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

arXiv: https://arxiv.org/abs/2402.14374 · HTML: https://mlsanity.com/paper/2402.14374/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Feb 2024.

## Built on by (most cited first, 1 of 1)

- [Hierarchical Decision Making with Structured Policies: A Principled Design via Inverse Optimization](https://mlsanity.com/paper/2606.28764/) (2026)

## Abstract (arXiv)

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.