  In this paper, we propose a data-driven approach to derive explicit
predictive control laws, without requiring any intermediate identification
step. The keystone of the presented strategy is the exploitation of available
priors on the control law, coming from model-based analysis. Specifically, by
leveraging on the knowledge that the optimal predictive controller is expressed
as a piecewise affine (PWA) law, we directly optimize the parameters of such an
analytical controller from data, instead of running an on-line optimization
problem. As the proposed method allows us to automatically retrieve also a
model of the closed-loop system, we show that we can apply model-based
techniques to perform a stability check prior to the controller deployment. The
effectiveness of the proposed strategy is assessed on two benchmark simulation
examples, through which we also discuss the use of regularization and its
combination with averaging techniques to handle the presence of noise.
