Extended higher order dynamic mode decomposition incorporating control input with Abkowitz-inspired dictionary for ship maneuvering motion prediction

Real-time prediction of ship maneuvering motion is fundamental to the navigation and control of Maritime Autonomous Surface Ships (MASS). Higher Order Dynamic Mode Decomposition incorporating Control Input (HODMD-CI) has previously been developed for this task, but its linear and independent treatment of motion states and control inputs cannot adequately capture the nonlinearity of ship maneuvering motion or the coupling between motion states and the rudder angle. To address this limitation, the Extended Higher Order Dynamic Mode Decomposition incorporating Control Input (EHODMD-CI) is proposed by embedding an Abkowitz-inspired nonlinear observable dictionary into HODMD-CI. Two algorithmic formulations, two dictionary versions, and two predictive model construction modes are developed and compared. The configuration of EHODMD-CI is analyzed using numerical simulation datasets generated by the Maneuvering Modeling Group (MMG) model for the KVLCC2 ship, and its prediction performance is compared with HODMD-CI and three benchmark methods, Long Short-Term Memory (LSTM), Gaussian Process Regression (GPR), and Transformer, on a full-scale ship trial dataset of a small trimaran. EHODMD-CI achieves the smallest Root Mean Square Error (RMSE) and the Pearson Correlation Coefficient (PCC) closest to 1 among the five methods, while requiring much less training and prediction time than vanilla LSTM, GPR, and Transformer.