This article investigates the optimization consensus and constraint issues of multi-agent systems within a given time. By adopting a barrier function and the improved non-negative function, a new finite-horizon cost function is constructed. Based on this cost function, a simple single-critic network framework is proposed, which avoids the complex interaction and iterative update process between the actor and critic networks, thereby reducing the computational complexity. Under this framework, the temporal differential (TD) signal generated by the integral Bellman equation and the terminal constraint (TC) error are used to jointly guide the update of the critic learning law, and a concurrent learning technique is employed to adaptively adjust the weights without requiring persistent excitation conditions. The proposed adaptive dynamic programming (ADP) control strategy does not rely on the system model information of the controlled plant, enhancing the applicability of the algorithm in unknown dynamic environments. Furthermore, by incorporating the prescribed-time (PT) criterion into the optimization design process, a collaborative control protocol with explicit time constraints is designed, which strictly ensures that the controlled system achieves consensus within the specified time. At the same time, by adjusting the parameters of the PT criterion, the convergence rate and transient performance can be flexibly controlled. Finally, simulation results verify the effectiveness of the designed control algorithm and illustrate the impact of key parameters on system performance.

Large-scale assembly production suffers from inefficient resource allocation, difficulties in coordinating interests across workstations, and severe congestion issues due to massive scale, complex tasks, and fluctuating constraints. To address these challenges, this study proposes a resource-efficient scheduling decision-making method based on a mixture pulsation model (DMMPM). The main contributions are as follows: 1) quantitative criteria for pulsation rhythm (takt-time) consistency in assembly production are defined, and a mixture equilibrium model for multiworkstation collaborative scheduling is developed, to integrate production rhythm alignment with workforce optimization within a coalition-driven profit maximization framework; 2) a spatiotemporally constrained task-allocation method driven by theoretical allocation batches is designed, balancing interstation resource demand conflicts and production rhythm synchronization requirements; and 3) a bi-level "scheduling-collaboration" architecture is proposed, where scheduling agents generate workstation-level strategies and collaboration agents coordinate cross-workstation coalition strategies through profit distribution, thereby enabling the efficient integration of decentralized decision-making and global optimization. The mathematical model is validated using ILOG CPLEX. Compared with conventional approaches, DMMPM significantly reduces the integrated scheduling cost and demonstrates superior decision-making capability and improved control of pulsation rhythm in large-scale aircraft manufacturing scenarios.

This article investigates the distributed approximate optimal control problem for pursuit-evasion differential games (PEDGs) of multiagent systems (MASs). Initially, interactions between pursuer agents and the evader agents are formulated using a divide-and-conquer algebraic graph approach, where all agents desire to maintain cohesion with their teammates. Subsequently, a state event-triggered mechanism (ETM) is introduced to conserve communication resources. Meanwhile, a polymeric hierarchical sliding mode surface (HSMS) incorporating local neighbor errors is constructed such that the system response rate is improved. To enhance team coordination, a novel dynamic target allocation algorithm is designed to execute the rational allocation among pursuers. Furthermore, based on the adaptive dynamic programming (ADP) with a single-critic neural network (NN) architecture, the HSMS-based event-triggered optimal control policies are further designed via solving the coupling Hamilton-Jacobi-Bellman (HJB) equations. Finally, a simulation conducted in the representative two-pursuer-two-evader scenario is presented to validate the effectiveness of the proposed control scheme.

This study explores workforce resource optimization in aircraft assembly under a fixed production cycle time (CT), which is a critical challenge for enterprises operating pulsed assembly lines. Traditional methods often struggle due to limited operational data, weak generalization, and the lack of closed-loop adjustment mechanisms, which restrict their effectiveness in practical settings. To address these challenges, we propose a generation–prediction–scheduling (G-P-S) framework that establishes a closed-loop architecture for adaptive optimization. A diffusion-based generative model first augments sparse datasets with high-quality synthetic assembly scenarios. Then, a Transformer-based predictor trained on both real and generated data provides accurate multitype workforce demand forecasting. Finally, a CT-guided adaptive feedback mechanism integrates greedy scheduling with dynamic workforce adjustment, ensuring feasibility and efficiency under varying production conditions. Comparative studies demonstrate that the proposed framework achieves more accurate forecasting and more robust optimization performance than evolutionary and reinforcement learning baselines. Overall, the G-P-S framework offers a scalable and practical solution for intelligent resource optimization in complex assembly environments.

Low-dimensional representations that can fully preserve the key structural features of original process data constitute the foundation for constructing efficient process monitoring models. However, existing methods often suffer from incomplete and one-sided modeling of spatial structures and temporal dynamics when extracting the intrinsic low-dimensional manifold of process data. To address these limitations, a new method called collaborative preserving matrix factorization (CPMF) is proposed in this article and applied to process monitoring. Specifically, CPMF adaptively adjusts the spatial neighborhood size based on local data density and dynamically determines the temporal neighborhood according to the time-varying rate of change in the data. This dual-adaptive strategy enables CPMF to effectively preserve both the inherent spatial structure and dynamic characteristics of the data across spatial and temporal scales. Furthermore, by decomposing the low-dimensional representation into common and special feature components, CPMF mitigates the data point offset problem, thereby significantly improving monitoring accuracy. The effectiveness and competitive performance of CPMF are validated through experiments on the Tennessee Eastman process and a real industrial production process.

Aircraft assembly scheduling (AAS) grows increasingly complex in the presence of multiple uncertainties, given that these factors significantly influence assembly process efficiency and the optimal allocation of resources. Existing scheduling methods have exhibited their limitations in taking into consideration of the uncertainties related to assembly resources, the actual number of workers that may change in process, and the previous assembly experience with high productivity. To overcome these limitations, a workstation adjustment mechanism (WAM) is proposed to improve the availabilities of workstations. WAM is fully integrated with actual worker configurations to mitigate the shortages of workers in the task conversions in a schedule. A knowledge transfer-based multiobjective evolutionary algorithm (KT-MOEA) is developed as a systematic optimization framework for addressing multiobjective AAS problems. Moreover, a design of experiments systematically evaluates the impact of controllable variables across multiple instances, which enhances the robustness, interpretability, and generalizability of the proposed framework. This innovative approach systematically integrates transfer learning and the nondominated sorting genetic algorithm II to enhance optimization performance. Quantitative results demonstrate that the proposed KT-MOEA significantly enhances optimization performance, achieving up to 50% improvement in convergence (inverted generational distance), substantial gains in solution diversity (hypervolume), and at least a 7% enhancement in the quality of Pareto-optimal solutions compared with benchmark algorithms.

This article studies the optimal cluster synchronization (OCS) problem for multiagent systems (MASs) with the unknown perturbation under a multicluster game (MCG) framework. To estimate the unknown perturbation, a novel perturbation observer nested with a parameter adaptive law is first designed. Subsequently, a coupling performance index function relevant to the synchronization error and the control policy with the quadratic form is constructed. By utilizing the distributed adaptive dynamic programming (ADP) technology with a single-critic architecture, the optimal control policy is designed by solving the Hamilton–Jacobi–Bellman (HJB) equation associated with the coupling performance index function. Meanwhile, an adaptive OCS control policy with a single-critic neural network (NN) updating law is further proposed, and it is proven that the designed adaptive OCS control policy constitutes the generalized Nash equilibrium (GNE) point of the MCG. Based on the Lyapunov extension theorem, all signals of the closed-loop MASs are ensured to be bounded. Finally, a simulation example is presented to validate the effectiveness of the proposed adaptive OCS control method.

In this article, a distributed optimal security control method is proposed for multiagent systems (MASs) containing multiple attackers and defenders within a differential adversarial game framework. Initially, the control inputs of the defenders’ systems are considered to suffer from denial-of-service (DoS) attacks from the attackers, then the coupled performance index functions associated with the state errors are constructed. By using the distributed adaptive dynamic programming (ADP) technology, a modified radial basis function neural network (NN) is implemented such that the coupled performance index functions are approximately identified, and by solving the coupled Hamilton-Jacobi-Bellman (HJB) equation, an ADP-based optimal security control policy with a single-critic NN updating law is further proposed. Meanwhile, it is proven that the proposed optimal security control policy constitutes the Nash equilibrium point of the differential adversarial game. Finally, a simulation example is given to validate the effectiveness of the proposed distributed optimal security control method.

This article considers adaptive hierarchical sliding mode control (HSMC) for hyperbolic partial differential equation (PDE)-ordinary differential equation (ODE) cascade systems. Unlike existing PDE-ODE cascade systems, the ODE subsystem studied in this paper involves unknown nonlinear functions and unknown gain functions, and thus fuzzy logic systems (FLSs) are introduced to approximate them. Meanwhile, a projection algorithm is proposed to ensure that the designed controller does not have singularity issues. Subsequently, with the aid of integration by parts and Volterra integral (VI) transformation, the original system is equivalently transformed into a new target one. For this target system, an adaptive fuzzy control approach based on hierarchical sliding mode (HSM) is developed. Compared with the commonly used backstepping method, this method simplifies the controller design steps while also eliminating the algebraic loop and “complexity explosion” issues. In addition, a triggering mechanism with a switching threshold is introduced to alleviate communication burden. Ultimately, the proposed control algorithm ensures that all signals including system states and actuator states are bounded, and this fact is verified through a Josephson junction circuit simulation.

As an effective feature extraction and dimensionality reduction technique, nonnegative matrix factorization (NMF) has been widely applied in fault detection in recent years. The requirement for vectorization of samples causes NMF to disrupt the inherent structure of matrix data, making subsequent fault isolation and localization unachievable. In addition, existing statistical metrics used for fault detection are distance-based. Due to additional terms or other constraints, the data distribution in low-dimensional space deviates from the origin, resulting in excessively large decision boundaries and reduced fault detection performance. To directly utilize matrix data and address the issue of excessively large decision boundaries, a new method, named general semi-nonnegative matrix factorization, is proposed for statistical process monitoring. Its novelties include the following. First, the common features among the samples are extracted within a lower dimensional space, concurrently preserving the special features of the data. Second, by constructing two new statistical metrics, the latent variables extracted by GSNMF are combined with process monitoring techniques for fault detection. Third, the algorithm relieves the nonnegative restriction for original data, and allows samples to be input as vectors or matrices. On this basis, an abnormal variable isolation method named generic reconstruction-based contribution, which is suitable for matrix and variable data, is proposed for statistical process. The effectiveness of the proposed fault detection and abnormal variable isolation methods are verified on the benchmark dataset and the practical electrical-fused magnesia furnace process.

Detecting abnormal conditions in an electrical fused magnesia furnace (EFMF) is challenging due to the difficulties in measuring ultra-high temperature, fluctuation of raw materials, uncertain boundary conditions, and numerous processing variables. In practice, images acquired from the wall of furnace are used to reflect working conditions of furnace indirectly. In this article, a supervised matrix regression algorithm is proposed to detect abnormal conditions based on the matrix data. Bilinear analysis is conducted to connect matrix data with labels and thus preserve the correlations in matrix with decreased complexity. By supervising and adjusting the weights of outliers in the modeling process, neutral and chaotic datasets can be monitored in low-dimensional spaces accurately. Moreover, a common information extraction method is proposed to eliminate redundant data. To verify proposed methods, the images recorded from an actual EFMF are used to detect abnormal conditions, and it is found that the proposed methods are able to monitor actual EFMF and issue alarms timely and effectively.

Nonnegative matrix factorization (NMF) is a widely recognized approach for data representation. When it comes to clustering, NMF fails to handle data points located in complex geometries, as each sample cluster is represented by a centroid. In this article, a novel multicentroid-based clustering method called graph-based multicentroid NMF (MCNMF) is proposed. Because the method constructs the neighborhood connection graph between data points and centroids, each data point is represented by adjacent centroids, which preserves the local geometric structure. Second, because the method constructs an undirected connected graph with centroids as nodes, in which the centroids are divided into different centroid clusters, a novel data clustering method based on MCNMF is proposed. In addition, the membership index matrix is reconstructed based on the obtained centroid clusters, which solves the problem of membership identification of the final sample. Extensive experiments conducted on synthetic datasets and real benchmark datasets illustrate the effectiveness of the proposed MCNMF method. Compared with single-centroid-based methods, the MCNMF can obtain the best experimental results.

In the iron flotation production process, production stages often undergo updates due to equipment upgrades, changes in raw materials, and other reasons. The operating condition prediction model established based on data from previous production stages may not meet the requirements of the new stage, resulting in a significant waste of collected datasets. Data-driven models established using small samples collected during the current stage may lack accuracy due to the limited sample size. This study proposes a method based on knowledge transfer to effectively leverage a large amount of outdated data. It allows for the rapid establishment of a new model that aligns with production requirements while minimizing the need for additional data collection. In previous tailings grade soft sensors, more emphasis was placed on quality parameters such as flotation froth features, often overlooking production process parameters. To enhance model accuracy, we introduce a multivariate collaborative modeling approach. The experimental results and industrial applications validate the effectiveness of this method.

This article investigates the leader-follower consensus for nonlinear multiagent systems (MASs) and proposes an adaptive dynamic programming (ADP)-based hierarchical Stackelberg-Nash optimal game control method. Initially, a coupled performance index function associated with consensus errors is constructed. As the positive-definite function with the quadratic form is allocated to the constructed consensus errors-based performance index function, the original system stabilization problem is converted into the issue of seeking an optimal control strategy profile for the leader and followers. Under the hierarchical Stackelberg-Nash differential game framework, the optimal control strategies are derived in sequence and further proved to compose the equilibrium points of Stackelberg-Nash differential games. Afterward, based on the ADP technique, a modified single-critic neural network (NN) is implemented and the coupled Hamilton-Jacobi–Bellman (HJB) equation is approximately identified. Under the proposed control scheme, the leader-follower consensus of the considered MAS can be achieved while consuming less control cost. Meanwhile, all signals of the MAS are ensured to be uniformly ultimately bounded. Finally, a numerical simulation and an application to the electrode regulating system of the three-phase electric arc furnace are given to verify the effectiveness of the proposed control method.

In this paper, a novel hierarchical sliding-mode surface (HSMS)-based adaptive event-triggered optimal control (ETOC) method is proposed for switched nonlinear systems using single-critic adaptive dynamic programming (ADP). Initially, an ameliorative HSMS containing all system states is constructed to improve the system response rate. With positive quadratic functions being assigned for the developed HSMS-based cost function, the original stabilization problem is further transformed into an array of ETOC problems. Subsequently, by implementing a single-critic neural network (NN) whose weights are tuned based on an aperiodic manner and the historical data, a series of event-triggered Hamilton-Jacobi-Bellman (HJB) equations are approximately solved. Meanwhile, the condition for the persistence of excitation existing in the traditional actor-critic dual NNs framework is relaxed. Furthermore, the uniformly ultimate boundedness (UUB) of all signals in the closed-loop system is guaranteed by the Lyapunov extension theorem. Finally, a practical continuous stirred tank reactor plant is provided to substantiate the efficacy of the proposed HSMS-based adaptive single-critic ETOC method.Note to Practitioners—Switched nonlinear systems have attracted much attention due to their flexibility in characterizing multi-mode features in practice. The control synthesis and stability analysis of switched nonlinear systems have been the research focus in the control field. However, with the development of adaptive dynamic programming (ADP), it is no longer limited to the study of control synthesis and stability of switched systems. How to improve the response rate and achieve optimal control of switched nonlinear systems with less control cost becomes critical. On the other hand, the persistent information transmission of control signals not only occupies more bandwidth, but also causes severe transmission delays, thus it is important to conduct the signal transmission only when necessary. This paper discusses the optimal control problem for switched nonlinear systems. Meanwhile, an event-triggered adaptive dynamic programming optimal control policy based on a hierarchical sliding-mode surface is proposed, which consumes less control cost while improving the system response rate and saving communication resources.

Multimode process monitoring is critical in practical industrial processes, as it directly affects the quality and safety of product. The disadvantages of existing multimode process monitoring methods are as follows. 1) The operation mode isolation is not accurate since the interference from the common information in the original data space. 2) The coordinated operation mode isolation strategy is not considered in the traditional method. 3) The local spatial properties are ignored in multisubspace methods. In this article, a multimode process monitoring algorithm called common and unique subspace decomposition (CUSD) is proposed. Advantages of the proposed method are as follows. 1) The unique mode subspace containing the unique information for each mode and the common mode subspace containing the common information between different modes are decomposed in order to eliminate the influence from the common information. 2) The local and global spatial properties are exhaustively extracted in each subspace by the fusion of the principal components and the manifold information. 3) A coordinated Bayesian inference strategy based on the extracted properties in the decomposed unique mode subspace is proposed for operation mode isolation purpose. Simulations on three different processes have validated that there is an approximately 20% improvement of average operation mode isolation accuracy in the unique mode subspace of CUSD than in the original data space.

Aircraft assembly scheduling (AAS) with multiconstraints, multitype workers, and the orders of tasks has become a key research focus in advanced industrial manufacturing. An elite gene retention metaheuristic algorithm (EGHA) is proposed in this article as a transfer knowledge generator, and the elite gene transfer learning heuristic algorithm (TL-EGHA) is also utilized as an optimized framework to tackle these issues for the AAS problem. Fully considered characteristics of the AAS problem, double time windows are proposed to deal with the constraints of worker type and space restrictions, and this guarantees that the proposed algorithm can obtain the solution quickly. The transfer learning strategy imports transfer knowledge associated with features and previous experiences, which prompts the initialization results closer to the task goals and supports dynamic adjustments of the parameters in TL-EGHA to enhance the global searching capability significantly. TL-EGHA has been a verified advancement in scheduling four real-world aircraft assembly lines by a comparative study with some existing scheduling algorithms, including well-known genetic transfer learning.

In this article, the genetic transfer learning (GTL) method is proposed for knowledge transfer of sustainable assembly manufacturing systems. Existing methods for the assembly line balancing problem, such as genetic algorithms (GAs), suffer from three significant limitations, i.e., tedious “trial-and-error” processes, no utilization of existing system solutions, and no consideration of new constraints on system reconfiguration. To address these problems, we propose GTL to migrate the knowledge of the GA setup in system reconfiguration. The contributions of this article are as follows. First, transfer pretreatment is performed to formulate knowledge of existing systems and adapt to the new constraints of future systems. Second, the similarity of existing and future systems is defined quantifiably to determine transfer conditions and avoid weak and negative transfer for maximizing knowledge transfer. Finally, the transfer strategy is made to determine the method and knowledge to be transferred. The case study of a computer assembly line shows that adopting transfer learning has helped to improve assembly line efficiency and sustainability.

The stability property of delayed neural networks (NNs) along the whole delay axis is studied in this paper. Such a complete stability problem with respect to the delay parameter has not been addressed in the community of NNs. Most of the existing studies focus on the stability interval of delay starting from zero and are not applicable for the complete stability problem. In this paper, we will present some examples to show that there are various types of stability intervals for NNs, demonstrating the necessity of the complete stability analysis. We will adopt a frequency-sweeping approach to study delayed NNs in this paper. As a result, the complete stability problem with respect to delay for NNs can be systematically solved. The approach is applicable in the general case and simple to implement. Finally, some representative examples illustrate the approach.

A fault diagnosis method based on knowledge from a Bayesian perspective was proposed in this paper. This discriminative model was obtained on the basis of knowledge, which including both labeled data that is labeled by prior knowledge from experts and unlabeled data set sampled from industry process. Bayesian theorem and Laplace approximation were implemented in the modeling and prediction of the state for a new point. The proposed method was applied to process monitoring of fused magnesia furnace. Experiment results show that our approach has satisfactory diagnosis performance and its prediction performance is particularly evident when the amount of unlabeled data is large compared to the labeled data.

In this paper, a fault detection method based on intermediate phase dependency analysis for multiphase batch process is proposed. The contributions of the proposed method are as follows: 1) multi-way kernel independent component analysis (MKICA) are used to extract the principal information; 2) the subspace separation is completed by establishing the relationship of intermediate phase using MKICA; after that, the relative changes (increased part, decreased part and unchanged part) from previous phase to latter phase are obtained; 3) the detection model establishing by the proposed approach is more accurately comparing with the conventional method. The advantage and effectiveness of the proposed method are illustrated with penicillin fermentation process.

In this paper, a new regression and reconstruction method for process monitoring is proposed. The main contributions of the proposed approaches are as follows: 1) a new nonlinear regression algorithm is proposed to extract the output-relevant variation, which, compared with the conventional algorithm, builds a more direct relationship between the input and output variables; 2) the fault direction is determined by possible fault magnitude of every possible principal component; and 3) the fault is effectively diagnosed compared with the conventional kernel partial least-squares (KPLS) method. The proposed method is applied to a continuous annealing process and is compared with the KPLS method. Experiment results show that the proposed method can more effectively detect fault compared with the KPLS method. In addition, the selection of fault direction is more accurate using the proposed reconstruction algorithm compared with the KPLS reconstruction approach.

For fault classification in industrial processes, the performance of the classification model highly depends on the size of labeled dataset. Unfortunately, labeling the fault types of data samples need expert experiences and prior knowledge of the process, which is costly and time consuming. As a result, semisupervised modeling with both labeled and unlabeled data have recently become an interest in industrial processes. In this paper, a kernel-driven semisupervised fisher discriminant analysis (FDA) model is proposed for nonlinear fault classification. Two discriminant analytical strategies are introduced for online fault assignment, namely k-nearest neighborhood and Bayesian inference. Detailed comparative studies are carried out through two industrial benchmark processes between the linear and kernel-driven semisupervised FDA models, in which the best fault classification performance is obtained by the kernel semisupervised model with Bayesian inference as its discriminant strategy.