Data Science and Model Predictive Control:

Model Predictive Control (MPC) is an established control framework, based on the solution of an optimisation problem to determine the (optimal) control action at each discrete-time sample. Accordingly, major theoretical advances have been provided in the literature, such as closed-loop stability and recursive feasibility certificates, for the most diverse kinds of processes descriptions. Nevertheless, identifying good, trustworthy models for complex systems is a task heavily affected by uncertainties. As of this, developing MPC algorithms directly from data has recently received a considerable amount of attention over the last couple of years. In this work, we review the available data-based MPC formulations, which range from reinforcement learning schemes, adaptive controllers, and novel solutions based on behavioural theory and trajectory representations. In particular, we examine the recent research body on this topic, highlighting the main features and capabilities of available algorithms, while also discussing the fundamental connections among approaches and, comparatively, their advantages and limitations.