This paper presents a Neural-Network Assisted Model Predictive Control (NN-A-MPC) framework for robust control of complex systems such as flow reactors. The approach combines an iterative neural-network-based design-space exploitation (DSE) with physics-based model (PBM) optimization. The DSE provides a promising warm start and reduces the search space for the PBM optimization in which relevant input regions are refined to ensure accuracy and physical feasibility. An integral compensation state enhances robustness against model mismatch and disturbances. Experimental validation on a Paal-Knorr flow reactor demonstrates accurate tracking while satisfying real-time constraints.
Ensuring safety in robust nonlinear model predictive control requires to consider all states that are reachable from a given initial condition due to uncertainty in the system model. However, calculating an exact representation of these reachable sets is difficult in the general nonlinear case and is prone to conservatism, especially for high-dimensional uncertainty. In this paper, we propose an approach to approximate the propagation of reachable sets with zonotopic parameterizations using a neural network. By doing this, we avoid the system specific effort to calculate an analytical over-approximation of the reachable set propagation. Additionally, the complexity of the online optimization problem is independent of the number of uncertain parameters. We then integrate the data-based zonotopic reachable sets in a robust MPC approach and propose a methodology to introduce feedback in the predictions to increase the closed-loop performance of the approach. The applicability of the proposed workflow is demonstrated by the means of a nonlinear polymerization reactor example with nine states and ten uncertainties.
Conventional hierarchical approaches to optimization and control of industrial processes separate steady-state optimization from dynamic control, leading to inefficient coordination and suboptimal performance. Although single-layer integrated strategies have been proposed, they typically rely on weighted formulations that are sensitive to manual tuning in practice. To address these challenges, this paper proposes an IMPC-guided lexicographic reinforcement learning (RL) framework for integrated zone tracking and economic optimization. A strict lexicographic hierarchy is enforced to prioritize zone tracking over economic objectives, thereby eliminating the need for manual weight selection. Constraint violations on the zone tracking objective are reformulated as dynamic system states, and an incremental model predictive control (IMPC) mechanism is introduced as a high-level regulator to predict and adaptively adjust Lagrangian multipliers in a receding-horizon manner. The proposed framework enables proactive constraint satisfaction by anticipating future violations. The main advantages over weighted-sum and standard constrained RL are the elimination of manual weight tuning, a guaranteed strict priority order, and predictive penalty adaptation. Simulation studies on both a linear system and a nonlinear continuous stirred-tank reactor (CSTR) demonstrate that the method achieves accurate zone tracking while significantly improving economic performance compared to conventional weighted-sum approaches.
In this work we propose a nonlinear passive control approach based on the Port-Hamiltonian framework for a multistage anaerobic digestion (AD) system. The process that we analyze has two coupled bioreactors that treat a high-strength organic wastewater. The model is introduced as a simple mass-balance equations with Monod and Haldane type kinetics. A Gibbs-free-energy-based storage function is first used to characterize the passive behavior of the open-loop process and its internal dissipation mechanisms.For controller synthesis, a separate quadratic Hamiltonian is introduced within the control-oriented IDA-PBC formulation. The controller is designed with the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) method that reshapes the dynamics to follow a desired closed-loop energy profile. In the proposed design, the physical interconnections and biochemical constraints are kept explicit, while the desired operating point is locally stabilized without requiring model inversion. The control input acts on the dilution rate of each reactor. In this way, the main process variables, such as Chemical Oxygen Demand (COD) and Volatile Fatty Acids (VFA), stay close to their reference values, even in the presence of the influent composition perturbations.The performance of the proposed strategy is tested by numerical simulations. The numerical results show satisfactory disturbance rejection and recovery of the steady-state regime under the evaluated operating scenarios. Practical implementation will require online estimation of unmeasured biomass states and suitable computational hardware.
Neural-network (NN) controllers trained by imitation learning can reproduce the behavior of conventional PID controllers, but their deployment requires assessing whether the stability and robustness properties of the teacher are preserved after replacement. This paper proposes a post-training framework to certify robustness inheritance when a PID is replaced by a NN controller. The method uses the balanced disk margin of the PID-controlled loop as the reference robustness measure and evaluates the robustness level inherited by the local-affine realization of the trained NN around the nominal operating point. The certificate is formulated as an integral quadratic constraint (IQC) condition expressed through a linear matrix inequality (LMI), whose feasibility certifies a plant-side robustness bound for the local-affine NN controller closed-loop system. The framework is evaluated on the Van de Vusse continuous stirred-tank reactor (CSTR), an inverse response nonlinear benchmark. The results show that the proposed pipeline, combining imitation training, autonomous validation, local-affine LMI certification, and nonlinear simulations, identifies NN controllers that preserve autonomous viability and inherit a significant fraction of the PID teacher disk margin.
Accurate fault detection and diagnosis are essential in chemical processes, but identifying a fault is only the first step. Once an abnormal event is detected, operators must implement corrective actions to mitigate its effects. This paper presents an operator advisory framework that links online fault diagnosis directly to the generation of optimal corrective actions. The approach integrates a Transformer-based classifier with fault-specific surrogate models to ensure that the recommendations accurately reflect the process dynamics under faulty conditions. To reduce decision complexity, the system employs an interpretable variable selection method to identify the most effective operational levers. Corrective actions are computed via a discrete, time-staggered optimization scheme designed to mitigate the fault progression. Furthermore, if the predicted trajectory drifts from the actual plant response, a plan-deviation monitor recalculates the strategy to provide the operator with updated corrective actions. Functioning purely as a decision-support tool, the system recommends these actions to the operational team, who retains full decision-making authority over their execution on the process. Validation on a non-isothermal CSTR and the Tennessee Eastman Process (TEP) demonstrates the practical viability of the approach. Across 12 complex TEP scenarios, the proposed framework achieves an average operational cost reduction of 15.9%. The system dynamically adapts the corrective action updates for the operator based on the evolution of the fault.
The performance of economic model-based optimization algorithms for bio-processes is significantly limited by model-plant mismatch that is pervasive in such processes due to their complexity and nonlinear behavior. Such a mismatch causes model-based optimizers to drive the process to sub-optimal operating conditions. This work presents an economic model predictive control (eMPC) framework designed to address model–plant mismatch in continuous and perfusion bio-processes. The methodology combines recursive parameter estimation with a gradient correction step, ensuring convergence toward the true plant optimum even in the presence of structural errors and noise. To improve robustness and reduce tuning effort, event-triggered execution and adaptive selection of the gradient history length are introduced. The framework is validated through two case studies: continuous penicillin fermentation and CHO cell perfusion. In the penicillin case, gradient correction outperforms conventional eMPC, achieving less than 3.7% deviation from the true optimum. In the CHO case, the proposed method improves stability and increases total obtained productivity by 75% compared to conventional eMPC. These results demonstrate the robustness and industrial relevance of the proposed gradient-correction based framework.
Population balance models provide a mathematical framework for describing the dynamics of particulate systems. For aggregation processes, such as twin-screw wet granulation, population balance models critically depend on accurate aggregation kernels, yet first-principles derivation is often impractical, and data-driven methods can lack physical interpretability. This work presents a sparse identification framework for learning physically plausible aggregation kernels directly from data. The approach enforces physical constraints, exploits structural properties, applies a systematic scaling strategy, and extends naturally to actuated systems. Validation on experimental data from a continuous twin-screw wet granulation process confirms the method’s robustness and its ability to recover physically meaningful aggregation kernels from real-world measurement data. The identified population balance model was able to predict the median particle size with a mean absolute error of 134.8µm (10%).
Accurate and early fault diagnosis in chemical processes is critical to prevent abnormal situations from escalating, yet most data-driven fault detection and diagnosis (FDD) methods are inherently reactive: they require long sequences of post-fault data before a fault signature becomes identifiable. This paper proposes the Five-Stage Cascade (FSC), a single Transformer model that learns multistep process prediction and fault classification together, so that the prediction is trained to expose the deviations that distinguish the faults. Early diagnosis is measured with an onset protocol: each model sees only the first samples recorded after the fault. On the Tennessee Eastman Process, against nine baselines tuned with the same budget, the prediction branch improves the diagnosis at all tested detection times. One hour after the fault, it reduces confident wrong fault labels from eleven to one and false alarms from four to zero, converting unsafe misdiagnoses into safe deferrals in which an emerging fault is still labeled nominal. The internal prediction is more accurate than a persistence baseline at every horizon and, combined with a causal map of the process, gives early fault propagation paths that point to the physical root cause of each fault about half an hour before the measurements confirm it. A SHAP analysis shows that the gain comes from the representations shared between the two tasks rather than from the predicted values read as extra input.
Industrial energy systems typically operate under a hierarchical decision-making architecture, where the upper scheduling layer optimizes economic energy allocation and the lower control layer tracks the resulting references. However, neglecting closed-loop dynamics in existing model-based and data-driven optimization approaches often results in overly conservative or aggressive scheduling schemes. To address this issue, a data-driven closed-loop dynamic optimization framework that deeply integrates scheduling and control is proposed. First, a two-stage data-driven representation for nonlinear conversion units is established. Furthermore, at the scheduling layer, a distributed architecture decomposes the system-level problem into energy network and conversion unit subproblems. For each unit, a data-driven optimization with embedded closed-loop prediction is developed, which embeds nonparametric, data-driven predictive models representing tracking behavior into the scheduling problem. Meanwhile, at the control layer, data-driven predictive control is deployed for reference tracking. Case studies based on real industrial data from a steel enterprise in China demonstrate that the proposed method reduces total operating costs by 14.70% compared with conventional model-based distributed optimization and by 4.49% relative to a data-driven distributed optimization without closed-loop embedding. In addition, it maintains favorable robustness and tracking performance under load fluctuations, model mismatch, and measurement noise.
This paper presents a robust funnel synthesis framework for uncertain continuous stirred tank reactors (CSTRs), aimed at providing a certificate for safe operation around a nominal reactor trajectory. First, Koopman lifting is used to construct a control-oriented linear representation of the reactor dynamics in a finite-dimensional observable space. The lifting is chosen to include the dominant Arrhenius reaction coordinate, while the remaining finite dictionary modelling error is explicitly bounded. Second, sparse polynomial chaos expansion (sparse-PCE) is used to describe how uncertainty in the kinetic parameters affects the identified lifted model. This gives structured matrix uncertainty bounds without relying only on Monte Carlo sampling for bound construction. Third, these uncertainty bounds are incorporated into a robust funnel synthesis problem that computes a time-varying invariant tube and a feedback law for safe trajectory tracking. A CSTR case study is used to demonstrate the complete workflow, including Koopman model identification, sparse uncertainty propagation, funnel synthesis, and nonlinear closed-loop validation. The results show that the sparse polynomial chaos representation captures the dominant parametric dependence of the lifted model using only a small active basis. In the reported reduced projected implementation, all sampled admissible nonlinear Monte Carlo trajectories remain inside the projected funnel under bounded kinetic uncertainty and disturbances, subject to the stated Koopman residual and sparse-PCE residual assumptions. The results indicate that Koopman-based lifted modelling, when combined with sparse uncertainty quantification and robust funnel synthesis, provides a promising route towards safe and uncertainty-aware control of nonlinear process systems.
Parallel fermentation monitoring must distinguish process changes from measurement degradation because the two conditions require different operational responses. Identification becomes difficult when reactor-specific measurement channels contain unknown heteroscedastic sensor noise. This paper proposes a multitask variational Bayesian (MTVB) framework that treats each reactor-specific measurement channel as a related task and exploits shared information across reactors. Under a mean-field approximation, posterior noise moments enter the shared-parameter posterior updates, and then task contributions are updated according to their posterior statistics, enabling unreliable measurement channels to be down-weighted while retaining information from all available reactors. A synthetic benchmark and a fermentation case study demonstrate improved identification accuracy and prediction performance compared with representative state-of-the-art techniques.
This paper investigates the optimal control of transport-reaction phenomena in a jacketed tubular reactor, where the internal temperature distribution is regulated through the heat flux applied at the outer radial surface of the jacketed reactor. The governing dynamics are described by a second-order hyperbolic partial differential equation arising from a Cattaneo-type heat flux model. The reactor domain is formulated in a cylindrical co-ordinate system, which accounts for axial and radial variations but neglects the angular dependence. An optimal control framework based on a linear quadratic regulator is developed at the formal modal level. As well, a Luenberger observer is designed using pole-placement. The stabilizability and detectability of the resulting modal representation are analyzed to ensure feasibility of the proposed control framework. Numerical simulations confirm that the proposed controller effectively stabilizes the reactor and regulates the temperature distribution within the domain.
Uncertainty is prevalent in process systems engineering, but quantification of uncertainty is less studied in the field of process monitoring. This paper presents a novel uncertainty-calibrated process monitoring (UCPM) framework that augments encoder–decoder residuals with sample-specific confidence for the process monitoring index. An autoencoder is trained to learn a low-dimensional manifold of normal process behavior. Then, its reconstruction residuals are compressed into a scalar out-of-distribution indicator using weighting metrics. Building on this indicator, a monotone bin-wise calibration is conducted to map this indicator to the empirical uncertainty measure of the monitoring index. In this way, monotonicity can be enforced during the calibration by an isotonic projection, and a per-sample uncertainty scale can be quantified to form a soft monitoring index. Case studies on the enhanced Tennessee Eastman process and a real multi-phase flow facility demonstrate the feasibility and effectiveness of the proposed uncertainty-aware process monitoring framework. This methodology requires the encoding–decoding structure only, calibrates uncertainty without parametric assumptions, and is applicable to existing autoencoder monitoring methods.
Modern industrial process data exhibit strong topological coupling and temporal evolution, while faults propagate in a directional manner, which makes accurate fault detection and root-cause localisation highly challenging. In this paper, a TopoCausFormer based spatio-temporal fault diagnosis framework (TCF-STAE) is proposed. First, a directed causal graph is inferred from normal-operation data and used as a structural prior to guide subsequent representation learning. Then, a topology- and causality-aware transformer (TopoCausFormer) is designed to incorporate causal graph centrality encoding and topology-aware spatial bias into spatio-temporal feature extraction. On this basis, a causal graph-embedded spatio-temporal encoder combining graph attention, TopoCausFormer, and long short-term memory is constructed to jointly capture structural coupling, short-term temporal interactions, and long-range dynamic evolution. Finally, a reconstruction decoder and a joint fault-scoring strategy based on reconstruction error and Kullback–Leibler divergence are developed to achieve both fault detection and variable-level localisation. The effectiveness and advantages of the proposed method are validated through dataset of the standard Tennessee Eastman process and actual data from the hot strip mill process. The case study reveal clear latent-space separation between normal and faulty conditions and interpretable variable-level localisation consistent with process mechanisms.
