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Deep DeePC: Data-enabled predictive control with low or no online optimization using deep learning

Xuewen Zhang, Kaixiang Zhang, Zhaojian Li, Xunyuan Yin

TL;DR

A deep neural network is employed to learn the DeePC vector operator, which is an essential component of the non‐parametric representation of DeePC, and this neural network is trained offline using historical open‐loop input and output data of the nonlinear process.

Abstract

Data-enabled predictive control (DeePC) is a data-driven control algorithm that utilizes data matrices to form a non-parametric representation of the underlying system, predicting future behaviors and generating optimal control actions. DeePC typically requires solving an online optimization problem, the complexity of which is heavily influenced by the amount of data used, potentially leading to expensive online computation. In this paper, we leverage deep learning to propose a highly computationally efficient DeePC approach for general nonlinear processes, referred to as Deep DeePC. Specifically, a deep neural network is employed to learn the DeePC vector operator, which is an essential component of the non-parametric representation of DeePC. This neural network is trained offline using historical open-loop input and output data of the nonlinear process. With the trained neural network, the Deep DeePC framework is formed for online control implementation. At each sampling instant, this neural network directly outputs the DeePC operator, eliminating the need for online optimization as conventional DeePC. The optimal control action is obtained based on the DeePC operator updated by the trained neural network. To address constrained scenarios, a constraint handling scheme is further proposed and integrated with the Deep DeePC to handle hard constraints during online implementation. The efficacy and superiority of the proposed Deep DeePC approach are demonstrated using two benchmark process examples.

Deep DeePC: Data-enabled predictive control with low or no online optimization using deep learning

TL;DR

A deep neural network is employed to learn the DeePC vector operator, which is an essential component of the non‐parametric representation of DeePC, and this neural network is trained offline using historical open‐loop input and output data of the nonlinear process.

Abstract

Data-enabled predictive control (DeePC) is a data-driven control algorithm that utilizes data matrices to form a non-parametric representation of the underlying system, predicting future behaviors and generating optimal control actions. DeePC typically requires solving an online optimization problem, the complexity of which is heavily influenced by the amount of data used, potentially leading to expensive online computation. In this paper, we leverage deep learning to propose a highly computationally efficient DeePC approach for general nonlinear processes, referred to as Deep DeePC. Specifically, a deep neural network is employed to learn the DeePC vector operator, which is an essential component of the non-parametric representation of DeePC. This neural network is trained offline using historical open-loop input and output data of the nonlinear process. With the trained neural network, the Deep DeePC framework is formed for online control implementation. At each sampling instant, this neural network directly outputs the DeePC operator, eliminating the need for online optimization as conventional DeePC. The optimal control action is obtained based on the DeePC operator updated by the trained neural network. To address constrained scenarios, a constraint handling scheme is further proposed and integrated with the Deep DeePC to handle hard constraints during online implementation. The efficacy and superiority of the proposed Deep DeePC approach are demonstrated using two benchmark process examples.
Paper Structure (31 sections, 1 theorem, 25 equations, 7 figures, 10 tables, 1 algorithm)

This paper contains 31 sections, 1 theorem, 25 equations, 7 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries and problem formulation
  3. Applicability of DeePC for nonlinear systems
  4. Deep learning-based DeePC control approach
  5. Event-based constraint handling
  6. Extension of the proposed method
  7. Case study on gene regulatory network
  8. Case study on chemical process
  9. Conclusion
  10. Acknowledgment
  11. Data availability statement

Key Result

Lemma 1

(Willems' fundamental lemma willems2005note) Consider an LTI system (lti-sys) and assume this system is controllable. Consider that $\mathbf{u}_T^d := \{u^d\}_1^T \in \mathbb{R}^{n_u T}$ and $\mathbf{y}_T^d := \{y^d\}_1^T \in \mathbb{R}^{n_y T}$ are the T-step input and output sequences for system ( for vector $g \in \mathbb{R}^{T-L+1}$.

Figures (7)

  • Figure 1: A graphical illustration of the proposed deep learning-enabled DeePC pipeline.
  • Figure 2: A graphical illustration of the construction of training data based on system historical data collected offline.
  • Figure 3: A block diagram of the online implementation of the proposed deep learning-enabled DeePC design with an event-based constraint handling scheme.
  • Figure 4: Output and control input trajectories of GRN under designs with reference input.
  • Figure 5: A schematic diagram of the reactor-separator process.
  • ...and 2 more figures

Theorems & Definitions (6)

  • Definition 1
  • Lemma 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4