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Plasma start-up is typically achieved manipulating poloidal magnetic fields, gas injection and possibly auxiliary heating. Model-based design techniques have been gaining increasing attention in view of future large tokamaks which have more stringent constraints and less room for trial-and-error. In this paper, we formulate the tokamak start-up scenario design problem as a constrained optimization problem and introduce a novel shot-to-shot correction algorithm, based on the Iterative Learning Control concept, to compensate for unavoidable modeling errors based on experimental data. The effectiveness of the approach is demonstrated in experiments on the TCV tokamak showing that the target ramp-up scenario could be obtained in a small number of shots with a rough electromagnetic model.