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

arXiv: https://arxiv.org/abs/2203.10846 · HTML: https://mlsanity.com/paper/2203.10846/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Mar 2022.

## Built on by (most cited first, 4 of 4)

- [Nonlinear sparse variational Bayesian learning based model predictive control with application to PEMFC temperature control](https://mlsanity.com/paper/2404.09519/) (2024)
- [Recursive Gaussian Process State Space Model](https://mlsanity.com/paper/2411.14679/) (2024)
- [Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes](https://mlsanity.com/paper/2501.15849/) (2025)
- [Robust Least-Squares Optimization for Data-Driven Predictive Control: A Geometric Approach](https://mlsanity.com/paper/2511.09242/) (2025)

## Abstract (arXiv)

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 γ-DDPC, an efficient two-stage scheme that splits the optimization problem into 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 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.