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Data-driven Model Predictive Control using MATLAB

Midhun T. Augustine

TL;DR

The paper surveys data-driven model predictive control (D-MPC), delineating model-based pathways like D-LMPC and D-NMPC alongside model-free approaches such as DeePC. It details concrete identification techniques (Ho-Kalman-Kung, PEM, SPC) and NN-based nonlinear predictors (RNN, SSNN) with numerical examples on standard LTI and nonlinear CSTR systems. Key contributions include a structured taxonomy of data-driven LMPC/NMPC methods, explicit data-driven constraints, and demonstrative simulations that validate stability, tracking, and constraint satisfaction under data-driven paradigms. The work highlights ongoing advancements, practical considerations, and future directions, including model-free data-driven strategies and the integration of reinforcement learning with MPC for adaptive and robust control.

Abstract

This paper presents a comprehensive overview of data-driven model predictive control, highlighting state-of-the-art methodologies and their numerical implementation. The discussion begins with a brief review of conventional model predictive control (MPC), which discusses both linear MPC (LMPC) and nonlinear MPC (NMPC). This is followed by a section on data-driven LMPC, outlining fundamental concepts and the implementation of various approaches, including subspace predictive control and prediction error methods. Subsequently, the focus shifts to data-driven NMPC, emphasizing approaches based on neural network models. The paper concludes with a review of recent advancements in data-driven MPC and explores potential directions for future research.

Data-driven Model Predictive Control using MATLAB

TL;DR

The paper surveys data-driven model predictive control (D-MPC), delineating model-based pathways like D-LMPC and D-NMPC alongside model-free approaches such as DeePC. It details concrete identification techniques (Ho-Kalman-Kung, PEM, SPC) and NN-based nonlinear predictors (RNN, SSNN) with numerical examples on standard LTI and nonlinear CSTR systems. Key contributions include a structured taxonomy of data-driven LMPC/NMPC methods, explicit data-driven constraints, and demonstrative simulations that validate stability, tracking, and constraint satisfaction under data-driven paradigms. The work highlights ongoing advancements, practical considerations, and future directions, including model-free data-driven strategies and the integration of reinforcement learning with MPC for adaptive and robust control.

Abstract

This paper presents a comprehensive overview of data-driven model predictive control, highlighting state-of-the-art methodologies and their numerical implementation. The discussion begins with a brief review of conventional model predictive control (MPC), which discusses both linear MPC (LMPC) and nonlinear MPC (NMPC). This is followed by a section on data-driven LMPC, outlining fundamental concepts and the implementation of various approaches, including subspace predictive control and prediction error methods. Subsequently, the focus shifts to data-driven NMPC, emphasizing approaches based on neural network models. The paper concludes with a review of recent advancements in data-driven MPC and explores potential directions for future research.
Paper Structure (24 sections, 1 theorem, 78 equations, 8 figures, 6 algorithms)

This paper contains 24 sections, 1 theorem, 78 equations, 8 figures, 6 algorithms.

Table of Contents

  1. Introduction
  2. Conventional MPC
  3. Conventional LMPC
  4. Output-based LMPC
  5. State-based LMPC
  6. Conventional NMPC
  7. Output-based NMPC
  8. State-based NMPC
  9. Data-driven Linear MPC
  10. Ho-Kalman-Kung Algorithm based D-LMPC
  11. D-LMPC based on Ho-Kalman-Kung algorithm: Numerical Example
  12. Subspace Predictive Control
  13. SPC: Numerical example
  14. Data-enabled Predictive Control (DeePC)
  15. DeePC: Numerical example
  16. ...and 9 more sections

Key Result

Lemma 1

Suppose $\{\mathbf{u}_{0},\mathbf{u}_{1},\dots,\mathbf{u}_{\mathrm{D}-1}\}$ is persistently exciting of order $\mathrm{N}+\mathrm{M}+n$. Then for every trajectory $(\mathbf{Y}_{k+1},\mathbf{U}_{k})$ of the system there exists a solution $\mathbf{v}_{k} \in \mathbb{R}^{\mathrm{H}}$ satisfies:

Figures (8)

  • Figure 1: Data-driven MPC block diagram.
  • Figure 2: Ho-Kalman-Kung based D-LMPC (a) Training input and output (b) State response (c) Control input.
  • Figure 3: SPC (a) Training input and output (b) Output response with SPC (c) Control input.
  • Figure 4: DeePC (a) Training input and output (b) Output response with DeePC (c) Control input.
  • Figure 5: PEM-based D-LMPC (a) Training input and output (b) Output with D-LMPC (b) Control input.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Definition 1: bJW05
  • Lemma 1: Fundamental lemma bJW05