To improve the reliability and interpretability of industrial process monitoring, this article proposes a causal graph spatial-temporal autoencoder (CGSTAE). The network architecture of CGSTAE combines two components: a correlation graph structure learning module based on spatial self-attention mechanism (SSAM) and a spatial-temporal encoder-decoder module utilizing graph convolutional long short-term memory (GCLSTM). The SSAM learns correlation graphs by capturing dynamic relationships between variables, while a novel three-step causal graph structure learning algorithm is introduced to derive a causal graph from these correlation graphs. The algorithm leverages a reverse perspective of causal invariance principle to uncover the invariant causal graph from varying correlations. The spatial-temporal encoder-decoder, built with GCLSTM units, reconstructs time series process data within a sequence-to-sequence framework. The proposed CGSTAE enables effective process monitoring and fault detection through two statistics in the feature space and residual space. Finally, we validate the effectiveness of CGSTAE in process monitoring through the Tennessee Eastman process (TEP) and a real-world air separation process (ASP).

The data-driven sliding mode control (SMC) method proves to be highly effective in addressing uncertainties and enhancing system performance. In our previous work, we implemented a co-design approach based on an input-mapping data-driven technique, which effectively improves the convergence rate through historical data compensation. However, this approach increases computational complexity in multi-input and multi-output (MIMO) systems due to the dependency of the number of online optimization variables on system dimensions. To improve applicability, this paper introduces a novel input-mapping-based online learning SMC strategy with low computational complexity. First, a new sliding mode surface is established through online convex combination of pre-designed offline surfaces. Then, an input-mapping-based online learning sliding mode control (IML-SMC) strategy is designed, utilizing a reaching law with adaptively adjusted convergence and switching coefficients to minimize chattering. The input-mapping technique employs the mapping relationship between historical input and output data for predicting future system dynamics. Accordingly, an optimization problem is formulated to learn from the past dynamics of the uncertain system online, thereby enhancing system performance. The optimization problem in this paper features fewer variables and is independent of system dimension. Additionally, the stability of the proposed method is theoretically validated, and the advantages are demonstrated through a MIMO system. Note to Practitioners—The design of control strategies that reduce the impact of mismatches between practical systems and models on system performance, while also ensuring applicability, is crucial. To address this issue, this paper proposes a low-complexity IML-SMC strategy. This strategy uses historical real input-output information and the mapping relationship with future dynamics to compensate for the impact of unknown dynamics and improve the system’s convergence rate. Notably, the control strategy introduced in this paper significantly reduces online computational complexity, ensuring applicability, and stability is proven. When there is a deviation between the model and the actual system, practitioners can implement the low-complexity IMC-SMC strategy proposed in this paper to more quickly achieve the control objectives in the actual system.

Iterative learning model predictive control (ILMPC) has become an excellent data-driven intelligent control strategy for digitized batch manufacturing, featured by the progressive improvement of tracking performance along trials, and the persistent rejection of stochastic disturbance along time. The point-to-point learning mechanism of existing ILMPC generally relies on identical operating conditions along trials to guarantee the integrity and accuracy of historical data. However, the variations of production requirements usually lead to trial-varying operating references and durations, resulting in incomplete and inaccurate historical information for the iterative learning of subsequent trials. To promote the adaptability and flexibility of ILMPCs with unconformable prior information, a data-driven self-modification scheme is originally embedded into ILMPC in this article to transfer the prior knowledge contained in the historical operating data into the form consistent with the condition of each current trial. The control actions are imitated along trials by an adaptive deep neural network (DNN), which is then utilized to generate reference control signals for iterative learning in each trial. For attenuating the influence of the considerable DNN approximation error in early trials with limited data accumulation, the 2-D optimization of ILMPC is performed under a tube control frame to ensure the time-domain bounded stability. Based on the intrinsic recursive feasibility and the guaranteed time-domain stability, the iteration-domain bounded convergence of the developed ILMPC system is theoretically validated. Simulations on the nonlinear injection molding process verify the superiority of the proposed method in adapting to significant changes in operating reference and duration.

Few-shot fault diagnosis is a challenging problem for complex engineering systems due to the shortage of enough annotated failure samples. This problem is increased by varying working conditions that are commonly encountered in real-world systems. Meta-learning is a promising strategy to solve this point, open issues remain unresolved in practical applications, such as domain adaptation, domain generalization, etc. This article attempts to improve domain adaptation and generalization by focusing on the distribution-shift robustness of meta-learning from the task generation perspective. In fact, few-shot fault diagnosis under varying working conditions allows to address the distribution shift problem in a natural way. An unsupervised across-tasks meta-learning strategy with distributional similarity preference is proposed, where the core is the distribution-distance-weighting mechanism. Differently from the naive random meta-train task generation strategy used in existing meta-learning methods, the source instances that present a more similar distribution with respect to the target instances gain larger weightings in the task generation. This strategy leads to a meta-task training set that is enough diverse, and at the same time can be easily learned due to the distribution similarity features of the source tasks. The proposed method introduces the concept of maximum mean discrepancy that is applied to derive the distribution distance of the measurements. Moreover, a model-agnostic meta-learning is applied to realize few-shot fault diagnosis under varying working conditions. The proposed solutions are verified and compared by considering two public datasets used for bearing fault diagnosis. The results show that the proposed strategy outperforms different related few-shot fault diagnosis methods under varying working conditions. Moreover, it is thus proved that, meta-learning with distribution similarity feature represents an effective approach for domain adaptation and generalization.

This article examines for the first time an integrated structure of smart injection molding systems (IMS) based on Industry 4.0 technologies and provides a system-level solution for manufacturing smart products. The fully automated smart IMS structure allows manufacturers to produce thermoplastic products directly from raw materials without requiring any human labor. Following this, we focus on the control problem associated with the auxiliary robot manipulators that support the smart IMS. A cooperative distributed predictive control (DPC) algorithm with one-tap memory is proposed to achieve optimal closed-loop performance for multiple robot manipulators simultaneously performing their respective tasks. Using one-tap memory in smart IMS, we optimize the local performance index, which includes penalized terms diverging from it, and the global cooperation effort with limited memory acceleration to reach manifold consensus, without requiring manipulators to exchange information iteratively at each step. The cooperative DPC algorithm is also applied to five robot manipulators in the smart IMS, which require them to work cooperatively to achieve rhythmic and synchronized movements. Industrial experiment results demonstrate the feasibility of smart IMS combined with the cooperative DPC. Moreover, the cooperative DPC method outperforms the other two predictive control methods based on three metrics of the smart IMS.

Model-based control plays an important role in batch process control. With more data collected online, real-time model updates using Gaussian process regression (GPR) are becoming increasingly practical for improving the performance of model-based control strategies. However, in batch processes, process configurations are often adjusted, which can be costly if a new model has to be identified from scratch each time. Although several GPR migration methods exist, they are primarily designed for static models and are not well-suited for dynamic system modeling for control purposes. Therefore, we propose a selective migration-based online GPR identification method that enables the dynamic model for batch process control to learn selectively from the previously identified old process model as needed. In our method, we present selective migration strategies for two types of GPR model parameters: 1) hyperparameters and 2) data points. Additionally, we provide a complete algorithm for online dynamic model identification. Beyond that, for data point parameters selective migration, we propose a fast migration dataset-seeking method for a smaller computational cost and a mixed integer programming migration dataset-seeking method for a smaller prediction loss. Theoretical analysis of the framework reveals the initial improvement and final convergence. Finally, we provide two illustrative numerical examples to show the effectiveness of the proposed methods.

Batch processes are typically nonlinear systems with constraints. Model predictive control (MPC) and iterative learning control (ILC) are effective methods for controlling batch processes. By combining batch-wise ILC and time-wise MPC, this article proposes a multirate control scheme for constrained nonlinear systems. Two-dimensional (2-D) framework is used to combine historical batch data with current measurements. The ILC part uses run-to-run control with previous iteration data, and the MPC part uses real-time control with current sampled measurements. Real-time feedback-based MPC in the time axis and run-to-run ILC in the batch axis are combined to optimize the current inputs based on previous batch input–output data and real-time system measurements. Rather than achieving control objectives in a single batch, our design allows multiple batches to be executed successively. To establish the stability of the combined scheme, rigorous theoretical analysis is presented next. The combined scheme with improved performance is then validated through two illustrative numerical examples.

The data generated by modern industrial processes often exhibit high-dimensional, nonlinear, timing, and multiscale characteristics. Presently, most of the fault diagnosis methods based on deep learning only consider the part of the characteristics of industrial data, which will cause the loss of part of the feature information during training, thereby affecting the final diagnosis effect. In order to solve the above problems, this article proposes an end-to-end multiscale feature learning method based on model fusion, which can simultaneously extract multiscale spatial features and temporal features of data, effectively reducing the loss of feature information. First, this article combines the convolutional neural network (CNN) with residual learning and designs a multiscale residual network (MRCNN) to extract high-dimensional nonlinear spatial features of different scales in the data. Then, the extracted features are input into the long and short-term memory (LSTM) network to further extract the temporal features of the data. After the fully connected layer, it is input into the classifier for final fault classification. The residual learning in MRCNN can effectively avoid the problem of model degradation and improve the training efficiency of the model. Through the fusion of MRCNN and LSTM, we can significantly improve the feature extraction ability of the model, thereby greatly improving the diagnosis effect. In the final case experiment, the method improved the comprehensive diagnostic accuracy of the Tennessee-Eastman (TE) process and industrial coking furnace datasets to 94.43% and 97.80%, respectively, which was significantly better than the existing deep learning model and proves the effectiveness and superiority of this method.

Iterative learning model predictive control (ILMPC) has been recognized as an excellent batch process control strategy for progressively improving tracking performance along trials. However, as a typical learning-based control method, ILMPC generally requires the strict identity of trial lengths to implement 2-D receding horizon optimization. The randomly varying trial lengths extensively existing in practice can result in the insufficiency of learning prior information, and even the suspension of control update. Regarding this issue, this article embeds a novel prediction-based modification mechanism into ILMPC, to adjust the process data of each trial into the same length by compensating the data of absent running periods with the predictive sequences at the end point. Under this modification scheme, it is proved that the convergence of the classical ILMPC is guaranteed by an inequality condition relative with the probability distribution of trial lengths. Considering the practical batch process with complex nonlinearity, a 2-D neural-network predictive model with parameter adaptability along trials is established to generate highly matched compensation data for the prediction-based modification. To best utilize the real process information of multiple past trials while guaranteeing the learning priority of the latest trials, an event-based switching learning structure is proposed in ILMPC to determine different learning orders according to the probability event with respect to the trial length variation direction. The convergence of the nonlinear event-based switching ILMPC system is analyzed theoretically under two situations divided by the switching condition. The simulations on a numerical example and the injection molding process verify the superiority of the proposed control methods.

In this article, we study the optimal iterative learning control (ILC) for constrained systems with bounded uncertainties via a novel conic input mapping (CIM) design methodology. Due to the limited understanding of the process of interest, modeling uncertainties are generally inevitable, significantly reducing the convergence rate of the control systems. However, huge amounts of measured process data interacting with model uncertainties can easily be collected. Incorporating these data into the optimal controller design could unlock new opportunities to reduce the error of the current trail optimization. Based on several existing optimal ILC methods, we incorporate the online process data into the optimal and robust optimal ILC design, respectively. Our methodology, called CIM, utilizes the process data for the first time by applying the convex cone theory and maps the data into the design of control inputs. CIM-based optimal ILC and robust optimal ILC methods are developed for uncertain systems to achieve better control performance and a faster convergence rate. Next, rigorous theoretical analyses for the two methods have been presented, respectively. Finally, two illustrative numerical examples are provided to validate our methods with improved performance.

In this article, we develop data-driven optimal synchronization control architectures for leader-follower multiagent systems with additive disturbances and unknown system matrices. To minimize output synchronization error, algebraic Riccati equations (AREs) are derived, and unique feedback gains are determined by policy iteration. On that basis, two data-driven optimal synchronization control algorithms are developed without relying on the dynamics of the system, which guarantee output synchronization while minimizing synchronization errors and rejecting disturbances. The first algorithm uses the output synchronization error data to perform online data-driven learning (DDL), while the second algorithm uses the input data to perform DDL, where both data sample requirements are transformed into rank conditions. We have presented rigorous theoretical analyses of our proposed algorithms, which demonstrate that if an initial control protocol can make the system achieve output synchronization under mild conditions, our proposed two algorithms can take advantage of the data from reaching synchronization to optimize the closed-loop performance. Finally, a numerical example is provided to emphasize the effectiveness of our methods.

Deep learning technology has been widely used in fault diagnosis for chemical processes. However, most deep learning technologies currently adopted only use a single network stack or a certain network stack with multilayer perceptron (MLP) behind it. Compared with traditional fault diagnosis technologies, this method has made progress in both the diagnosis accuracy and speed, but due to the limited performance of a single network, the accuracy or speed cannot meet the requirements to the greatest extent. In order to overcome such problems, this article proposes a fault diagnosis method using deep learning multimodel fusion. Different from previous deep learning diagnosis methods, this method uses long short-term memory (LSTM) and convolutional neural network (CNN) to extract features separately. The extracted features are then fused and MLP is taken as the input for further feature compression and extraction, and finally the diagnosis results will be obtained. LSTM has long-term memory capabilities, the extracted features have temporal characteristics, and CNNs have a good effect on the extraction of spatial features. The proposed method integrates these two aspects for diagnosis such that the features finally extracted by the network have both spatial and temporal characteristics, thereby improving the network's diagnostic performance. Finally, a TE chemical process and an industrial coking furnace process are taken for simulation testing. It is proved that the performance of this method is superior to existing deep learning fault diagnosis methods with simple sequential stacking for unilateral feature extraction.

In batch processes, the ability to learn from previous process data results in high-value and batch-improved products. For batch processes with constraints and state-dependent uncertainty, this article presents a conic iterative learning control (ILC) approach, which uses cone theory to incorporate historical process data into optimization-based ILC design. The proposed conic ILC approach uses rank conditioning to select distinct data samples and conic mapping to map the data to the to-be-optimized control input variables, since adding all historical process data would be computationally intensive. Our method yields a tradeoff between learning ability from historical experience and computational efficiency from solving the optimization problem. Provable constraint satisfaction and robust stability are considered separately. To demonstrate the proven properties and effectiveness of the approach, we present a case study of the injection molding process.

Optimal iterative learning control (OILC) has been recognized as an excellent model-based means for regulating batch process with abundant successful applications reported in the past decades but also received considerable criticisms for its poor robustness against model mismatch that is common for many industrial situations. Despite numerous attempts to address the issue, many of them are still not able to yield satisfactory control performance particularly in the presence of a possible combination of time-varying uncertainties and conservatively designed controllers, which may compromise the learning mechanism, hence rendering the robustness issue of OILC far from well explored. This article intends to investigate the aforementioned issue by proposing a new OILC method resting upon the minimization of a dynamic upper bound on tracking error which is distilled from better exploitation of the time variation of uncertainties. We also show that the problem can be formulated in the framework of convex–concave game that can be efficiently solved by a subgradient method with an excellent balance of optimality and computation time. Such a formulation enables us to gain: 1) guaranteed monotonic convergence on tracking error; 2) remarkably reduced conservatism on controller synthesis; and 3) controllable computation complexity. It is further shown that the proposed method is capable of handling nonlinearity, for example Volterra system, a classic representation of nonlinear process. The efficacy of the method is verified by numerical experiments on a continuous stirred tank reactor model.

Asynchronous switching between the controller and the active subsystems in multiphase batch processes may cause the systems to be unstable around the switching instants. In view of this, an average dwell-time method-based iterative learning control (ILC) scheme is proposed in this paper. First, the multiphase process is represented as an equivalent closed-loop two-dimensional (2-D) switched system composed of stable and unstable subsystems, based on which new relevant concepts on the stability of the switched system are given. Second, using an average dwell-time method, the ILC law is designed to guarantee the system exponentially stable. Minimum running time for the stable subsystems and maximum running time for the unstable ones are obtained. Lastly, depending on the maximum time for the unstable subsystems, the idea of putting the controller switching step forward is proposed. In this way, the asynchronous switching is removed such that the unstable subsystem can be avoided. The case study on an injection molding process demonstrates the effectiveness and superiority of the proposed method in comparison with the existing 2D-MPC and one-dimensional traditional control methods.

To achieve improved control performance of batch processes under uncertainty, a novel two-dimensional model predictive iterative learning control (2D-MPILC) scheme is proposed. First, a new two-dimensional (2-D) extended nonminimal state space model is formulated where more degrees of freedom are offered for further controller design; second, a new error compensation strategy is introduced in the controller design to improve the ensemble control performance. The two merits are combined together to form a new control strategy where the model predictive control and iterative learning control are united based on the 2-D framework. By employing the novel model formulation and the system error compensation approaches, the effects caused by uncertainty in the batch processes can be eliminated gradually from cycle-to-cycle such that the desired control performance will be obtained finally. The effectiveness of the proposed 2D-MPILC is tested on the packing pressure in the injection molding batch process.

Dynamics and nonlinearity may exist in the time and batch directions for batch processes, thereby complicating the monitoring of these processes. In this article, we propose a two-dimensional deep correlated representation learning (2D-DCRL) method to achieve the efficient fault detection and isolation of the nonlinear batch processes. Three-way historical data are first unfolded as two-way time-slice data. Second, a stacked autoencoder based deep neural network is constructed to characterize the correlation among the process variables. Considering that the time and batch directions may be dynamic, for each time-slice measurement, a constructed 2-D measurement containing samples from the previous time instants and batches is then obtained. Subsequently, DCRL is performed between the current running-batch measurements and the constructed 2-D measurements to characterize the 2-D dynamics and nonlinearity. The 2D-DCRL-based monitoring examines the status of a sample by considering the 2-D nonlinear and dynamic information, providing improved monitoring performance. Applications on two typical batch processes demonstrate the effectiveness of the proposed 2D-DCRL monitoring scheme.

To cope with the control problem of industrial processes with partial actuator failure and disturbance, an improved synthetic minmax optimization design-based H∞linear quadratic (LQ) tracking control strategy is presented in this paper. A new state space model that integrates the dynamics of the process states and the tracking error is first formulated as the basic dynamic process representation. By introducing the new state space model formulation, a new minmax optimization of the H∞norm of the system performance is presented for LQ tracking control design, where more degrees of freedom are offered through the simultaneous adjusting of the tracking dynamics and the state regulation in the cost function, resulting in the enhanced control performance over traditional H∞LQ tracking control. Meanwhile, the nominal closed-loop system stability and robustness under uncertainty are discussed and the monotonicity conditions that are sufficient for both nominal and robust system stability are derived. The case studies on an injection molding process and a nonlinear batch reactor under partial actuator failures and disturbance show the effectiveness of the proposed strategy.

In this paper, we develop an adaptive output trajectory tracking control (AOTTC) method for a class of affine nonlinear discrete-time systems. The controller designed by this AOTTC method can make real-system output track the given expected trajectory asymptotically. Our method has some advantages: 1) it requires relatively few assumptions about the system model; 2) it can simplify the control problem by dynamically linearizing the system model and designing and adjusting the feedback gain matrix to adaptively stabilize the system online; and 3) it can estimate the system parameters by using an optimization scheme without using vast amounts of sampled data. This designing and adjusting procedure of the feedback gain matrix has a clear physical meaning and is easily applied. We also give out the convergence condition of the AOTTC method. Then, a voltage-controllable permanent magnet linear motor system is employed for computer simulation, whose results demonstrate the feasibility of our control method.

In this study, a predictive-p control system is developed for the level process in an industrial coke fractionation tower. Such processes typically have integrating and nonlinear dynamics causing the performance of conventional control designs and tuning to be poor or to require significant effort in practice. The process model is derived using data of step-response test and control implementation is designed through a new state-space structure. The closed-loop control system contains both the improved predictive control and P control. The performance of the proposed control for regulatory/servo, disturbance rejection, and measurement noise problems are studied and the obtained results show that the control system is of simple implementation with more robustness and provides better responses than conventional predictive control.

This paper proposes an enhanced model predictive control (MPC) using a new state space structure for temperature control of an industrial coke furnace. The advantage of the proposed controller lies in the fact that its implementation only requires a simple step-response process model, whereas controller design can be based on state space formulation to improve temperature regulation. To ensure control performance effectiveness under model/process mismatch and uncertainties, model predictions and the cost function optimization are done on the basis of a new improved state space model. The proposed MPC is applied to an industrial coke furnace, where the outlet temperature in the radiation room is regulated. Simulation comparisons with traditional state space MPC are illustrated first. Then experimental results are shown in comparison with the original proportional-integral differential (PID) controller, demonstrating the effectiveness of the proposed methodology.