  This work introduces the Data-Enabled Predictive iteRative Control (DeePRC)
algorithm, a direct data-driven approach for iterative LTI systems. The DeePRC
learns from previous iterations to improve its performance and achieves the
optimal cost. By utilizing a tube-based variation of the DeePRC scheme, we
propose a two-stage approach that enables safe active exploration using a
left-kernel-based input disturbance design. This method generates informative
trajectories to enrich the historical data, which extends the maximum
achievable prediction horizon and leads to faster iteration convergence. In
addition, we present an end-to-end formulation of the two-stage approach,
integrating the disturbance design procedure into the planning phase. We
showcase the effectiveness of the proposed algorithms on a numerical
experiment.
