# Regularized and Distributionally Robust Data-Enabled Predictive Control

## TL;DR

This paper introduces a distributionally robust version of data-enabled predictive control (DeePC) for stochastic systems, providing theoretical guarantees and demonstrating improved robustness through numerical case studies.

## Contribution

It develops a distributionally robust formulation of DeePC, linking it to regularization techniques, and offers probabilistic performance guarantees for unknown stochastic LTI systems.

## Key findings

- Robust DeePC coincides with a regularized optimization problem.
- The approach provides probabilistic guarantees for control performance.
- Numerical case studies demonstrate enhanced robustness.

## Abstract

In this paper, we study a data-enabled predictive control (DeePC) algorithm applied to unknown stochastic linear time-invariant systems. The algorithm uses noise-corrupted input/output data to predict future trajectories and compute optimal control policies. To robustify against uncertainties in the input/output data, the control policies are computed to minimize a worst-case expectation of a given objective function. Using techniques from distributionally robust stochastic optimization, we prove that for certain objective functions, the worst-case optimization problem coincides with a regularized version of the DeePC algorithm. These results support the previously observed advantages of the regularized algorithm and provide probabilistic guarantees for its performance. We illustrate the robustness of the regularized algorithm through a numerical case study.