Fast Explicit Machine Learning-Based Model Predictive Control of Nonlinear Processes Using Input Convex Neural Networks

Aug 4, 2026

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Explicit machine learning-based model predictive control (explicit ML-MPC) reduces real-time computational load versus traditional ML-MPC, but evaluating candidate actions can remain time-consuming because learned models create non-convex optimization. This work introduces an explicit ICNN-MPC by leveraging Input Convex Neural Networks (ICNN) so the control problem becomes a convex optimization task. ICNN captures nonlinear process dynamics, with conditions guaranteeing convexity in the resulting MPC. Candidate actions are then organized into MIQP problems derived from multi-parametric QP solutions, enabling real-time solution of convex MIQPs. Effectiveness is validated on a chemical reactor and a chemical process network simulated in Aspen Plus Dynamics, with Python-based control integrated via a programmable interface.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages50

Reading Time2 h 6 min

AccessFree to download

Abstract

Introduction

Machine learning-based MPC and nonconvex optimization challenges

Explicit ML-MPC framework and computational burden

Convex machine learning and ICNN properties

Improved ICNN-MPC with convex objectives

Case studies with Aspen Plus Dynamics

arXiv :2408 .06580v1 [math .OC] 13 Aug 2024 Fast Explicit Machine Learning-Based Model Predictive Control of Nonlinear Processes Using Input Convex Neural Networks Wenlong Wang,† Haohao Zhang,†,‡,¶ Yujia Wang,† Yuhe Tian,§ and Zhe Wu∗ ,† †Department of Chemical and Biomolecular Engineering, National University of Singapore, 117585, Singapore ‡Key Laboratory of Green Process and Engineering, Institute of Process Engineering, Chinese Academy of Sciences, Beijing 100190, China ¶School of Chemical Engineering, University of Chinese Academy of Sciences, Beijing 100049, China §Department of Chemical and Biomedical Engineering, West Virginia University, Morgantown, WV 26506, United States E-mail: [wuzhe@nus.edu.sg](wuzhe@nus.edu.sg) Abstract Explicit machine learning-based model predictive control (explicit ML-MPC) has been developed to reduce the real-time computational demands of traditional MLMPC. However, the evaluation of candidate control actions in explicit ML-MPC can be time-consuming due to the non-convex nature of machine learning models. To address this issue, we leverage Input Convex Neural Networks (ICNN) to develop explicit ICNN-MPC, which is formulated as a convex optimization problem. Specifically, ICNN is employed to capture nonlinear system dynamics and incorporated into MPC, with sufficient conditions provided to ensure the convexity of ICNN-based MPC. We then formulate mixed-integer quadratic programming (MIQP) problems based on the candidate control actions derived from the solutions of multi-parametric quadratic programming (mpQP) problems within the explicit ML-MPC framework. Optimal control actions are obtained by solving real-time convex MIQP problems. The effectiveness of the proposed method is demonstrated through two case studies, including a chemical reactor example, and a chemical process network simulated by Aspen Plus Dynamics, where explicit ML-MPC written in Python is integrated with Aspen dynamic simulation through a programmable interface. Introduction Machine learning (ML) models have exhibited great potential in various industrial applications due to their ability to effectively model highly nonlinear processes in chemical plants and petroleum refineries where first-principles models are rarely available. 1,2 Model predictive control (MPC), an advanced process control method, uses a predictive model for processes dynamics to obtain optimal control actions based on state measurements. 3–5 In recent years, machine learning-based model predictive control (ML-MPC) has been developed for nonlinear processes with data-driven models implemented by ML methods. 6,7 Although the use of ML models allows efficient modeling of nonlinear processes, it also poses challenges to the real-time implementation of ML-MPC due to the nonconvexity of ML models and the resulting non-convex ML-based optimization problems. 8 In our previous work, explicit ML-MPC 8 has been proposed to mitigate this issue following the idea of explicit MPC in which multi-parametric programming is utilized to convert real-time optimization problems into numerical evaluations. 9 A key step in the proposed explicit ML-MPC framework is the linearization of ML models via piecewise linear affine functions such that multi-parametric quadratic programming (mpQP) problems can be formulated for each segment of the discretized state-space. The solutions to mpQP problems provide a convenient and efficient way to obtain the optimal control actions based on real- time state measurements, compared to traditional implicit ML-MPC. However, the evaluation of candidate control actions in explicit ML-MPC can be time-consuming and computationally intensive due to the strong non-convexity introduced by ML models. Although the proposed explicit ML-MPC has managed to reduce the number of candidate control actions by converting the original continuous space to its discretized counterpart, finding the optimal one from these candidat

FAQs

What problem does explicit ML-MPC address, and what limitation remains?

Explicit ML-MPC reduces real-time computation by replacing optimization with offline multiparametric evaluation. However, candidate-action evaluation can still be time-consuming because ML models make the optimization non-convex, often leading to MIQP difficulties.

How does the proposed method use Input Convex Neural Networks (ICNN)?

ICNN is used as the predictive model inside MPC to ensure convexity properties. The work further improves ICNN so that the resulting MPC problem adopts a convex objective function, enabling a more tractable formulation.

How are optimal actions computed in real time?

Candidate control actions are generated from solutions of multi-parametric quadratic programming (mpQP). Real-time control is then obtained by solving convex MIQP problems constructed from those candidates.

Aug 4, 2026

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