknown disturbances, including control input uncertainties. To improve computational efficiency, an adaptive ESN-based reservoir computing framework is introduced as a lightweight training architecture in conjunction with stochastic optimization, reducing training costs while preserving flexibility and robustness. Stability characteristics are evaluated through closed-loop system analyses using data-driven solutions to Lyapunov equations for nonlinear systems and contraction analysis. The effectiveness of the proposed approach is demonstrated through a lunar landing mission, in which its robustness and stability are verified through Monte Carlo simulations and system analyses.