Robust Data-Enabled Predictive Control: Tractable Formulations and Performance Guarantees

TL;DR

This paper presents a robust, model-free predictive control framework for linear systems that guarantees performance despite data uncertainties, using tractable min-max optimization reformulations and demonstrating effectiveness in power system simulations.

Contribution

It introduces a robust DeePC framework with computationally tractable reformulations and performance guarantees, extending regularized DeePC methods.

Findings

Robust DeePC provides performance guarantees despite data noise.

The framework is computationally tractable with various uncertainty sets.

Demonstrated effectiveness on nonlinear, noisy power system simulations.

Abstract

We introduce a general framework for robust data-enabled predictive control (DeePC) for linear time-invariant (LTI) systems. The proposed framework enables us to obtain model-free optimal control for LTI systems based on noisy input/output data. More specifically, robust DeePC solves a min-max optimization problem to compute the optimal control sequence that is resilient to all possible realizations of the uncertainties in the input/output data within a prescribed uncertainty set. We present computationally tractable reformulations of the min-max problem with various uncertainty sets. Furthermore, we show that even though an accurate prediction of the future behavior is unattainable in practice due to inaccessibility of the perfect input/output data, the obtained robust optimal control sequence provides performance guarantees for the actually realized input/output cost. We further show that the robust DeePC generalizes and robustifies the regularized DeePC (with quadratic regularization or 1-norm regularization) proposed in the literature. Finally, we demonstrate the performance of the proposed robust DeePC algorithm on high-fidelity, nonlinear, and noisy simulations of a grid-connected power converter system.