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

TL;DR

This paper introduces a systematic approach to handle uncertainty in data-driven predictive control caused by finite sample effects, using statistical analysis and regularization strategies with pre-tuning capabilities.

Contribution

It presents the first formal method to address stochastic data uncertainty in DDPC, including new regularization techniques with pre-tuning without extra experiments.

Findings

Regularization improves closed-loop performance under uncertainty.

Pre-tuning of hyper-parameters is feasible before deployment.

Simulation confirms effectiveness of the proposed strategies.

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.