  In this paper we discuss distributional robustness in the context of
stochastic model predictive control (SMPC) for linear time-invariant systems.
We derive a simple approximation of the MPC problem under an additive zero-mean
i.i.d. noise with quadratic cost. Due to the lack of distributional
information, chance constraints are enforced as distributionally robust (DR)
chance constraints, which we opt to unify with the concept of probabilistic
reachable sets (PRS). For Wasserstein ambiguity sets, we propose a simple
convex optimization problem to compute the DR-PRS based on finitely many
disturbance samples. The paper closes with a numerical example of a double
integrator system, highlighting the reliability of the DR-PRS w.r.t. the
Wasserstein set and performance of the resulting SMPC.
