Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Rogier Dinkla, Sebastiaan Mulders, Tom Oomen, Jan-Willem van Wingerden

TL;DR

The paper addresses the problem of closed-loop identification bias in data-driven predictive control (DeePC) when data are collected in closed-loop under noise. It introduces Closed-loop Data-enabled Predictive Control (CL-DeePC), which uses instrumental variables to build consistent single or multi-step-ahead predictors and provides a computationally efficient sequential implementation. The authors show an equivalence between the proposed CL-DeePC and Closed-loop Subspace Predictive Control (CL-SPC) and demonstrate via simulations that CL-DeePC achieves better reference tracking and reduced noise sensitivity compared with DeePC (notably a 48% reduction in noise-induced deterioration). They also discuss future work on exploring alternative instrumental variables and settings for the unified CL-DeePC framework.

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.

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

TL;DR

The paper addresses the problem of closed-loop identification bias in data-driven predictive control (DeePC) when data are collected in closed-loop under noise. It introduces Closed-loop Data-enabled Predictive Control (CL-DeePC), which uses instrumental variables to build consistent single or multi-step-ahead predictors and provides a computationally efficient sequential implementation. The authors show an equivalence between the proposed CL-DeePC and Closed-loop Subspace Predictive Control (CL-SPC) and demonstrate via simulations that CL-DeePC achieves better reference tracking and reduced noise sensitivity compared with DeePC (notably a 48% reduction in noise-induced deterioration). They also discuss future work on exploring alternative instrumental variables and settings for the unified CL-DeePC framework.

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.
Paper Structure (5 sections, 3 figures)

This paper contains 5 sections, 3 figures.

Table of Contents

  1. Parametric sensitivity analysis
  2. Number of past data samples: $\bar{N}$
  3. Noise level: $\Sigma(e_k)$
  4. Data window lengths: $p=f$
  5. Conclusion

Figures (3)

  • Figure 6: Effect of $\bar{N}$ on reference tracking performance. Shaded regions indicate the 10th, 30th, 70th and 90th percentiles of 120 simulations.
  • Figure 7: Effect of $\Sigma(e_k)$ on reference tracking performance. Shaded regions indicate the 10th, 30th, 70th and 90th percentiles over 120 simulations.
  • Figure 8: Effect of $f=p$ on reference tracking performance. Shaded regions indicate the 10th, 30th, 70th and 90th percentiles of 120 simulations.