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Efficient Recursive Data-enabled Predictive Control (Extended Version)

Jicheng Shi, Yingzhao Lian, Colin N. Jones

TL;DR

This paper introduces a novel recursive updating algorithm for DeePC that emphasizes the use of Singular Value Decomposition (SVD) for efficient low-dimensional transformations of DeePC in its general form, as well as a fast SVD update scheme.

Abstract

In the field of model predictive control, Data-enabled Predictive Control (DeePC) offers direct predictive control, bypassing traditional modeling. However, challenges emerge with increased computational demand due to recursive data updates. This paper introduces a novel recursive updating algorithm for DeePC. It emphasizes the use of Singular Value Decomposition (SVD) for efficient low-dimensional transformations of DeePC in its general form, as well as a fast SVD update scheme. Importantly, our proposed algorithm is highly flexible due to its reliance on the general form of DeePC, which is demonstrated to encompass various data-driven methods that utilize Pseudoinverse and Hankel matrices. This is exemplified through a comparison to Subspace Predictive Control, where the algorithm achieves asymptotically consistent prediction for stochastic linear time-invariant systems. Our proposed methodologies' efficacy is validated through simulation studies.

Efficient Recursive Data-enabled Predictive Control (Extended Version)

TL;DR

This paper introduces a novel recursive updating algorithm for DeePC that emphasizes the use of Singular Value Decomposition (SVD) for efficient low-dimensional transformations of DeePC in its general form, as well as a fast SVD update scheme.

Abstract

In the field of model predictive control, Data-enabled Predictive Control (DeePC) offers direct predictive control, bypassing traditional modeling. However, challenges emerge with increased computational demand due to recursive data updates. This paper introduces a novel recursive updating algorithm for DeePC. It emphasizes the use of Singular Value Decomposition (SVD) for efficient low-dimensional transformations of DeePC in its general form, as well as a fast SVD update scheme. Importantly, our proposed algorithm is highly flexible due to its reliance on the general form of DeePC, which is demonstrated to encompass various data-driven methods that utilize Pseudoinverse and Hankel matrices. This is exemplified through a comparison to Subspace Predictive Control, where the algorithm achieves asymptotically consistent prediction for stochastic linear time-invariant systems. Our proposed methodologies' efficacy is validated through simulation studies.
Paper Structure (18 sections, 12 theorems, 49 equations, 3 figures, 1 table, 6 algorithms)

This paper contains 18 sections, 12 theorems, 49 equations, 3 figures, 1 table, 6 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Efficient recursive updates in the DeePC framework
  4. An equivalent low-dimensional transformation
  5. Efficient SVD updates
  6. Conclusion of the algorithm
  7. An extension to data-driven methods based-on Pseudoinverse
  8. Comparison to Data-driven prediction
  9. Comparison to SPC
  10. Simulation
  11. Validation of Algorithm \ref{['alg:ERdeepc']}
  12. Comparison to SPC
  13. Conclusion
  14. Proofs of Lemmas \ref{['lemma:deepc_spc1']} and \ref{['lemma:deepc_spc2']}
  15. Data-driven prediction: a specific form
  16. ...and 3 more sections

Key Result

Lemma 1

willems2005note Given a controllable linear system where $\{u_i\}_{i=1}^T$ is persistently exciting of order $L+ n_x$, the condition $\text{colspan}(^\top) = \mathfrak{B}_L(A,B,C,D)$ is satisfied.

Figures (3)

  • Figure 1: Comparison of Algorithm 1 and Algorithm 3.
  • Figure 2: Consisteny analysis by open-loop data. SPC: from \ref{['eqn:spc_1']} and \ref{['eqn:spc_2']}; DDP1: from \ref{['eqn:bilevel_deepc_op']}; DDP2: from \ref{['eqn:bilevel_deepc_cl']}. $K_{\cdot}^{\text{ground}}$ indicates the matrix from the ground truth.
  • Figure 3: Consisteny analysis by closed-loop data

Theorems & Definitions (27)

  • Lemma 1
  • Lemma 2
  • proof
  • Remark 1
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Remark 2
  • Lemma 5
  • ...and 17 more