  Data-driven predictive control (DDPC) has been recently proposed as an
effective alternative to traditional model-predictive control (MPC) for its
unique features of being time-efficient and unbiased with respect to the oracle
solution. Nonetheless, it has also been observed that noise may strongly
jeopardize the final closed-loop performance since it affects both the
data-based system representation and the control update computed from the
online measurements. Recent studies have shown that regularization is
potentially a successful tool to counteract the effect of noise. At the same
time, regularization requires the tuning of a set of penalty terms, whose
choice might be practically difficult without closed-loop experiments. In this
paper, by means of subspace identification tools, we pursue a three-fold goal:
$(i)$ we set up a unified framework for the existing regularized data-driven
predictive control schemes for stochastic systems; $(ii)$ we introduce
$\gamma$-DDPC, an efficient two-stage scheme that splits the optimization
problem into two parts: fitting the initial conditions and optimizing the
future performance, while guaranteeing constraint satisfaction; $(iii)$ we
discuss the role of regularization for data-driven predictive control,
providing new insight on $when$ and $how$ it should be applied. A benchmark
numerical case study finally illustrates the performance of $\gamma$-DDPC,
showing how controller design can be simplified in terms of tuning effort and
computational complexity when benefiting from the insights coming from the
subspace identification realm.
