On the Predictive Capability of Dynamic Mode Decomposition for Periodic Solutions of Nonlinear Systems with Focus on Orbital Mechanics

Abstract This paper discusses the predictive capability of Dynamic Mode Decomposition (DMD) in the context of orbital mechanics. The focus is specifically on the Hankel variant of DMD which uses a stacked set of time-delayed observations for system identification and subsequent prediction. A theory on the minimum number of time delays required for accurate reconstruction of periodic trajectories of nonlinear systems is presented and corroborated using experimental analysis. In addition, the window size for training and prediction regions, respectively, is presented. The need for a meticulous approach while using DMD is emphasized by comparing its performance on two candidate satellites, the ISS and MOLNIYA-3-50. Experiments are also presented for quasi-periodic scenarios with applied perturbing forces.