(372d) Explicit Machine Learning-Based Model Predictive Control of Nonlinear Processes

Machine learning-based model predictive control (ML-MPC) has been developed to control nonlinear processes with unknown first-principles models [1]. Although ML models can capture the nonlinear dynamics of complex systems, the complexity of ML models leads to increased computation time for real-time implementation of ML-MPC. A promising solution to this issue is to take advantage of explicit MPC to develop explicit ML-MPC, in which real-time optimization problems are converted to numerical evaluations [2]. Over the past few decades, multi-parametric programming, the mathematical tool behind explicit MPC, has been extensively studied by many researchers, including multi-parametric linear/quadratic programming (mpLP/mpQP), multi-parametric mixed-integer linear/quadratic programming (mpMILP/mpMIQP), and multi-parametric nonlinear programming (mpNLP) [3]. Substantial progress has been made regarding efficient algorithms and their computer-based implementations. Multi-parametric programming has received considerable attention as it can provide the full solution map of an optimization problem prior to the determination of its uncertain parameters [4]. However, the black-box nature of ML models brings challenges to the existing multi-parametric programming algorithms when developing explicit ML-MPC, since ML models generally do not have explicit expressions (or difficult to represent). Recent studies on explicit ML-MPC focused primarily on neural networks that feature rectified linear unit (ReLU) as their nonlinear activation function [5]. At this stage, how to develop explicit ML-MPC for a general class of (nonlinear) ML models with more complicated architectures (e.g., using tanh or softmax as activation functions to gain stronger nonlinearity), is an open question.

In this work, we propose an explicit ML-MPC framework for nonlinear processes via multi-parametric programming. Specifically, a self-adaptive approximation algorithm is first developed to obtain piecewise linear affine functions that approximate the behaviors of ML models. Subsequently, the corresponding mpNLP problems are approximated by mpQP problems whose solutions can be efficiently found by existing algorithms. Furthermore, a neighbor-first search (NFS) algorithm is proposed and implemented together with parallel computing to mitigate the issues due to the linearization of ML models. Finally, a chemical process is used as an example to demonstrate that the proposed explicit ML-MPC scheme can achieve similar closed-loop performance as the traditional implicit ML-MPC, while the computational efficiency is significantly improved.

References:

[1] Daoutidis, P., Megan, L., Tang, W., 2023. The future of control of process systems. Computers & Chemical Engineering 178, 108365.

[2] Pappas, I., Kenefake, D., Burnak, B., Avraamidou, S., Ganesh, H.S., Katz, J., Diangelakis, N.A., Pistikopoulos, E.N., 2021. Multiparametric programming in process systems engineering: Recent developments and path forward. Frontiers in Chemical Engineering 2, 620168.

[3] Pistikopoulos, E.N., Diangelakis, N.A., Oberdieck, R., 2020. Multi-parametric optimization and control. John Wiley & Sons, London.

[4] Tian, Y., Pappas, I., Burnak, B., Katz, J., Pistikopoulos, E.N., 2021. Simultaneous design & control of a reactive distillation system–a parametric optimization & control approach. Chemical Engineering Science 230, 116232.

[5] Katz, J., Pappas, I., Avraamidou, S., Pistikopoulos, E.N., 2020. Integrating deep learning models and multiparametric programming. Computers & Chemical Engineering 136, 106801.