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Learning-Based Efficient Approximation of Data-Enabled Predictive Control

Yihan Zhou, Yiwen Lu, Zishuo Li, Jiaqi Yan, Yilin Mo

TL;DR

An efficient approximation of DeePC, whose size is invariant with respect to the amount of data collected, via differentiable convex programming is proposed, which can reduce the computational time of DeePC by a factor of 5 while maintaining its control performance.

Abstract

Data-Enabled Predictive Control (DeePC) bypasses the need for system identification by directly leveraging raw data to formulate optimal control policies. However, the size of the optimization problem in DeePC grows linearly with respect to the data size, which prohibits its application to resource-constrained systems due to high computational costs. In this paper, we propose an efficient approximation of DeePC, whose size is invariant with respect to the amount of data collected, via differentiable convex programming. Specifically, the optimization problem in DeePC is decomposed into two parts: a control objective and a scoring function that evaluates the likelihood of a guessed I/O sequence, the latter of which is approximated with a size-invariant learned optimization problem. The proposed method is validated through numerical simulations on a quadruple tank system, illustrating that the learned controller can reduce the computational time of DeePC by a factor of 5 while maintaining its control performance.

Learning-Based Efficient Approximation of Data-Enabled Predictive Control

TL;DR

An efficient approximation of DeePC, whose size is invariant with respect to the amount of data collected, via differentiable convex programming is proposed, which can reduce the computational time of DeePC by a factor of 5 while maintaining its control performance.

Abstract

Data-Enabled Predictive Control (DeePC) bypasses the need for system identification by directly leveraging raw data to formulate optimal control policies. However, the size of the optimization problem in DeePC grows linearly with respect to the data size, which prohibits its application to resource-constrained systems due to high computational costs. In this paper, we propose an efficient approximation of DeePC, whose size is invariant with respect to the amount of data collected, via differentiable convex programming. Specifically, the optimization problem in DeePC is decomposed into two parts: a control objective and a scoring function that evaluates the likelihood of a guessed I/O sequence, the latter of which is approximated with a size-invariant learned optimization problem. The proposed method is validated through numerical simulations on a quadruple tank system, illustrating that the learned controller can reduce the computational time of DeePC by a factor of 5 while maintaining its control performance.
Paper Structure (11 sections, 1 theorem, 15 equations, 4 figures, 1 table, 1 algorithm)

This paper contains 11 sections, 1 theorem, 15 equations, 4 figures, 1 table, 1 algorithm.

Table of Contents

  1. INTRODUCTION
  2. PRELIMINARIES
  3. Problem Formulation
  4. Data-Enabled Predictive Control (DeePC)
  5. COMPUTATIONALLY EFFICIENT DEEPC VIA LEARNING-BASED APPROXIMATION
  6. DeePC through the Lens of Scoring Function
  7. Learning Objective
  8. Approximator Form: Differentiable Convex Program
  9. Learning Algorithm
  10. SIMULATION
  11. CONCLUSIONS

Key Result

Proposition 1

With sufficiently large $n_z$ and $m_z$, the true $S(\tau)$ is representable by eq:score_approx.

Figures (4)

  • Figure 1: Illustration of the overall framework. The optimization objective of DeePC can be split into two parts: the control cost $\ell(\tau)$ and the score function $S(\tau)$. Subsequently, $S(\tau)$ is approximated by $\hat{S}(\tau)$, which is learned offline. The learning-based efficient approximation of DeePC is formulated as minimizing the sum of the control cost $\ell(\tau)$ and the learned approximate score $\hat{S}(\tau)$.
  • Figure 2: Illustration of evaluating $\operatorname{Prox}_{\hat{S}}$ with unrolled DRS iterations. The input is an I/O sequence $\tau$ and the initial values of $z, \tau, \xi, \eta$, and the output is $\operatorname{Prox}_{\hat{S}}({\tau})$, denoted as $\hat{\tau}^{\star}$. The learnable parameters are $d_1, d_2, G, W$. is the soft-thresholding operator \ref{['eq:sh']}, and the Affine block is the composition of all affine transformations in each iteration \ref{['eq:DRS']}.
  • Figure 3: Tracking performance of DeePC and our approach.
  • Figure 4: Comparison of the cost-time curves between DeePC and our approach. The average computation time for DeePC is influenced by the number of I/O sequences in the data matrix, whereas our approach's computation time primarily depends on the size of the learned approximate scoring function.

Theorems & Definitions (3)

  • Remark 1
  • Proposition 1
  • proof