Abstract
Data-driven Koopman operator methods, particularly Extended Dynamic Mode Decomposition (EDMD) and Hankel Dynamic Mode Decomposition (Hankel-DMD), have emerged as promising reduced-order models for nonlinear spacecraft attitude dynamics. However, their performance is typically evaluated using one-step prediction accuracy, leaving their reliability for autonomous long-horizon propagation largely unverified. This study investigates the closed-loop rollout performance of a Hankel-DMD surrogate for a gravity-gradient-stabilized 3U CubeSat with reaction-wheel momentum bias and compares it with a conventional equilibrium linearization. The Hankel-DMD model achieves excellent one-step prediction accuracy (RMSE = 0.049°), but its autonomous rollout error increases from 7.49° after 0.05 orbital periods to 90.58° after 3 orbital periods, despite incorporating delay embedding, feature standardization, ridge regularization, and spectral-radius stabilization. In contrast, the equilibrium linearization maintains prediction errors below 3.5° throughout the evaluated horizons and consistently outperforms the data-driven model. To quantify this discrepancy, this work introduces the Rollout Amplification Factor (RAF), which measures the growth of autonomous rollout error relative to one-step prediction and reaches 1,849× after three orbital periods. The results demonstrate that excellent local prediction accuracy does not necessarily imply reliable autonomous long-horizon performance and identify a previously overlooked closed-loop rollout validation gap in Koopman-based spacecraft attitude modelling. These findings establish that autonomous rollout evaluation against classical analytical baselines should complement conventional one-step validation when assessing Koopman-based reduced-order models for spacecraft applications.