Data-driven predictive control in a stochastic setting: a unified framework. (June 2023) - Breschi, Valentina; Chiuso, Alessandro; Formentin, Simone
Abstract: 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; ( i i ) we introduce γ -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; ( i i i ) 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 γ -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.