Data-driven predictive control in a stochastic setting: a unified framework

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 in 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. (c) 2023 Elsevier Ltd. All rights reserved.