Closed-loop Data-Enabled Predictive Control and its equivalence with Closed-loop Subspace Predictive Control

TL;DR

This paper introduces CL-DeePC, a unified framework for data-driven predictive control that mitigates noise bias and is computationally efficient, showing superior performance over DeePC in simulations.

Contribution

The paper proposes CL-DeePC, which incorporates instrumental variables for consistent prediction and demonstrates its equivalence to CL-SPC, improving robustness and efficiency.

Findings

CL-DeePC outperforms DeePC in reference tracking.

CL-DeePC exhibits 48% lower sensitivity to noise.

The framework unifies and extends existing predictive control methods.

Abstract

Factors like improved data availability and increasing system complexity have sparked interest in data-driven predictive control (DDPC) methods like Data-enabled Predictive Control (DeePC). However, closed-loop identification bias arises in the presence of noise, which reduces the effectiveness of obtained control policies. In this paper we propose Closed-loop Data-enabled Predictive Control (CL-DeePC), a framework that unifies different approaches to address this challenge. To this end, CL-DeePC incorporates instrumental variables (IVs) to synthesize and sequentially apply consistent single or multi-step-ahead predictors. Furthermore, a computationally efficient CL-DeePC implementation is developed that reveals an equivalence with Closed-loop Subspace Predictive Control (CL-SPC). Compared to DeePC, CL-DeePC simulations demonstrate superior reference tracking, with a sensitivity study finding a 48% lower susceptibility to noise-induced reference tracking performance degradation.