{"title":"Enabling robust mixed-integer nonlinear model predictive control via self-supervised learning and combinatorial integral approximation","authors":"Joshua Adamek, Lukas Lüken, Sergio Lucia","doi":"10.1016/j.jprocont.2026.103636","DOIUrl":"10.1016/j.jprocont.2026.103636","url":null,"abstract":"<div><div>We present a novel approach that enables the solution of nonlinear model predictive control with integer decisions in real time even when when the model is subject to many uncertainties. Our approach tightly integrates three different ideas.</div><div>First, we use combinatorial integral approximation as a powerful heuristic to approximate the mixed-integer nonlinear problems with two nonlinear problems. Next, we formulate a scenario tree formulation to deal with uncertain parameters. To tackle the large number of uncertainties, we propose a scenario decomposition method to solve each scenario problem in parallel. We integrate the combinatorial approximation within this scenario decomposition method to provide a method for uncertain parameters within mixed-integer model predictive control. This method leads to many smaller optimization problems that can be solved in parallel. As the third idea, we propose the use of learned iterative solvers, as opposed to traditional numerical solvers, to solve each subproblem. This methodology can be massively parallelized by evaluating neural networks on powerful GPUs. As a result, the proposed approach leads to an order of magnitude faster solutions when compared to a solution of the entire robust problem with a traditional numerical solver, as well as to improved accuracy in comparison to a supervised learning approach. This is illustrated in the simulation example of an uncertain nonlinear reactor with mixed-integer decisions.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"159 ","pages":"Article 103636"},"PeriodicalIF":3.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146045295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Kaixun He , Xiaolong Chen , Hongyu Guo , Maiying Zhong , Han Jiang , Xin Peng
{"title":"A deep KM-GRU learning approach to time series prediction for non-linear dynamic industry process with outlier and time delay","authors":"Kaixun He , Xiaolong Chen , Hongyu Guo , Maiying Zhong , Han Jiang , Xin Peng","doi":"10.1016/j.jprocont.2026.103653","DOIUrl":"10.1016/j.jprocont.2026.103653","url":null,"abstract":"<div><div>In non-linear dynamic industrial processes, time delay often lead to numerous misalignment time labels and outliers in the raw data, thereby considerably compromising the accuracy and robustness of time series prediction models. To deal with these issues, a novel framework based on deep learning is proposed, which adopts gated recurrent unit (GRU) to construct a long-term time-series prediction model. In addition, kernel density estimation (KDE) and the maximum information coefficient (MIC) are employed for outlier detection and time delay calibration, respectively. Then, an improved variable selection mechanism is designed to identify important features. Furthermore, a differential evolution (DE) based algorithm is designed to obtain the optimal parameters of GRU model. Finally, to show the effectiveness of the proposed approach, two real-world industrial dataset exhibiting pronounced temporal nonlinear dynamics and a simulation dataset are considered. It is shown from the experimental results that the proposed approach can achieve accurate prediction performance.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"159 ","pages":"Article 103653"},"PeriodicalIF":3.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146190701","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Sparse optimization assisted adaptive and smart hybrid data-driven modeling for process systems","authors":"Shubhasmita Behera, Santhosh Kumar Varanasi","doi":"10.1016/j.jprocont.2026.103642","DOIUrl":"10.1016/j.jprocont.2026.103642","url":null,"abstract":"<div><div>Integration of data-driven and physics-based modeling approaches has become essential for achieving intelligent monitoring and control in modern process industries. This paper presents an adaptive hybrid data-driven identification framework for process systems that operate under varying conditions. The proposed method uses B-spline representations along with model-based regularization to ensure consistency. A sparsity constraint on model parameters improves interpretability and simplicity. To handle process variations, we developed an error-triggered adaptive mechanism that automatically updates the model structure and parameters when significant deviations occur. The resulting framework effectively captures dynamic behavior across multiple operating regimes. Validation on a quadruple-tank system and a non-isothermal continuous stirred-tank reactor shows improved prediction accuracy and greater robustness compared to standard methods. These results highlight the potential of the proposed framework as a tool for adaptive process modeling and predictive control in the context of Industry 4.0.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"159 ","pages":"Article 103642"},"PeriodicalIF":3.9,"publicationDate":"2026-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yu Wang , Xiao Chen , Hubert Schwarz , Véronique Chotteau , Elling W. Jacobsen
{"title":"A predictive modular approach to constraint satisfaction under uncertainty — with application to glycosylation in continuous monoclonal antibody biosimilar production","authors":"Yu Wang , Xiao Chen , Hubert Schwarz , Véronique Chotteau , Elling W. Jacobsen","doi":"10.1016/j.jprocont.2026.103632","DOIUrl":"10.1016/j.jprocont.2026.103632","url":null,"abstract":"<div><div>The paper proposes a modular-based approach to constraint handling in process optimization and control. This is partly motivated by the recent interest in learning-based methods, e.g., within bioproduction, for which constraint handling under uncertainty is a challenge. The proposed constraint handler, called predictive filter, is combined with an adaptive constraint margin and a constraint violation cost monitor to minimize the cost of violating soft constraints due to model uncertainty and disturbances. The module can be combined with any controller and is based on minimally modifying the controller output, in a least squares sense, such that constraints are satisfied within the considered horizon. The proposed method is computationally efficient and suitable for real-time applications. The effectiveness of the method is illustrated through a realistic case study of glycosylation constraint satisfaction in continuous monoclonal antibody biosimilar production using Chinese hamster ovary cells, employing a metabolic network model consisting of 23 extracellular metabolites and 126 reactions. In the case study, the average constraint-violation cost is reduced by more than 60% compared to the case without the proposed constraint-handling method.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103632"},"PeriodicalIF":3.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A microbial fuel cell with an optimal controller based on improved reptile search algorithm","authors":"Chenlong Wang, Fengying Ma","doi":"10.1016/j.jprocont.2026.103629","DOIUrl":"10.1016/j.jprocont.2026.103629","url":null,"abstract":"<div><div>Microbial fuel cells (MFCs) are novel energy technologies that convert the chemical energy of organic matter in wastewater into electrical energy. However, MFC systems generally require external control to achieve stable voltage output. In this paper, an optimal controller for MFC systems is designed. By adopting the <span><math><mi>θ</mi></math></span>–<span><math><mi>D</mi></math></span> technique, the intractable Hamilton–Jacobi–Bellman (HJB) equation is transformed into a set of algebraic equations, which enables the solution of the optimal control problem with large initial states. To address parameter uncertainty in the optimal controller, an optimization algorithm is employed to tune its parameters. Furthermore, to overcome the limitations of existing optimization algorithms, including slow convergence speed, low solution accuracy, and premature convergence, an improved reptile search algorithm is proposed by integrating chaotic mechanisms, an elite-guided differential perturbation strategy, and an adaptive crossover probability control mechanism. Simulation results demonstrate that the improved algorithm achieves faster convergence and higher accuracy. Moreover, the designed optimal controller exhibits smaller overshoot and steady-state error in the MFC.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103629"},"PeriodicalIF":3.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979671","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Thamires A.L. Guedes , Sergio A.C. Giraldo , Marcelo L. de Lima , Mario C.M.M. Campos , Daniel M. Lima , Leonardo D. Ribeiro , Argimiro R. Secchi
{"title":"Fuzzy advanced control: Boosting efficiency and economic benefits in offshore gas compression systems","authors":"Thamires A.L. Guedes , Sergio A.C. Giraldo , Marcelo L. de Lima , Mario C.M.M. Campos , Daniel M. Lima , Leonardo D. Ribeiro , Argimiro R. Secchi","doi":"10.1016/j.jprocont.2026.103635","DOIUrl":"10.1016/j.jprocont.2026.103635","url":null,"abstract":"<div><div>In this work, an advanced control system based on fuzzy logic is analyzed and implemented for a gas compression system on an offshore platform. This solution was applied after identifying an operational problem causing substantial economic losses due to unscheduled stops from high-temperature events at the compressor discharge. A detailed analysis of process variables that could be employed within the controller to mitigate this phenomenon was conducted, identifying compressor discharge temperatures as controlled variables and the machine’s discharge pressure setpoint as the primary manipulated variable. Through dynamic simulations and using a digital twin, it was possible to validate the behavior and effect of the variables, along with implementing the control system. Operational tests on the platform were conducted to verify the proposal and confirm the simulation results. The open-loop implementation of the control algorithm, i.e. the computed control action was not sent to the process, allowed the tracking and observation of the control system’s reaction to critical incidents, which validated its expected behavior. The activation of the closed-loop control successfully prevented machine stops, avoiding economic losses in production. This preventive approach avoided operational stops and highlighted the potential of advanced control systems to significantly improve safety, efficiency, and reliability in complex industrial environments.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103635"},"PeriodicalIF":3.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Collin R. Johnson , Kerstin Wohlgemuth , Sergio Lucia
{"title":"A tutorial overview of model predictive control for continuous crystallization: Current possibilities and future perspectives","authors":"Collin R. Johnson , Kerstin Wohlgemuth , Sergio Lucia","doi":"10.1016/j.jprocont.2026.103630","DOIUrl":"10.1016/j.jprocont.2026.103630","url":null,"abstract":"<div><div>Continuous crystallization processes require advanced control strategies to ensure consistent product quality, yet deploying optimization-based controllers such as model predictive control remains challenging. Combining spatially distributed crystallizer models with detailed particle size distributions leads to computationally demanding problems that are difficult to solve in real-time. This tutorial provides a comprehensive overview of how to address this challenge. Topics include numerical methods for solving population balance equations, modeling of crystallizers, and data-driven surrogate modeling. We show how these elements combine within a model predictive control framework to enable real-time control of particle size distributions. Two case studies illustrate the complete workflow: a well-mixed crystallizer that allows comparison with established methods, and a spatially distributed plug-flow crystallizer that demonstrates application to more complex systems. Readers gain a practical roadmap for implementing model predictive control in continuous crystallization, supported by open-source code and interactive examples. The tutorial concludes by outlining open challenges and emerging opportunities in the field.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103630"},"PeriodicalIF":3.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145979670","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Shaoyuan Li, Haolei Yin, Xiaohong Yin, Wenjian Cai
{"title":"A physics-guided hybrid model for calendering width prediction in rubber tire manufacturing","authors":"Shaoyuan Li, Haolei Yin, Xiaohong Yin, Wenjian Cai","doi":"10.1016/j.jprocont.2025.103612","DOIUrl":"10.1016/j.jprocont.2025.103612","url":null,"abstract":"<div><div>The width in rubber extrusion-calendering is a crucial process parameter in the rubber production workflow, as it directly influences both the quality and performance of rubber products, as well as overall production efficiency. However, the rubber extrusion-calendering process involves strong coupling among multiple parameters, with operating condition variations and significant external disturbances, leading to complex dynamic characteristics such as nonlinearity and time delays, which severely impact the accuracy of width prediction. To address these challenges, a hybrid modeling approach that integrates physical mechanisms with data-driven methods has been proposed within the framework of Physics-Informed Neural Networks (PINN). Firstly, a data-driven prediction model for calendering width was developed using a combination of a Temporal Convolutional Network and a Bidirectional Long Short-Term Memory network (TCN-BiLSTM). Secondly, an analysis of the physical mechanism underlying the extrusion-calendering process was conducted based on the power-law constitutive relationship to provide essential physical constraints for the prediction model. Furthermore, a dynamically adaptive weighting strategy was proposed to effectively reconcile conflicts between physical constraints and data fitting in the PINN model. Validation experiments demonstrate that this hybrid modeling approach can sustain high prediction accuracy even when faced with limited training data, noise interference, and varying operating conditions.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103612"},"PeriodicalIF":3.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928436","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Gain-scheduled tube-based MPC for quasi-LPV systems using vertex models","authors":"Rangoli Singh , Sandip Ghosh , Devender Singh , Pawel Dworak","doi":"10.1016/j.jprocont.2025.103617","DOIUrl":"10.1016/j.jprocont.2025.103617","url":null,"abstract":"<div><div>This work develops a tube-based model predictive control (MPC) scheme for quasi–linear parameter-varying (quasi-LPV) systems affected by bounded disturbances and time-varying but measurable scheduling parameters. The controller uses a polytopic model together with a gain-scheduled feedback law to maintain robustness against parameter variations and external disturbances. To describe the terminal region more flexibly, a parameter-dependent terminal cost is introduced. In addition, an auxiliary cost function, evaluated only at the vertices of the polytope, removes the need to update parameters at every prediction step. Although the proposed formulation increases the computational load slightly, it provides stronger disturbance rejection and improved constraint handling. Experiments on a coupled-tank setup demonstrate that the method is both effective and practical for real-time implementation.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103617"},"PeriodicalIF":3.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"On data-driven robust optimization with multiple uncertainty subsets: Unified uncertainty set representation and mitigating conservatism","authors":"Yun Li , Neil Yorke-Smith , Tamas Keviczky","doi":"10.1016/j.jprocont.2025.103611","DOIUrl":"10.1016/j.jprocont.2025.103611","url":null,"abstract":"<div><div>Constructing uncertainty sets as unions of multiple subsets has emerged as an effective approach for creating compact and flexible uncertainty representations in data-driven robust optimization (RO). This paper focuses on two separate research questions. The first concerns the computational challenge in applying these uncertainty sets in RO-based predictive control. To address this, a monolithic mixed-integer representation of the uncertainty set is proposed to uniformly describe the union of multiple subsets, enabling the computation of the worst-case uncertainty scenario across all subsets within a single mixed-integer linear programming (MILP) problem. The second research question focuses on mitigating the conservatism of conventional RO formulations by leveraging the structure of the uncertainty set. To achieve this, a novel objective function is proposed to exploit the uncertainty set structure and integrate the existing RO and distributionally robust optimization (DRO) formulations, yielding less conservative solutions than conventional RO formulations, while avoiding the high-dimensional continuous uncertainty distributions and the high computational burden typically associated with existing DRO formulations. Given the proposed formulations, numerically efficient computation methods based on <em>column-and-constraint generation</em> (CCG) are also developed. Extensive simulations across three case studies are performed to demonstrate the effectiveness of the proposed schemes.</div></div>","PeriodicalId":50079,"journal":{"name":"Journal of Process Control","volume":"158 ","pages":"Article 103611"},"PeriodicalIF":3.9,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145928383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}