  Data-Driven Predictive Control (DDPC) has been recently proposed as an
effective alternative to traditional Model Predictive Control (MPC), in that
the same constrained optimization problem can be addressed without the need to
explicitly identify a full model of the plant. However, DDPC is built upon
input/output trajectories. Therefore, the finite sample effect of stochastic
data, due to, e.g., measurement noise, may have a detrimental impact on
closed-loop performance. Exploiting a formal statistical analysis of the
prediction error, in this paper we propose the first systematic approach to
deal with uncertainty due to finite sample effects. To this end, we introduce
two regularization strategies for which, differently from existing
regularization-based DDPC techniques, we propose a tuning rationale allowing us
to select the regularization hyper-parameters before closing the loop and
without additional experiments. Simulation results confirm the potential of the
proposed strategy when closing the loop.
