A Multi-Scale Physics-Informed Neural Network Approach for Adaptive Orbit Control of Spacecraft Around Asteroids

Deep-space asteroid exploration is of significant importance for both deep-space exploration and scientific research. However, the complex gravitational fields near asteroids pose challenges for traditional model-based orbit control strategies. While artificial intelligence can estimate asteroid dynamics using sampled data, ensuring stability for real-time applications remains difficult. Most current methods rely on offline training, lack real-time autonomous adjustment, and require large volumes of training data. To overcome these limitations, this paper proposes, for the first time, a multi-scale adaptive orbit control framework that combines conventional control methods with artificial intelligence, using physics-informed neural networks (PINNs) to achieve high-precision trajectory tracking around rotating asteroids. Different from existing methods that rely on offline-trained networks or only approximate residual dynamics, the proposed approach employs physics-constrained online PINNs to directly estimate the complete unknown orbital dynamics. By embedding prior orbital dynamic laws into network training, the method is inherently explainable and non-black-box, while eliminating the dependence on high-precision prior gravity field models. This framework combines offline physics-constrained pre-training, fast-timescale Lyapunov-based online adaptation, and slow-timescale periodic retraining using buffered measurement data, where a dual-timescale learning structure ensures both rapid closed-loop stabilization and long-term model refinement. By the Lyapunov direct method and LaSalle–Yoshizawa theorem, the uniform ultimate boundedness of all closed-loop signals and the asymptotic convergence of tracking errors are rigorously proven. The simulation results show that the novel approach, which achieves 99.3% lower tracking error than traditional feedback control and 37.1% improvement over standard DNN, is more accurate in trajectory tracking and more robust to model uncertainties and sensor noises than conventional methods.