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Data-Driven Predictive Control Using Closed-Loop Data: An Instrumental Variable Approach

Yibo Wang, Yiwen Qiu, Malika Sader, Dexian Huang, Chao Shang

TL;DR

This letter points out that the original DDPC fails to represent all admissible trajectories due to feedback control, and the use of two forms of IVs is suggested to address this issue and the correlation between inputs and noise.

Abstract

Current data-driven predictive control (DDPC) methods heavily rely on data collected in open-loop operation with elaborate design of inputs. However, due to safety or economic concerns, systems may have to be under feedback control, where only closed-loop data are available. In this context, it remains challenging to implement DDPC using closed-loop data. In this paper, we propose a new DDPC method using closed-loop data by means of instrumental variables (IVs). By drawing from closed-loop subspace identification, the use of two forms of IVs is suggested to address the closed-loop issues caused by feedback control and the correlation between inputs and noise. Furthermore, a new DDPC formulation with a novel IV-inspired regularizer is proposed, where a balance between control cost minimization and weighted least-squares data fitting can be made for improvement of control performance. Numerical examples and application to a simulated industrial furnace showcase the improved performance of the proposed DDPC based on closed-loop data.

Data-Driven Predictive Control Using Closed-Loop Data: An Instrumental Variable Approach

TL;DR

This letter points out that the original DDPC fails to represent all admissible trajectories due to feedback control, and the use of two forms of IVs is suggested to address this issue and the correlation between inputs and noise.

Abstract

Current data-driven predictive control (DDPC) methods heavily rely on data collected in open-loop operation with elaborate design of inputs. However, due to safety or economic concerns, systems may have to be under feedback control, where only closed-loop data are available. In this context, it remains challenging to implement DDPC using closed-loop data. In this paper, we propose a new DDPC method using closed-loop data by means of instrumental variables (IVs). By drawing from closed-loop subspace identification, the use of two forms of IVs is suggested to address the closed-loop issues caused by feedback control and the correlation between inputs and noise. Furthermore, a new DDPC formulation with a novel IV-inspired regularizer is proposed, where a balance between control cost minimization and weighted least-squares data fitting can be made for improvement of control performance. Numerical examples and application to a simulated industrial furnace showcase the improved performance of the proposed DDPC based on closed-loop data.
Paper Structure (9 sections, 1 theorem, 33 equations, 4 figures)

This paper contains 9 sections, 1 theorem, 33 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Instrumental Variable-Aided Data-Driven Control
  4. IV based on future reference
  5. IV based on LCF of controller
  6. IV-aided DDPC and regularization
  7. Numerical Examples
  8. Application To A Simulated Tubular Furnace
  9. Conclusion

Key Result

Theorem 1

Assume that $\mathbb{U}$ and $\mathbb{Y}$ are convex sets. For $\lambda\ge0$, the regularized DDPC problem equation: regularized DeePC is a convex relaxation of the following variant of SPC, which is an indirect DDPC formulation: where $\Omega^*$ is a multi-step predictor fitted in a weighted least-squares sense based on the weighting matrix $\Phi^\top\Phi$.

Figures (4)

  • Figure 1: Overall control performance of different approaches at various noise levels in $200$ Monte Carlo simulations
  • Figure 2: Performance of the regularized DDPC \ref{['equation: regularized DeePC']} with IV \ref{['equation: IV closed loop']} averaged over $200$ data sets for different $\lambda$ from $10^{-3}$ to $10^5$ with SNR = $25$dB.
  • Figure 3: Structural diagram of industrial tubular furnace
  • Figure 4: Outputs of the tubular furnace system controlled by different controllers, including SPC, the proposed DDPC-IV and the stabilizing controller $C(z)$ designed as \ref{['equation: controller matrices Unisim']}.

Theorems & Definitions (2)

  • Theorem 1
  • proof