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For future extremely large telescopes, error in extreme adaptive optics systems at small angular separations will be highly impacted by the lag time of the correction, which is typically on millisecond timescales; one solution is to apply a predictive correction to catch up with the system delay. Predictive control leads to significant RMS error reductions in simulation (on the order of 5-10x improvement in RMS error compared with a standard integral controller), but shows only modest improvement on-sky (less than 2x in RMS error). This performance limitation is likely impacted by elements of pseudo open loop (POL) reconstruction, which requires assumptions about the response of the deformable mirror and accuracy of the wavefront measurements that are difficult to verify in practice. In this work, we explore a closed-loop method for data-driven prediction using a reformulated empirical orthogonal functions (EOF). We examine the performance of the open and closed-loop methods in simulation on perfect systems and systems with an inaccurate understanding of the DM response.