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Uncertainty-aware data-driven predictive control in a stochastic setting

Valentina Breschi, Marco Fabris, Simone Formentin, Alessandro Chiuso

TL;DR

This work addresses the sensitivity of data-driven predictive control (DDPC) to finite-sample uncertainty in stochastic settings. Building on the gamma-DDPC framework, it derives a statistical characterization of data-driven predictors and introduces two regularization strategies—regularizing $\gamma_2$ with $\beta_2$ and adding a slack via $\gamma_3$ with $\beta_3$—that can be tuned without additional experiments. Offline and online tuning analyses demonstrate that these strategies stabilize closed-loop performance and deliver results close to oracle, enabling safer deployment under noise and limited data. The approach provides a practical, uncertainty-aware DDPC workflow with direct implications for robust data-driven control in real-world systems.

Abstract

Data-Driven Predictive Control (DDPC) has been recently proposed as an effective alternative to traditional Model Predictive Control (MPC), in that the same constrained optimization problem can be addressed without the need to explicitly identify a full model of the plant. However, DDPC is built upon input/output trajectories. Therefore, the finite sample effect of stochastic data, due to, e.g., measurement noise, may have a detrimental impact on closed-loop performance. Exploiting a formal statistical analysis of the prediction error, in this paper we propose the first systematic approach to deal with uncertainty due to finite sample effects. To this end, we introduce two regularization strategies for which, differently from existing regularization-based DDPC techniques, we propose a tuning rationale allowing us to select the regularization hyper-parameters before closing the loop and without additional experiments. Simulation results confirm the potential of the proposed strategy when closing the loop.

Uncertainty-aware data-driven predictive control in a stochastic setting

TL;DR

This work addresses the sensitivity of data-driven predictive control (DDPC) to finite-sample uncertainty in stochastic settings. Building on the gamma-DDPC framework, it derives a statistical characterization of data-driven predictors and introduces two regularization strategies—regularizing with and adding a slack via with —that can be tuned without additional experiments. Offline and online tuning analyses demonstrate that these strategies stabilize closed-loop performance and deliver results close to oracle, enabling safer deployment under noise and limited data. The approach provides a practical, uncertainty-aware DDPC workflow with direct implications for robust data-driven control in real-world systems.

Abstract

Data-Driven Predictive Control (DDPC) has been recently proposed as an effective alternative to traditional Model Predictive Control (MPC), in that the same constrained optimization problem can be addressed without the need to explicitly identify a full model of the plant. However, DDPC is built upon input/output trajectories. Therefore, the finite sample effect of stochastic data, due to, e.g., measurement noise, may have a detrimental impact on closed-loop performance. Exploiting a formal statistical analysis of the prediction error, in this paper we propose the first systematic approach to deal with uncertainty due to finite sample effects. To this end, we introduce two regularization strategies for which, differently from existing regularization-based DDPC techniques, we propose a tuning rationale allowing us to select the regularization hyper-parameters before closing the loop and without additional experiments. Simulation results confirm the potential of the proposed strategy when closing the loop.
Paper Structure (9 sections, 42 equations, 1 figure)

This paper contains 9 sections, 42 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Background
  3. Problem setting
  4. Finite sample uncertainty of data-driven predictors
  5. Regularization design
  6. Regularizing $\gamma_2$
  7. Slack on output prediction
  8. Numerical examples
  9. Conclusions

Figures (1)

  • Figure 1: (a): Oracle tuning: average closed-loop costs $J_{AV,a}$ and their minimizers $\bar{\beta}_a$, $a=2,3$. (b),(c),(d): Distributions of the closed loop performance, control effort and relative tracking error over $1000$ Monte Carlo runs. Costs with bars refer to "oracle" tuning whereas costs with hats refer to online (feasible) strategy.