Prediction-Oriented Hankel Matrix Reduction for Data-Driven Predictive Control: Application to Wind Turbine Control

Data-driven predictive control methods based on Hankel matrices predict future system behavior directly from measured input–output data without requiring an explicit mathematical model. Their practical application, however, is often limited by the large Hankel matrices needed to achieve satisfactory prediction accuracy, which increase memory requirements and online computational complexity. This paper proposes a prediction-oriented Hankel matrix reduction framework that selects a subset of stored trajectories according to their contribution to the prediction map rather than conventional matrix-based criteria. A direct proof of the constructive part of Willems’ Fundamental Lemma, based only on linearity and time invariance rather than a state-space realization, is first presented, leading to an output-based prediction model that serves as the theoretical foundation of the proposed approach. Three trajectory-selection algorithms with different computational characteristics are then developed to preserve the prediction map while reducing the number of retained Hankel columns. The proposed methods are evaluated through closed-loop control of a nonlinear wind turbine using data-driven predictive control. Simulation results show that substantial reductions in Hankel matrix size can be achieved while maintaining prediction accuracy and comparable closed-loop tracking performance. The proposed framework is structurally applicable to a broad class of Hankel-based data-driven predictive control formulations and can reduce computational complexity while approximately preserving the prediction map.