Data-driven modeling and prediction of ship course keeping in shallow water waves using higher order dynamic mode decomposition incorporating control input

The implementation of autonomous navigation of Maritime Autonomous Surface Ships (MASS) in complex environments critically depends on accurate and real-time prediction of ship motions. To address the combined challenges of wave excitations and shallow water effects, this paper proposes a novel data-driven modeling framework called Higher Order Dynamic Mode Decomposition incorporating Control Input (HODMD-CI). It extends the standard HODMD by explicitly integrating the time-delayed control inputs, including both actuator commands (i.e., rudder angle) and measurable environmental disturbances (i.e., wave elevation), into a state-space prediction model. The proposed method is validated using the free-running model test data of the Duisburg Test Case (DTC) container carrier performing course keeping in regular head waves under shallow water conditions. The prediction performance of HODMD-CI under three control-input configurations (rudder angle only, wave elevation only, and both) is evaluated and compared against the standard HODMD and several neural network models. Results demonstrate that HODMD-CI with combined rudder angle and wave elevation inputs achieves the highest overall accuracy and trend consistency, as evidenced by the lowest Average Relative Root Mean Square Error (ARRMSE) and the Pearson Correlation Coefficient (PCC) values closest to 1. Furthermore, HODMD-CI exhibits stronger noise resistance compared to neural network counterparts, particularly for roll motion prediction. This study confirms the efficacy of jointly modeling rudder angle and wave elevation for accurate ship motion prediction in complex, shallow water wave scenarios, offering a promising data-driven tool for intelligent ship navigation and control.