Data-driven design of explicit predictive controllers using model-based priors

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.