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Reduced-order Koopman modeling and predictive control of nonlinear processes

Xuewen Zhang, Minghao Han, Xunyuan Yin

TL;DR

This work tackles the challenge of controlling large-scale nonlinear processes in real time by introducing a data-driven, reduced-order Koopman framework. It combines Kalman-GSINDy to automatically select lifting functions with POD to compress lifted dynamics into a small number of latent states, enabling a linear predictor that can be controlled with robust MPC. The approach is validated on a reactor-separator process, showing comparable set-point tracking performance to full-order models while reducing computation time by roughly 45%. The methodology offers a practical path to scalable, data-driven control of nonlinear systems with rigorous stability considerations and improved computational efficiency.

Abstract

In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to select lifting functions for Koopman identification. The selected lifting functions are used to project the original nonlinear state-space into a higher-dimensional linear function space, in which Koopman-based linear models can be constructed for the underlying nonlinear process. To curb the significant increase in the dimensionality of the resulting full-order Koopman models caused by the use of lifting functions, we propose a reduced-order Koopman modeling approach based on proper orthogonal decomposition. A computationally efficient linear robust predictive control scheme is established based on the reduced-order Koopman model. A case study on a benchmark chemical process is conducted to illustrate the effectiveness of the proposed method. Comprehensive comparisons are conducted to demonstrate the advantage of the proposed method.

Reduced-order Koopman modeling and predictive control of nonlinear processes

TL;DR

This work tackles the challenge of controlling large-scale nonlinear processes in real time by introducing a data-driven, reduced-order Koopman framework. It combines Kalman-GSINDy to automatically select lifting functions with POD to compress lifted dynamics into a small number of latent states, enabling a linear predictor that can be controlled with robust MPC. The approach is validated on a reactor-separator process, showing comparable set-point tracking performance to full-order models while reducing computation time by roughly 45%. The methodology offers a practical path to scalable, data-driven control of nonlinear systems with rigorous stability considerations and improved computational efficiency.

Abstract

In this paper, we propose an efficient data-driven predictive control approach for general nonlinear processes based on a reduced-order Koopman operator. A Kalman-based sparse identification of nonlinear dynamics method is employed to select lifting functions for Koopman identification. The selected lifting functions are used to project the original nonlinear state-space into a higher-dimensional linear function space, in which Koopman-based linear models can be constructed for the underlying nonlinear process. To curb the significant increase in the dimensionality of the resulting full-order Koopman models caused by the use of lifting functions, we propose a reduced-order Koopman modeling approach based on proper orthogonal decomposition. A computationally efficient linear robust predictive control scheme is established based on the reduced-order Koopman model. A case study on a benchmark chemical process is conducted to illustrate the effectiveness of the proposed method. Comprehensive comparisons are conducted to demonstrate the advantage of the proposed method.
Paper Structure (17 sections, 27 equations, 8 figures, 6 tables)

This paper contains 17 sections, 27 equations, 8 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Koopman identification for controlled systems
  4. Proper orthogonal decomposition
  5. Problem formulation
  6. POD-based Koopman modeling using Kalman-GSINDy
  7. Architecture of the proposed mechanism
  8. Kalman-GSINDy
  9. POD-based reduced-order Koopman identification
  10. Robust MPC with reduced-order Koopman operators
  11. Application to a reactor-separator process
  12. Process description and process operation objective
  13. Simulation setting
  14. Reduced-order Koopman modeling
  15. Control performance
  16. ...and 2 more sections

Figures (8)

  • Figure 1: A graphical illustration of the proposed reduced-order Koopman model for control.
  • Figure 2: A block diagram of the reduced-order robust Koopman MPC.
  • Figure 3: Reactor-separator process.
  • Figure 4: Trajectories of the heat inputs generated for modeling.
  • Figure 5: Prediction trajectories under the full-order Koopman and reduced-order Koopman model. The order of the full-order Koopman state is $N=16$, and the order of the reduced-order Koopman state is $r=8$.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Remark 1
  • Remark 2