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In this letter we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over a linearly interpolated initial state constraint in combination with a simplified affine disturbance feedback policy. We consider a moment-based ambiguity set with data-driven radius for the second moment of the disturbance, where we derive a minimum number of samples in order to ensure user-given confidence bounds on the chance constraints and closed-loop performance. This letter closes with a numerical example, highlighting the performance gain and chance constraint satisfaction based on different sample sizes.

Recursively Feasible Data-Driven Distributionally Robust Model Predictive Control With Additive Disturbances