In multi-view multi-label (MVML) classification, each sample is represented by multiple heterogeneous views and annotated with multiple labels. Existing methods typically exploit pairwise semantic relationships to mine intra-view correlations and align inter-view features for generating structural representations. However, these methods ignore the direct expression of high-order semantic similarities and alignments from a group perspective, which necessitates multi-step aggregation for subsequent feature fusion, leading to the inefficient and incomplete integration of key semantic information. To overcome this limitation, we propose a novel hypergraph-based MVML method with Adaptive High-Order Semantic Fusion (HyperAHSF), which leverages hypergraphs to adaptively model group-level semantic similarities within each view and group-level semantic alignments across different views, enabling more effective feature fusion. Specifically, we first construct view-specific hyperedges by selecting multiple groups of node representations exhibiting high semantic similarity, which captures the group-level semantic similarities within each view, forming view-specific hypergraphs. Furthermore, we establish cross-view hyperedges to connect the multi-view node representations of each sample, which characterizes the group-level semantic alignments across different views, accordingly forming a unified multi-view hypergraph. Afterwards, we employ hypergraph neural networks to efficiently aggregate view-specific information and consensus information from their corresponding hypergraphs via group-level message passing. During the passing process, we impose a label-driven contrastive loss on the consensus information to encourage these representations to cluster toward their corresponding class prototypes, enhancing their discriminability. Finally, the consensus information together with the view-specific information is jointly integrated for multi-label classification. Extensive experiments demonstrate that HyperAHSF outperforms other state-of-the-art methods.

Blockchain technology has been widely used in the field of Internet of Things, providing effective support for solving security challenges in Internet of Things systems. However, due to the immature development language and deployment platform, smart contracts are prone to various vulnerabilities. Considering the immutability of smart contracts, efficient vulnerability detection before deployment is particularly critical. The existing detection methods have two main limitations: they can only identify a limited number of specific vulnerabilities, resulting in low coverage; the implicit correlation information between vulnerability types is ignored. In order to solve these problems, this paper proposes a smart contract multi-vulnerability detection model CorrelaScan (correlation-aware smart contract analyzer) that integrates vulnerability type correlation awareness. The model is based on a multi-task learning architecture, including a shared layer and a specific task layer. The shared layer uses BERT to extract shared features, while the specific task layer uses BiGRU to learn specific task features for vulnerability detection and type classification. In addition, a vulnerability type embedding module is integrated in the task-specific layer. The module mines potential associations by calculating the similarity between smart contract opcodes and vulnerability types, thereby enhancing detection guidance and improving model performance. Experimental verification on public datasets shows that the model can simultaneously detect 10 types of vulnerabilities such as integer overflow or underflow, reentrancy and timestamp dependence, with an average F1 value of 85.22%. Its detection performance exceeds the current state-of-the-art methods.

Disassembly lines play a crucial role in the recycling and reuse of end-of-life (EOL) products to promote environmental protection and economic benefits. However, the diverse characteristics of EOL products necessitate the adoption of different disassembly modes, posing challenges to existing models that rely solely on non-destructive or complete disassembly. Thus, a dual-layer multi-objective particle swarm algorithm (DMOPSO) is proposed to solve the partial destructive incomplete disassembly line balancing problem (PDI-DLBP), with optimization of economic profit and energy consumption. Firstly, a tailored encoding-decoding scheme is designed for disassembly sequence, mode selection, and task assignment to obtain high-quality disassembly schedules. Then, a dual-layer learning-based particle updating mechanism is designed, incorporating a constraint-based mode updating operator and a multi-source segment learning strategy to enhance search efficiency and optimization stability. Additionally, a dual-layer local search based on molecular forces is introduced to enhance the exploitation ability. The proposed DMOPSO algorithm is applied to several test cases and a real-world disassembly line of TV. Experiment results show that DMOPSO outperforms state-of-the-art algorithms in solving PDI-DLBP. Specifically, the proposed DMOPSO achieves a 5.7% increase in disassembly profit and a 6.5% reduction in disassembly energy consumption compared to the existing best algorithm for solving the real-world case.

Differentiable architecture search (DARTS) suffers from over-parameterized supernetworks that make architecture search difficult to perform in complex detection scenarios. In this paper, a shareable attention-mask for object detection architecture search (SAM-Det) is proposed, which is designed to address the high computational cost and poor performance caused by search over-parameterization. To reduce the search cost, a series of convolutional candidate operations is merged by using a shareable attention mask to represent the operations as a single convolution with shared weights. Moreover, to reduce the interference of redundant features on the search, the features are shuffled in groups to learn the attentional importance, thus selecting the important channels to be transferred into the search space. The experimental results show that SAM-Det is able to obtain network architectures with better detection performance and lower search cost in different detection scenarios compared to other Search methods.

Nonlinear networked systems (NSs) subject to actuator faults are addressed in this paper through proposed fault diagnosis (FD) and fault-tolerant control (FTC) schemes. The nonlinear NSs are represented by an interval type-2 Takagi-Sugeno (IT2 T-S) fuzzy model with mismatched membership functions (MFs), in which uncertainties are described as a fuzzy interval with upper and lower bounds. To concurrently estimate system states and actuator faults, an interval type-2 (IT2) T-S fuzzy fault diagnosis observer is developed, serving to improve the system’s resilience against uncertainties and external disturbances. Following the observer’s fault estimation, an FTC strategy is formulated to guarantee asymptotic stability andH∞performance in the closed-loop system. The proposed framework employs Lyapunov stability theory, with sufficient conditions for the FD observer and FTC gain matrices derived via linear matrix inequalities. Finally, through simulation experiments, the effectiveness and practicality of the designed FD and FTC strategies are validated.

This paper addresses two challenging issues in distributed Nash equilibrium seeking for a class of nonaffine, high-order nonlinear systems. The first lies in the complexity explosion that arises in adaptive feedback control when dealing with intricate system nonlinearities. The second concerns the oscillations caused by uncertain high-order nonaffine dynamics with unknown control directions. To overcome these challenges, a modified finite-time nonlinear tracking differentiator with linear damping components is established, settling down the high sensitivity of traditional filters. A unified framework is developed to handle input nonlinearities, including backlash-like hysteresis and dead zones, by integrating neural network approximation mechanisms with advanced Nussbaum functions, enabling effective compensation for such nonlinear effects. Building on leader-following consensus protocols and gradient-based game theory, distributed adaptive filtered feedback Nash equilibrium seeking strategies are constructed, with both centralized and decentralized control gains designed accordingly. Finally, a simulation example under different input nonlinearity scenarios is presented to demonstrate the validity of the proposed strategy.

Bitcoin money laundering detection faces critical challenges including labeled data scarcity, extreme class imbalance, and transactional heterogeneity. To address these issues, we propose DyHom-SSL, a semisupervised learning framework integrating dynamic pseudolabel optimization, and homophily-aware graph learning. The framework operates in two stages: in the warm-up stage, a similarity-based mechanism dynamically generates thresholds for high-quality pseudolabels, replacing confidence-based selection to enhance flexibility, while in the consistency training stage, a learnable data augmentation module is introduced and optimized through the dual objectives of consistency (semantic preservation) and diversity (feature variation). In addition, homophily distribution leverages topological differences between illicit and licit nodes to resolve class imbalance without distorting data distribution. Extensive evaluations on elliptic, elliptic++, and AMLworld datasets demonstrate state-of-the-art performance, achieving 92.29% precision, 77.30% recall, and 84.02% F1-score on the elliptic dataset. DyHom-SSL outperforms graph and nongraph baselines in both homogeneous and heterogeneous datasets, proving its effectiveness for real-world antimoney laundering (AML) applications.

Detection Transformers (DETRs) have achieved notable performance and outperformed traditional deep neural network models in object detection. However, the self-attention of encoder tokens incurs significant computational overhead. To improve computational efficiency and maintain detection precision simultaneously, we propose an efficient detection transformer model based on learnable query queuing and encoder self-distillation, QD-DETR. Specifically, we first design a query queuing mechanism to select object-relevant queries with the guidance of supervising signals and spatial features. Second, we construct the query representation variational information bottleneck module to optimize the query queuing via mutual information regularization. Lastly, we develop an encoder feature self-distillation method to compensate for the information loss by directly distilling the encoder output token sequences. We conducted experiments on multiple datasets and verified the accuracy and efficiency of QD-DETR in comparison with mainstream detection models. The experiment results demonstrate that QD-DETR reduces computational complexity by 46% and increases inference speed by 69% while maintaining high accuracy in complex object detection scenarios.

For stochastic sampled-data systems characterized by unknown nonlinear dynamics (SSDUNSs), it is a great challenge to design an appropriate controller to achieve stable tracking control. In this article, a perceptron-based adaptive model predictive control (PAMPC) scheme is developed for SSDUNSs with multiple discrete stochastic sampling intervals. The activation frequency of each sampling interval can be statistically obtained, which can be described by the categorical distribution. First, a PAMPC structure is developed for the tracking control of SSDUNS. A perceptron with a cost function is designed to incorporate the exploration of the environmental state, encompassing the sampling interval, predictive error, and tracking error. Second, an adaptive predictive horizon (APH) is incorporated into the predictive model to provide the necessary predicting information for the controller. APH is adjusted based on the activation frequency of stochastic sampling intervals. Third, an optimal control problem (OCP) combined with the penalty of the perceptron is designed to stabilize SSDUNS. Then, the control law can be computed to achieve the stable tracking control of SSDUNSs. Finally, the stability of the proposed method is analyzed theoretically to ensure its reliability and robustness. In addition, the effectiveness of the designed method is verified by numerical simulations and real-world applications in the context of wastewater treatment processes (WWTPs).

In wastewater treatment processes (WWTPs), the presence of aeration equipment faults (actuator faults) prevents the desired tracking control effect of the state-constrained dissolved oxygen concentration (DOC). To solve this problem, an adaptive fixed-time fault-tolerant control (AFTFTC) strategy based on the asymmetric integral barrier Lyapunov function (AIBLF) is developed in this article. First, in order to directly consider asymmetric state constraints in the controller design process, an AIBLF is constructed. Second, a fixed-time FTC method is proposed to compensate for the effects of actuator faults on DOC regulation and achieve fast tracking of the DOC setpoint. Specifically, the adaptive compensation term with DOC asymmetric constraint boundaries is used to estimate the unknown boundary of the actuator bias fault (BF). Furthermore, it is proven that the designed controller can ensure the fixed-time stability of the closed-loop system. Finally, the validity of the control strategy is validated on the benchmark simulation model 1 (BSM1).

Multimodal multiobjective optimization aims to provide diversified acceptable decisions (ADs), including global optimal solution with consistent objective evaluations and local optimal solutions (LOSs) with acceptable objective evaluations. However, the discrimination of LOSs highly depends on the distribution of candidate solutions, which may result in the catastrophic elimination of LOSs to damage the diversity in the decision space. To address this problem, a local regularity model (LRM) method is proposed to improve the distribution of candidate solutions. There are three novelties of LRM. First, a hierarchical principal component analysis is developed to extract principal components for different nondominated sets. Then, the distribution features of different nondominated sets are described in segments by a small number of candidate solutions to construct LRM. Second, a self-organization strategy, based on the feature correlation and neighborhood violation analysis, is proposed to improve local fitting ability. Then, LRM are efficiently constructed to estimate the manifold of ADs. Third, a probability reproduction strategy is developed to reconstruct the population by LRM. Then, the population is reconstructed to enhance the distribution of candidate solutions in the decision space. Finally, the proposed optimization method is integrated into the popular multimodal multiobjective optimization algorithm to demonstrate its effectiveness in terms of the benchmark multimodal multiobjective optimization problem test suite.

The existence of stochastic sampling phenomena in wastewater treatment processes (WWTPs) breaks the assumption that the existing control strategies use periodic data, and the operational constraints of equipment and the requirements for effluent water quality impose constraints on the system's input and output. These factors collectively increase the difficulty of achieving stable control of dissolved oxygen concentration (DOC). To solve these problems, a data-driven model predictive control (DDMPC) strategy is proposed to achieve stable control of constrained WWTPs with stochastic sampling intervals. First, a DDMPC framework is designed, which involves designing the objective function based on the mathematical expectation of the predicted output and considering system input and output constraints. In this framework, the problem of stochastic data acquisition caused by stochastic sampling can be solved, and the stable operation of the system can be ensured under constraints. Second, a data-driven multimodel prediction structure is constructed based on the stochastic characteristics of the sampling intervals. Specifically, fuzzy neural networks (FNNs) that match possible sampling intervals are established, thereby providing predictive outputs for the control process at the corresponding sampling instants. Third, a controller solving algorithm based on the generalized multiplier method is proposed, in which the constrained optimization problem within the model-predictive control (MPC) framework is reformulated by incorporating system constraints into the objective function as penalty functions to obtain the optimal control input that satisfies the constraints. Finally, the stability of the proposed DDMPC strategy is demonstrated, and its effectiveness is verified through the simulations on the benchmark simulation model No. 1 (BSM1). The results show that the proposed DDMPC strategy can achieve stable control of DOC in constrained WWTPs with stochastic sampling intervals.

The data transmission in wastewater treatment processes (WWTPs) depends on wireless networks. However, limited network bandwidth frequently results in data packet losses. Moreover, intermittent sensor faults caused by sludge adhesion and sensor aging can induce probabilistic sampling (PS). These communication constraints degrade control system performance and stability, while external disturbances further complicate dynamics. To address these challenges, a data-driven robust model predictive control (DRMPC) approach is proposed to stabilize WWTPs under communication constraints and external disturbances. First, an equivalent PS (EPS) model is established to characterize the double randomness introduced by communication constraints, including PS and consecutive packet losses (CPLs). Then, based on the EPS model, a two-loop control framework is constructed. Specifically, a nominal model predictive control (MPC) is designed as a nominal control loop to steer the nominal output to the reference trajectory, where a multistep identifier is designed to capture the unknown dynamics of the nominal system. Then, the cost function is formulated by incorporating the expectation of predictive outputs and the variation in control error, which effectively enhances the tracking control capability of the nominal system. Furthermore, a fuzzy neural network (FNN) controller is constructed as a feedback control loop to regulate the error system to mitigate the effect of external disturbances, ensuring that the actual output converges to the nominal output. Finally, a theoretical proof of system stability is provided. Meanwhile, the proposed DRMPC scheme is experimentally validated on the Benchmark Simulation Model No.1 (BSM1) for WWTPs, demonstrating its effectiveness.

In nonlinear systems, the system response frequently fluctuates with the discrepancy of variation trends over a certain horizon. In this situation, type-2 fuzzy neural networks can be limited in capturing trend features from the point prediction process due to the inherent value mapping, which may suffer from trend blindness. To address this problem, a trend-aware-based type-2 vector fuzzy neural network (TA-T2VFNN) is designed for modeling nonlinear systems. First, a quantization framework with a hybrid encoding strategy is designed to process both the magnitude and trend information of variables. In this strategy, the trend information with the rate and direction of change is represented by vectors instead of scalars, which aims to compensate for the accumulated error caused by insufficient input information. Second, a directional attention mechanism-based vector fuzzy rule is proposed to capture the trend relationship to mimic the local fluctuation patterns. Then, the vector operation is embedded into fuzzy rules for geometric inference, which can obtain the vector features with point and trend. Third, a collaborative feedback learning algorithm is developed to update the magnitude and direction parameters of TA-T2VFNN. Then, the modeling accuracy can be maintained by obtaining trusted output points and output trends. Finally, the effectiveness of TA-T2VFNN is verified by multiple practical applications.

Accurate bed temperature prediction is crucial in the circulating fluidized bed (CFB) combustion process, as it provides early warning of abnormal conditions, allowing timely intervention to prevent potential safety risks. However, the inherently complex multiphase flows and nonlinear chemical reactions in CFB systems make time series prediction of bed temperature a highly challenging task. Starting from the intrinsic spatial correlations and the temporal dependencies, this article proposes an adaptive learning-based bed temperature prediction method. The proposed model integrates dynamic correlation-guided Graph Convolutional Networks (GCN) and Long Short-Term Memory (LSTM) networks. Specifically, the GCN guided by prior knowledge adaptively learns complex topological structures to capture spatial dependencies. LSTM receives both raw input features and the spatial features extracted by GCN as parallel inputs, effectively capturing the temporal evolution of bed temperature. The proposed method is then applied to the task of bed temperature prediction in CFB. The experimental findings indicate that the proposed method consistently outperforms other comparative methods across different forecasting horizons, achieving a leading level of performance.

In wastewater treatment processes (WWTPs), actuator faults (such as those of blowers) or input signal saturation may cause the constrained dissolved oxygen concentration (DOC) to exceed the preset range, which not only compromises the operational efficiency of WWTPs but also increases the risk of membrane fouling. To solve these challenges, the model-free fault-tolerant control (MFFTC) strategy based on a log-type barrier nonlinear transformation function (LNTF) is proposed. First, to directly incorporate the DOC constraint bounds into the MFFTC design process and achieve more robust boundary control, an LNTF is constructed. Based on this, an extended compact form dynamic linearization model for WWTPs subject to actuator faults is developed. Then, considering that the faults are unknown, the faults are estimated by the fuzzy neural network. Second, the integrated dynamic compensator (IDC) is designed to overcome the input saturation problem by combining the fault estimation information. In addition, MFFTC is designed based on the IDC to compensate for the impact of actuator faults. Third, the bounded input bounded output stability analysis is provided to ensure that the MFFTC maintains the DOC within the constraints under actuator faults and saturation. Finally, the correctness and effectiveness of MFFTC are verified through extensive simulations in the membrane bioreactor model.

Rail fasteners are crucial railroad infrastructure and their health status is directly connected to the safety of traveling trains. UAV-based rail fastener visual inspection has shown strong advantages over traditional inspection techniques. However, existing general-purpose object detection architectures inevitably suffer from the limitation that they can only detect objects that are clearly visible. Consequently, they tend to neglect objects affected by occlusion or shadows and lead to missed detection problem. The industrial application of such models can bring huge safety risks to long-term operations of safety-sensitive railroad systems. Concerning the issues, this paper proposes a visual prior-guided rail fastener integrity detection architecture (RFIDet) to realize coarse-to-fine detection of all rail fasteners, whether normally visible or visually obscured. RFIDet employs a two-stage pipeline: the visual prior guidance (VPG) stage generates standard rail fastener layout representation (SRFLR) for coarse priors, while the precise location search (PLS) stage enables NMS-free refinement using adaptive anchors designed from actual physical distance priors. SRFLR takes full advantage of inherent spatial priors of all rail fasteners to perceive a unified, interconnected, and coarse location distribution. Then all rail fastener candidates activated by those coarse locations are further trained to search and regress refined offsets to the final bounding boxes. Structural loss functions for both stages are customized to facilitate the detection of individual fasteners while constraining the overall spatial distribution of all fasteners. Experiments have verified the effectiveness and better robustness of the proposed RFIDet with the mAP50value increased by at least 5.9% compared to a series of general-purpose SOTA YOLO detectors. RFIDet outperforms the comparing algorithms especially when coming across unexpected occlusions or shadows.

Smart contract vulnerabilities have led to over $20 billion in losses, but existing methods suffer from coarse-grained detection, two-stage “detection-then-localization” pipelines, and insufficient feature extraction. This paper proposes SCFusionLocator, a statement-level vulnerability localization framework for smart contracts. It adopts a novel code-slicing mechanism (via function call graphs and data-flow graphs) to decompose contracts into single-function subcontracts and filter low-saliency statements, paired with source code normalization to reduce noise. A dual-branch architecture captures complementary features: the code-sequence branch uses GraphCodeBERT (with data-flow-aware masking) for semantic extraction, while the graph branch fuses call/control-flow/data-flow graphs into a heterogeneous graph and applies HGAT for structural modeling. SCFusionLocator enables end-to-end statement-level localization by framing tasks as statement classification.We release BJUT_SC02, a large dataset of over 240,000 contracts with line-level labels for 58 vulnerability types. Experiments on BJUT_SC02, SCD, and MANDO datasets show SCFusionLocator outperforms 8 conventional tools and nearly 20 ML baselines, achieving over 90% average F1 at the statement level, with better generalization to similar unknown vulnerabilities, and remains competitive in contract-level detection.

Predefined-time control (PTC) is employed to ensure that the system exhibits more definite and predictable behavior in the motor systems. However, as the system ages, sensors may be adversely affected by malfunctions, resulting in performance degradation, even leading to system instability. Thus, to solve this issue, a predefined-time sensor fault-tolerant control (PTSFTC) is developed for motor systems. First, a predefined-time fault compensation scheme is presented to extract the system operational state information. Then, this fault compensation method can judge the sensor fault within a predefined execution time. Second, a Nussbaum technique-based adaptive compensation strategy is introduced in PTSFTC to compensate for the unknown control coefficient. Then, the proposed PTSFTC can achieve safe and stable operation for motor systems with the unknown control gain. Third, the Lyapunov function is constructed to demonstrate the stability of PTSFTC scheme. Then, the comprehensive stability analysis can guarantee the successful application of PTSFTC. Finally, simulation and experiment results demonstrate that the PTSFTC can ensure the motor system exhibits excellent control performance.

Multitasking optimization (MTO), addressing multiple optimization problems synchronously, has achieved significant success in the field of evolutionary computation. However, in practice, few tasks are accomplished synchronously due to asynchronous initialization. In this article, an asynchronous MTO (AMTO) paradigm is proposed, which aims to deal with multiple optimization problems with asynchronous arrivals. Due to the asynchronous characteristic of tasks, there is multiple tenses knowledge in an AMTO environment. Transferring multitense knowledge may accelerate the optimization process of the target task. Also, an AMTO algorithm is proposed to transfer multitense knowledge. The past-tense knowledge is transferred by an initialization strategy, which selects effective knowledge to deal with mismatched tenses. And the present-tense knowledge is transferred by knowledge reuse, which aligns convergence intervals to handle mismatched evolutionary states. Finally, several AMTO test problem sets and a practical problem are designed to verify the performance of the proposed algorithm. The experimental results show that the performance of the algorithm can be improved by multitense knowledge transfer.

Multimodal multiobjective problems (MMOPs) are common in engineering and are characterized by multiple equivalent Pareto optimal sets. However, the asymmetric distribution of these sets makes it challenging to discover diverse solutions efficiently. To tackle this issue, an auto-topology particle swarm optimization (ATPSO) method is proposed for MMOPs, forming a dynamic search paradigm via a flexible information transmission topology. First, the multidimensional topology structure is proposed to construct a parallel information transmission topology. Then, the particles are partitioned for locally variable information transmission. Second, the topology performance indicators are designed to measure search disparities of multiple Pareto optimal sets. Then, the indicator growth between decision and objective spaces is compared to measure search disparities mapped in the multidimensional topologies. Third, a parallel optimization strategy for the topology structure is proposed to dynamically regulate the multidimensional topology structure. Then, the appropriate topology structure is automatically formed based on the indicator-oriented structure optimization. Finally, the experimental results illustrate that ATPSO has superior performance over state-of-the-art algorithms in addressing MMOPs.

A robust data-driven model predictive control (RDD-MPC) with a soft constrained strategy is proposed in this article. This method is designed to address model predictive control (MPC) constraint violations caused by external disturbances and outliers arising from measurement errors. First, a robust data-driven prediction model is constructed using kernel functions, and its parameters are updated via the soft-margin-based iterative quadratic programming (SMIQP) algorithm. This algorithm introduces a model slack variable (MSV) to tolerate the negative effects of outliers. This algorithm improves the robustness of the prediction model against outliers and ensures that the model can capture the complex dynamic characteristics of the system. Second, an enhanced soft constrained method (SCM) is designed to handle constraint violations. Unlike SCMs with a single slack variable, which may lead to excessive or insufficient constraint relaxation, this method employs two controller slack variables (CSVs) for coordinated constraint relaxation, thereby ensuring optimization feasibility. Combined with an adaptive weight penalty term, the proposed SCM maintains acceptable control performance in the presence of disturbances. Third, the input-to-state stability (ISS) of the proposed RDD-MPC method is rigorously proven. Finally, experimental results on classic nonlinear systems demonstrate that the proposed method can effectively improve both control performance and robustness. In addition, this method is evaluated on the Benchmark Simulation Model No. 1 (BSM1) for wastewater treatment processes (WWTPs). The experimental results further validate the effectiveness of the RDD-MPC method for systems engineering applications.

ABSTRACT Large language models (LLMs) have made significant progress in many tasks, but they may also generate biased or misleading outputs. Alignment techniques address this issue by refining models to reflect human values, but high‐quality preference datasets are limited. This study introduces a method to train a high‐performance reward model (RM) by integrating open knowledge with human feedback. We construct the Open Knowledge and Human Feedback (OK‐HF) dataset, comprising 39.8 million open preference data entries and 30,000 human feedback entries. The dual‐stage aligning strategy is proposed to combine preference pre‐training with domain adaptation, leveraging multi‐objective optimization to enhance learning from both preference data and fine‐grained human feedback. The Open Knowledge and Human‐feedback Reward Model (OKH‐RM), designed with the dual‐stage aligning strategy on the OK‐HF dataset, demonstrates exceptional performance in aligning LLMs with human preferences. The experimental results show that OKH‐RM outperforms Llama2‐RM, Qwen‐RM and Ultra‐RM, particularly achieving an accuracy of 85.93% on the Stanford SHP dataset. The model has shown advanced capabilities in detecting low‐quality repetitive responses and mitigating biases related to response length.

Sulfur dioxide (SO2) emissions are the main problems causing the air pollution and respiratory disease, which makes desulfurization important in the coal combustion and chemical industry processes. The wet-flue-gas desulfurization (WFGD) is currently an effective method to deal with this issue. However, the WFGD system is actually a complex process with multi-variable coupling, high nonlinearity and large time-delay, which brings great challenges for the traditional mechanism-based modeling and control. In this paper, a neurodynamics-driven model predictive control (NDMPC) with soft-measurement is proposed to predict and control the dynamics of SO2to improve the operational performance of the WFGD system. First, we design a self-organizing fuzzy neural network (SOFNN) as the soft-measuring model, which is driven by the data and neurodynamics to adaptively predict SO2in the WFGD system. Second, the designed SOFNN is considered as a predictive model that can give the predicted values for the future moments. Third, we also design a loss function where the one-step output of the predictive model and the control law are the independent variables. The resulting rolling optimization can give the optimal control law sequence by minimizing the loss function. Finally, simulation experiments on the practical data from the WFDG system show that the NDMPC outperforms the other methods in terms of the soft-measurement and control performance, especially generally reducing the SO2emission and economic cost by 60.25% and 22.27%, respectively.

The wastewater treatment system is a complex unknown system with nonlinear and uncertain characteristics. It is necessary to control the concentration of the dissolved oxygen and the nitrate nitrogen at the set value in the wastewater treatment process. However, traditional control methods are difficult to meet the accuracy requirements for the required concentration value. At the same time, the digital twin (DT) technology has been widely applied to practical industrial systems like the wastewater treatment system in recent years. Based on the above backgrounds, an online DT adaptive critic design (DTACD) is developed by combining the long short-term memory (LSTM) neural network with the action-critic structure. First, a set of historical data is collected, which is used to build a digital model using LSTM. Then, the digital model is used to guide the real wastewater treatment system to control the nitrate nitrogen concentration and the dissolved oxygen concentration at set values. Finally, we select the Benchmark Simulation Model No.1 as the model for the simulation experiment. Compared with other methods, DTACD shows a better performance.

With increasing market competition, integration between production and transportation in supply chain has been valued to improve the operational performance. Meanwhile, the distributed manufacturing has emerged as a modern paradigm, fostering flexible and intelligent development. In this paper, we address an integrated distributed production and transportation scheduling problem (IDPTSP), taking into account the production plan in distributed heterogeneous hybrid flow-shops, as well as the transportation decisions made by third-party logistics provider. First, the objective calculation is presented to minimize total costs and energy consumption during production and transportation process, and problem property is analyzed to obtain an optimal pickup time strategy. Second, a knowledge-driven cooperative coevolutionary algorithm (KCCA) is proposed, incorporating multiple problem-specific heuristics and operators based on the characteristics of the subproblems in IDPTSP. Third, Q learning assisted cooperative coevolutionary search is proposed via analyzing the interconnections among different subproblems to effectively and efficiently explore their search space. Fourth, local intensification search with multiple operators fusing prior knowledge is incorporated for low-density regions in objective space to enhance exploitation ability. Extensive experiments are carried out to test performances of the KCCA and the numerical comparisons demonstrate effectiveness of the specific designs and superiority of the KCCA over state-of-the-art algorithms in solving the IDPTSP. Note to Practitioners—Drawing inspiration from a real-life case in electronics supply, the focus on distributed manufacturing and the integration of manufacturing and logistics has garnered significant attention from managers due to the enterprises’ need to reduce intermediate stocks and enhance operational performance. The primary focus of enterprises is on reducing costs during production and transportation. Additionally, energy consumption has become a crucial consideration due to rising energy costs and limited energy supplies. However, the complexity of this practical scenario has significantly increased due to the presence of multiple subproblems and objectives. Traditional scheduling methods are unable to effectively and efficiently obtain a Pareto front with convergence and diversity. Based on the characterises of the scheduling problem, we provided a knowledge-driven cooperative coevolutionary algorithm to minimize total costs and energy consumption during production and transportation process. At production stage, factory assignment and job sequence are determined in distributed heterogeneous hybrid flow-shops, while job batching and vehicle routing are determined at transportation stage. Through the analysis of problem properties, an optimal pickup time strategy is introduced and multiple rules and search operators are provided to enhance optimization efficiency. Meanwhile, the framework of cooperative coevolutionary search offers an effective approach to addressing such complex integrated scheduling problems. From experimental comparisons, the effectiveness of the proposed algorithm is verified surpassing state-of-the-art algorithms. Therefore, practitioners can benefit from non-dominated schedules characterized by reduced costs and enhanced energy efficiency.

A robust soft constrained model predictive control (RSCMPC) method is proposed to address the effects of unknown disturbances for wastewater treatment processes (WWTPs). The disturbances involving inflow fluctuation and noises from WWTPs may result in the constraints violation of MPC due to its uncertainty of bioprocess, which may degrade the performance of the steady state. First, the artificial steady state is introduced to mimic the nearest feasible steady state when the reference steady state is not feasible. The deviation caused by disturbances between the artificial steady state and the reference steady state is also penalized to ensure that the output of MPC converges to the reference steady state. Second, the soft constraints, incorporating two slack variables and a penalty term, are designed to relax the state constraints of MPC and continuously mitigate the constraint violation, thereby ensuring its stability. Third, the input state stability (ISS) under disturbances is analyzed. Finally, the simulation tested on Benchmark simulation model 1 verifies the effectiveness of the proposed RSCMPC. The results demonstrate that RSCMPC improves the robustness of the system to maintain the stable operation of the WWTPs. Note to Practitioners—The external disturbances of wastewater treatment processes (WWTPs) will result in the constraints violation of model predictive control (MPC) and degrade the steady state performance. To overcome the influence of external disturbances, a robust soft constrained model predictive control (RSCMPC) method is designed. This method mainly includes three contributions: First, the artificial steady state is constructed with the prediction derived from fuzzy neural network, which is to mimic the nearest feasible steady state when the reference steady state is not feasible under disturbances. Second, the soft constrained method relaxes the state constraints of MPC through two slack variables to compensate the effects of disturbances and restore the feasibility of the controller. Third, the input state stability under disturbances is analyzed. Finally, the effectiveness of the proposed RSCMPC method is evaluated on a pilot platform of a real WWTPs. The experimental results show that RSCMPC can improves the control accuracy and robustness of the system under external disturbances. The proposed RSCMPC method can help practitioners improve the reliability of WWTPs operation.

Cryptocurrencies, underpinned by blockchain technology, face persistent threats such as money laundering and extortion due to their decentralized and anonymous nature. Detecting fraudulent transactions is crucial for ensuring the security of block-chain systems. However, the existing detection methods face the following challenges: lack of labeled data, severe class imbalance in labeled data, complex network structure, numerous parameters, and long training time. To address these challenges, we propose a novel semisupervised learning framework that combines the graph augmented with pseudolabels generation (GAPLG) model and postprocessing technique. Our framework employs graph learning networks to elucidate relationships between transactions and users. By utilizing pseudolabels for unlabeled transaction data and embedding them onto diverse graph nodes, we achieve precise labels, enhancing prediction accuracy. Additionally, we employ specific post-processing technique, such as correction and smoothing (C&S) technology, to rectify residuals and refine labels, ensuring our framework rivals the best parameter and baseline models. Our method boasts high scalability and flexibility, aiding in optimizing various evaluation indicators. Experimental verification through multiple real transaction datasets under varying data segmentations, demonstrated its effectiveness when compared with other representative frameworks. The analysis validates the effectiveness and benefits of our method.

Deep learning-driven object detection models are capable of accurately identifying and localizing objects. However, small objects contain limited information relative to global features, resulting in the fact that detection models often do not learn small object features adequately. To enhance the precision in detecting small objects, we propose a bi-directional and triangular circulation fusion neural network (BTFN). First, to selectively strengthen the position features of small objects, we propose a feature circulation extraction module composed of a bi-directional triangular densely nested convolutional network (BTF), thus achieving repetitive multi-layer feature fusion. Second, to fill up the semantic gaps between different scales of features, we design a mixed dual attention module (MDA) in the bi-directional triangular densely nested network. Third, to mitigate the lost information in the neural networks with deep layers as well as improve the inference time, we design a re-parameterization bi-directional composite feature fusion module (Rep-BFM) that fuses the features of multiple scales. The proposed model is evaluated extensively on the MS COCO, Tsinghua-Tencent 100k, and Haier dismantled parts of used home appliances datasets. The experiment results show that the proposed model improves the AP on MS COCO by 4%, especially the APS of small objects is improved by 7.7% compared with SOTA models.

In wastewater treatment process (WWTP), the dissolved oxygen concentration (DOC) sensor fault provides incorrect data to the control system, affecting the blower operation. This leads to insufficient aeration and increases the risk of membrane fouling. To solve this problem, a robust model-free fault-tolerant controller (RMFFTC) is designed. First, the pseudo partial derivative (PPD) approach is utilized to transform nonlinear WWTP into a compact form dynamic linearization (CFDL) data model with residual disturbances. Then, according to the CFDL model, a robust fault detection threshold is designed by the extended state observer (ESO) to timely detect the occurrence of faults. Second, after detecting the DOC sensor fault, the fault is estimated using the fuzzy neural network (FNN) considering that the fault is unknown. Third, an improved RMFFTC is designed based on the fault estimation information. In particular, to ensure stable DOC tracking under sensor faults, the controller design considers the output tracking error variation. In addition, the bounded-input-bounded-output (BIBO) stability result is provided to theoretically guarantee the usefulness of the proposed RMFFTC for DOC control affected by the sensor fault. Finally, the effectiveness of the RMFFTC are verified through extensive simulations in the membrane bioreactor (MBR) model.

Adaptive control (AC) has been extensively proved as a promising strategy for nonlinear systems, especially in the dynamic and changeable environments. However, due to the unavoidable existence of unknown interconnections in the real nonlinear systems, it is difficult for typical AC to guarantee its stability within the bounded convergence time. Thus, to solve this issue, a predefined-time adaptive neural control (PTANC) scheme is developed for nonlinear systems with unknown interconnections in this aritcle. First, an integrated control framework, where the controlled objectives not only relate with each other but also change over time, is able to catch more characteristics of nonlinear systems than the existing works. Then, the proposed control scheme can address the impact of unknown interconnections on the system stability. Second, a predefined adaptive law mechanism is employed to estimate the unknown interconnections to assist in PTANC. Then, the proposed PTANC scheme can ensure its predefined-time stable in the occurrence of unknown interconnections. Third, a neural network-based self-regulating strategy is designed to construct the Lyapunov function to prove the stability of PTANC. Then, the comprehensive stability analysis can make PTANC scheme be successful applied in nonlinear systems. Finally, the proposed PTANC scheme is tested on the numerical simulation and BSM1 simulation platform. The experimental results illustrate that the envisioned control method attains exceptional performance.

Neural network (NN) is a prominent intelligent model to process information through the connection and activation of multilayer neurons. However, NNs usually encounter with the incorrect activation of neurons because of the excessive coverage for the boundary of compound noises. To address this issue, this article proposes a robust reconstructed NN (RRNN) with spectral reshaping activation (SRA). Primarily, an SRA is designed to replace the original activation of NN, which shrinks the spectrums of the compound noises toward the cluster center through spectral subtraction. It enables RRNN to reshape a concentrated noise space for easy coverage. Then, a hierarchical gradient descent (HGD) algorithm is developed to update the parameters of RRNN. The HGD algorithm establishes a noise-contrastive degree of SRA to penalize the loss function of RRNN, which holds robust performance with different noises. Furthermore, the theoretical proof of RRNN is presented to validate its robustness. Finally, the experimental results confirm the superior robustness of RRNN for tackling noisy samples compared to other methods.

The competitive swarm optimizer (CSO) has been widely used for addressing multiobjective optimization problems owing to its diverse learning approach. However, the evolutionary process uncertainty within the algorithm weakens the optimization reliability. To deal with this concern, a robust multiobjective CSO with a predictive indicator (RMOCSO-PI), is proposed. This approach can reduce aimless and inefficient searches caused by the uncertainty to enhance algorithmic robustness. First, a predictive indicator is established based on the autoregressive model, which utilizes historical swarm distribution data to predict the evolutionary trends. Then, the particles are classified into winners and losers by evaluating their evolutionary potential, whose evolution would be guided differentially. Second, a space fusion-based competitive mechanism is designed to generate precise evolution directions for loser particles. The space fusion-based adaptive adjustment method integrates the learning cost metric in decision space with the learning worth metric in objective space for proper learning weight settings. Third, a dynamic cooperative mechanism is presented to purposefully guide the diversity exploration of particles. By estimating evolutionary states, three cooperative patterns are dynamically assigned to particles for purposeful diversity exploration. To provide theoretical support for the validity and reliability of RMOCSO-PI, a convergence analysis is given. Furthermore, experimental results verify that RMOCSO-PI has more stable and excellent optimization performance.

Wastewater treatment processes (WWTPs) are operated under multiple operating conditions. Designing an appropriate optimal control strategy based on the identification of operating conditions is crucial for ensuring the safe operation of WWTPs. To effectively deal with the problem of multiple operating conditions in WWTPs, a data-knowledge-driven multiobjective adaptive optimal control (DK-MAOC) strategy is proposed. First, a fuzzy neural network (FNN) is employed as the prediction model to obtain the concentrations of nitrate and total nitrogen. Then, the operating conditions of WWTPs can be determined. Second, an adaptive objective function (AOF) is proposed to dynamically adjust the weights of operating indices to meet the operational requirements of each operating condition. In particular, the AOF integrates operating requirements and tracking errors to simultaneously consider the feasibility of the controller when solving setpoints. Third, due to the differences in data distribution under each operating condition, real-time data during condition changing is insufficient to accurately predict. A data-knowledge-driven model, incorporating operational knowledge into the FNN-based predictive model, is established to predict the future dynamics of WWTPs. Finally, a collaborative gradient descent algorithm is proposed to simultaneously solve for setpoints and control laws. The effectiveness of the proposed DK-MAOC is tested on the Benchmark Simulation Model No. 1. The experimental results indicate that DK-MAOC can effectively avoid the situation of effluent nitrate nitrogen and total nitrogen exceeding the standards while reducing energy consumption of WWTPs. Therefore, the proposed DK-MAOC can guarantee optimal operation of WWTPs.

HCMOP are widespread in practical engineering such as vehicle routing problem and shop scheduling problem etc. The problems introduced above refer to optimization problems with complex constraints which lead to small and disconnected feasible regions. The optimization performance of general evolutionary algorithms decreases due to the small and dispersed feasible regions in highly constrained optimization problems. To address this problem, a multiobjective ant colony optimization algorithm based on dynamic constraint evaluation strategy (MOACO-DCE) is proposed in this article. First, a dynamic constraint violation metric is proposed to evaluate the constraint violation degree of solutions. The population is classified into the subpopulation with evolutionary advantages and the subpopulation with high constraint violation degree by this metric. Second, an evolutionary strategy based on dynamic transfer probabilities is proposed for the subpopulation with evolutionary advantages in order to improve the evolutionary efficiency. A Gaussian variation evolutionary strategy is proposed for the subpopulation with high constraint violation degree in order to improve the population diversity. Third, a pheromone collaborative updating strategy is proposed to achieve the synergistic pheromone updating between two subpopulations. A pheromone updating strategy considering the constraint violation metric is designed to improve the utilization of constraint violation information in the whole population. In addition, compared with other constrained multiobjective optimization algorithms, MOACO-DCE can obtain more satisfactory performance for the highly constrained optimization.

Due to the unreliable communication network, networked control systems (NCSs) are often subjected to communication imperfections including stochastic sampling intervals (SSIs) and packet dropouts, which can lead to degradation of control performance and even jeopardize the stability of the NCSs. In this article, the data-driven model predictive control (DMPC) strategy is proposed to stabilize a class of unknown nonlinear NCSs with SSIs and successive packet dropouts (SPDs). First, an equivalent stochastic sampling model is constructed by capturing the randomness of both SSIs and SPDs, which can determine the probability information of the equivalent sampling interval between consecutive no-packet -dropout update instants. Subsequently, a multimodel predictive structure is designed based on the possible lengths of the sampling interval in the equivalent stochastic sampling model, which can provide predictive outputs for the subsequent controller design. Furthermore, to reduce the computational burden associated with the prolongation of the prediction horizon in the multimodel predictive structure, a prediction data interpolation algorithm based on the Lagrange interpolation polynomial is introduced. Additionally, to ensure the accuracy of interpolation prediction output, an adaptive mechanism for updating interpolation nodes is designed to dynamically adjust the number and position of these nodes. Finally, a cost function that relies on the expectation of the predictive output is designed and solved to achieve stable tracking control of the considered NCSs. The stability of the DMPC strategy is demonstrated in detail. Numerical examples and industrial applications for the wastewater treatment process (WWTP) demonstrate that DMPC can obtain satisfied control performance.

Communication imperfections, such as variable sampling periods and packet dropouts induced by insufficient network bandwidth, can degrade the control performance and even jeopardize the stability of networked control systems (NCSs). A stochastic communication protocol (SCP) is usually adopted to ensure that only one sensor node can transmit the output signal to the controller at each sampling instant, thus conserving network bandwidth resources. This article focuses on the output feedback synthesis problem for NCSs in the presence of the SCP, considering two-channel successive packet dropouts (SPDs) and multiple probability sampling periods (MPSPs). Among these, MPSPs mean that there are three or more different sampling rates in system. To address the output feedback synthesis problem, we first obtain the discrete-time augmented model of the closed-loop NCS with a dynamic output feedback controller. This model incorporates an equivalent sampling period representation between adjacent nonpacket-dropout instants, which plays a pivotal role in our analysis. Furthermore, a general analysis model is established by considering the effects of the SCP. Based on this model, conditions for designing the dynamic output feedback controller, represented by linear matrix inequalities (LMIs), are established using a two-step synthesis approach. In particular, the dimension of the obtained controller design conditions remains unchanged with respect to the upper bound of SPDs and the number of possible sampling periods, especially through the introduction of a matrix decomposition method, which is more general than existing results. Finally, the proposed method is demonstrated through an illustrated example.

fault-tolerant control (FTC), due to its characteristic of fault prevention and mitigation, is an increasingly popular topic in wastewater treatment process (WWTP) for safety purpose. However, the presence of uncertainties and external disturbances inevitably leads to unknown faults in WWTP, making it challenging for FTC strategies using existing fault data to ensure continuous safe and stable operation. To address this issue, a knowledge compensation-based active fault-tolerant control (KC-AFTC) is designed in this article. First, a knowledge-based prescribed performance function (KPPF) is introduced to constrain the transient and steady-state performance of WWTP. Then, the proposed KPPF can assist in KC-AFTC to ensure the operation of WWTP with the desirable performance in the event of faults. Second, a knowledge compensation mechanism (KCM), which is extracted from KPPF and the fault data, is employed to reconstruct the control law for different fault conditions in active FTC (AFTC). Then, KC-AFTC can maintain the continuously safe and stable operation of WWTP. Third, the stability of knowledge compensation-based AFTC (KC-AFTC) is demonstrated through Lyapunov theory. Then, the stability analysis can provide theoretical basis for further application of KC-AFTC in practical experiments. Finally, the proposed control method is validated through both a simulation case and a real WWTP. The results demonstrate that KC-AFTC can achieve outstanding performance in terms of stability and fault tolerance.

Many-task differential evolutionary algorithm is an effective way to optimize multiple tasks simultaneously. The optimization performance of the algorithm decreases due to the negative transfer when the number of tasks is large. To address this problem, a many-task differential evolutionary algorithm based on bi-space similarity (MaTDE-BSS) is proposed to improve the positive transfer. First, the bi-space similarity metric is designed to characterize inter-task similarity quantitatively. The decision space similarity and objective space similarity are considered simultaneously in the bi-space similarity metric. Second, a task selection strategy based on evolutionary state is proposed to select the optimal source task from the source task library accurately. The source task library based on bi-space similarity metric is built for storing source tasks. Finally, a dynamic knowledge transfer strategy is proposed to improve the efficiency of knowledge positive transfer in the many-task optimization. Parameters of the knowledge transfer strategy are adjusted according to bi-space similarity metric adaptively. In addition, the experimental results show that MaTDE-BSS is able to evaluate the inter-task similarity more comprehensively. And MaTDE-BSS is more competitive compared to other many-task evolutionary algorithms.

With increasing energy concerns and development of globalization, energy-aware scheduling and distributed scheduling have become significant topics in modern manufacturing. However, realistic manufacturing scenarios, such as collaborative scheduling of distributed shops and limited transportation resources, are rarely taken into account. To bridge the gap, this paper addresses the energy-aware distributed flexible job-shop with transportation constraints (EDFJSP-T) and proposes a feedback learning-based memetic algorithm (FLMA) to minimize makespan and total energy consumption simultaneously. First, a mathematical model is formulated to represent the relationship between different sub-problems. Additionally, an encoding and decoding method based on forward insertion is designed to reduce the search space and obtain high-quality schedules. Second, various problem-specific operators are designed to focus on different sub-problems and objectives to enrich search patterns. Third, memetic search with feedback learning is proposed via introducing observer indexes for both population state and individual state to adaptively match appropriate operators for individuals. Besides, local intensification search with multiple operators is incorporated for low-density regions to further improve exploitation ability. The parameter setting is investigated and experimental tests are carried out using different types of instances. The comparisons demonstrate the effectiveness of the feedback learning mechanism and the superiority of the FLMA over existing algorithms for solving the EDFJSP-T.

Task similarity is a major requisite to trigger knowledge sharing in evolutionary multitasking optimization (EMTO). Unfortunately, most of the existing EMTO algorithms only focus on the similarity between population distributions of tasks, but ignore the search behavior of populations, which may degrade the performance of cross-task knowledge sharing. Motivated by this, an improved EMTO algorithm with similarity evaluation of search behavior (SESB-IEMTO), employing the particle swarm optimization (PSO) algorithm as a task solver for each task, is proposed. It comprises three key elements: 1) a dynamic similarity-based evaluation strategy, 2) a cross-task knowledge adaptation method, and 3) a search direction sharing mechanism. Primarily, the source tasks with similar search behavior are discriminated with the dynamic similarity-based evaluation strategy, where individuals can be fully exploited for cross-task evolution. Then, the knowledge derived from these source tasks is regulated by the cross-task knowledge adaption method for alleviating the risk of negative transfer caused by the heterogeneity between tasks. Moreover, to further promote knowledge sharing between tasks, the search direction sharing mechanism is developed to navigate tasks efficiently searching for promising regions. Finally, the convergence of SESB-IEMTO is analyzed, and the effectiveness and superiority are also verified with the experiments on several benchmark tests and a real-world application study.

For complex dynamic systems, it is a great challenge to design an appropriate control strategy to achieve stable tracking control. To solve this problem, a fuzzy terminal sliding-mode control method with adaptive switching gain (FTSC-ASG) is designed to improve the control performance in this paper. First, an adaptive interval type-2 fuzzy prediction model (AIT2-FPM) is designed to approximate the complex nonlinearity and parameter uncertainty. Specifically, the state prediction error evaluated by predictor is utilized to design the weight adaptive law to improve the accuracy of the AIT2-FPM. Second, a terminal sliding-mode controller is utilized to obtain control input of the system in a finite time. To suppress the chattering phenomenon, the switching gain is designed based on the output of AIT2-FPM and the changes of control input information can be utilized to evaluate the degree of chattering. Furthermore, a parameter adaptive strategy is designed to adjust the parameter of equivalent control law. Third, FTSC-ASG can achieve fast convergence of tracking error, and the finite time stability of FTSC-ASG is proven in detail. Finally, the simulation studies in the third-order nonlinear system and the inverted pendulum systems are given to evaluate the effectiveness of FTSC-ASG.

Fuzzy transfer learning (FTL) algorithms are capable of leveraging coarse-grained knowledge from source domains to learn related tasks in target domains characterized by inherent uncertainty. However, since the uncertainty in target domains can dynamically change, relying on a single knowledge granularity often proves ineffective for adapting to the learning tasks at hand. To address this challenge, we propose an adaptive multigranularity fuzzy transfer learning algorithm (AMG-FTL) that aims to utilize source knowledge across varying granularity levels. AMG-FTL is distinguished by three main features: First, we establish a knowledge mining mechanism to reconstruct source knowledge at different granularities: fine-grained, medium-grained, and coarse-grained knowledge, allowing the source knowledge to align more closely with the target tasks and bridge the gap between scenarios. Second, we propose an adaptive granularity learning framework aimed at effectively assimilating the diverse levels of source knowledge. This approach is designed to enhance the learning capabilities of the target fuzzy neural network, enabling it to better align with the complexity inherent in the source knowledge while also improving its generalization performance. Additionally, we conduct a theoretical analysis of the proposed AMG-FTL, offering insights into its convergence properties and error bounds. Experimental results across a range of benchmark problems and real-world applications indicate that AMG-FTL significantly outperforms several leading algorithms in the field.

Networked control systems (NCSs) suffer from various communication imperfections, including varying transmission intervals, packet losses, and false data injection (FDI) attacks. The majority of the existing literature on NCSs tends to emphasize certain aspects while neglecting others. In this article, we propose a general framework for addressing the stabilization problem of networked nonlinear systems that incorporates multiple stochastic transmission intervals (MSTIs), successive packet losses (SPLs), and FDI attacks. We assume that the nonlinear system can be precisely modeled using a Takagi–Sugeno (T–S) fuzzy system. MSTIs can be described using the categorical distribution, while both the sensor-to-controller channel and the controller-to-actuator channel are affected by SPLs and FDI attacks. In order to facilitate the stabilization problem, we first establish the equivalent stochastic transmission interval between adjacent nonpacket-loss instants, where the occurrence probability of the length of the equivalent transmission interval can be accurately calculated by using the probabilistic information of SPLs and MSTIs. Furthermore, considering two-channel FDI attacks, a discrete-time T–S fuzzy system model is obtained. The controller design conditions, represented by linear matrix inequalities (LMIs), are derived based on this model. Specifically, using a novel matrix reconstruction approach, the dimension of the obtained controller design condition does not change with the number of maximum packet losses and the number of MSTIs, which is more general than existing results and avoids the high computational complexity associated with solving LMIs in some cases. Finally, the effectiveness of the proposed method is demonstrated through a numerical example.

An essential component of the activated sludge method for wastewater treatment is the stable control of the dissolved oxygen (DO) concentration. However, the actuator failure and unavoidable external disturbances may cause deviations in the DO concentration, and even destabilize the system. In this article, a fault tolerant control approach utilizing adaptive dynamic programming (ADP) and experience replay (ER) is developed with the purpose of realizing robust control of the DO concentration under the influence of the actuator failure and external disturbances. First, a novel cost function considering actuator multiplicative failure and disturbances is constructed. Based on this cost function, the control law is designed, which can effectively suppress the adverse effects of the actuator failure and external disturbances on control performance. Second, the control input, failure input and cost function are estimated via two action networks and one critic network. Specifically, the collaborative interaction of the three networks contributes to get the optimal robust control law. Third, an improved ER technique named disturbance-focused experience replay (DFER) is designed for adjusting the critic network and action networks, where a metric rooted in disturbance magnitude and time-difference error is designed to dynamically adjust data and batch sizes, for effectively suppressing the external disturbances. Finally, the feasibility of the proposed fault tolerant control method based on ADP with ER is confirmed through simulation experiments.

For nonlinear coupled ODE-PDE systems with stochastic actuator failures, this article introduces an intermittent sampled-data fuzzy (ISDF) control under spatially local averaged measurements (LAMs). To precisely characterize the nonlinear coupled ODE-PDE system, a Takagi-Sugeno fuzzy model is firstly introduced. Second, considering the stochastic actuator failures caused by Markov jump, an ISDF control strategy is developed for the nonlinear coupled ODE-PDE system under spatially LAMs, which only demands a minimal number of sensors and actuators. Then, through constructing a time-dependent switched Lyapunov functional, the stochastically exponential stability conditions are given in terms of linear matrix inequalities (LMIs) and ISDF control gains are obtained by solving these LMIs. Finally, the effectiveness of the developed approach is validated through its application to hypersonic rocket car (HRC) control.

The constant fluctuation of operational conditions in industrial processes results in dimensional changes or corrosion of machine, consequently leading to recurring drift of its property parameters. This phenomenon poses a challenge for diagnosis models capturing fault features of machine by learning mapping patterns with the collected property parameters. To address this issue, a generalized mapping fault diagnosis model (GMFDM) is proposed to diagnose machine faults by using a multimode feature map (MFM) and a penalty gating LSTM (PG-LSTM). First, an MFM is built to obtain the features of faults using the interaction among the fault-related variables. Second, a penalty gating mechanism (PGM) is introduced and incorporated into PG-LSTM. PGM updates the gate units of LSTM based on the results of the MFM to regulate the flow and memory of information, which enables LSTM to dynamically sharpen multiple mapping patterns of faults under the recurring drift. Third, a pattern-aware learning algorithm is designed to update the parameters of PG-LSTM, shaping diverse mapping patterns with a regularization term. Finally, the experimental results show that the GMFDM achieves accuracy of 98.08% in diagnosing the faults of the pump in industrial processes.

The drastic fluctuations of influent pollutant load are inevitable in wastewater treatment process, which makes it difficult for nitrification to regulate dissolved oxygen concentrations with minimal effort to ensure the effluent quality. To solve this problem, a multispatial-scale optimal control with multisource information (MSI-MSSOC) is developed in this article. First, a multispatial-scale optimization model, making use of mechanism knowledge and process data, is designed to construct reasonable objectives and constraints. Then, the performance indexes can be described to evaluate the comprehensive adjustment effect of dissolved oxygen concentrations in different areas. Second, an adaptive knowledge acquisition strategy is employed to extract the interactivity between feasible and infeasible solutions. Then, the proposed strategy can assist in the optimal control to search for the optimal solutions. Third, a knowledge-aided optimization algorithm is introduced to update the feasible region to calculate the optimal solutions. Then, the optimal dissolved oxygen concentrations in different areas can be obtained to guarantee the effluent quality and reduce the energy consumption. Finally, the proposed MSI-MSSOC is applied to Benchmark Simulation Model No. 1 to verify its effectiveness. The experimental results demonstrate that MSI-MSSOC can achieve the desirable operation performance of nitrification.

The increasing demand for wastewater treatment processes is to improve the effluent quality and reduce the energy consumption. However, due to the existence of different time scales data acquisition for effluent quality and energy consumption, it is difficult to achieve optimum operation of wastewater treatment processes with multitime-scale property. To solve this problem, a knowledge-data driven multitime-scale optimal control (KDD-MTSOC) is designed in this article. First, a knowledge-data driven optimal control system is established by dividing the optimal control problem into different time scales, and solving it by matching with appropriate optimization algorithms. Then, the frequency of optimal control is improved and data is fully and reasonably used. Second, a knowledge-based regression kernel strategy is employed to establish the reasonable objective functions and constraints. Then, the objective functions and constraints are favorable to balance performance indexes and describe the multitime-scale characteristics. Third, a knowledge decision-based particle swarm optimization (KDPSO) algorithm is presented to solve the multitime-scale optimization problem of KDD-MTSOC. Then, the KDPSO algorithm can effectively improve the operational performance. Finally, the proposed KDD-MTSOC is applied to the Benchmark Simulation Model No. 1 to verify its effectiveness. The experimental results demonstrate that the KDD-MTSOC method can achieve outstanding operational performance.

Fault-tolerant control (FTC) has been developed as a remedial strategy, which can take action with fault information to inhibit the occurrence of abnormal condition, such as sludge bulking, further to ensure the safety and stability of wastewater treatment process (WWTP). However, since the coupling relationship among fault variables results in the complexity and obscurity of fault characteristic, especially in the early stage, it is difficult to extract the available fault information to design an efficient FTC. Therefore, to tackle this issue, a knowledge-guided fault-tolerant compensation control (KG-FTCC) with fault diagnosis is presented in this article. First, a knowledge fault diagnosis strategy is employed to analyze the variable causality to extract the root fault cause. Then, the proposed strategy can identify the fault characteristic with coupling relationship to assist in KG-FTCC. Second, a knowledge fault compensation mechanism, which can leverage the fault knowledge and data, is introduced in KG-FTCC to achieve the control law reconstruction. Then, the proposed KG-FTCC can catch the desired set-point to suppress the sludge bulking. Third, the stability of KG-FTCC is proved by using the Lyapunov theory. Then, the effective implementation of KG-FTCC can be guaranteed. Finally, the merit of KG-FTCC is verified in a real WWTP and a simulation application. The experimental results indicate that KG-FTCC can enhance its diagnosis and control performance to ensure the safe and stable operation of WWTP.

Sludge bulking in the municipal wastewater treatment process will cause low sludge settling performance and deterioration of effluent quality. Accurate identification and prediction of sludge bulking is an effective solution. Based upon the measured data, a fuzzy neural network-based identification model with self-organizing recurrent structure is established in this article, which can realize the high-precision identification of sludge bulking. First, a self-organized method of FNN with recurrent structure is designed. The recurrent parameters can realize weight allocation of different time series. Second, the network structure adjustment index and dynamic structure adjustment threshold are defined. A dynamic threshold structure increment and subtraction method for the self-organized FNN is designed. The neuron rules and the number of neurons are modified according to the conditions of increasing and decreasing, which can determine the most appropriate neurons number and neuronal rules. Then, the improved stochastic gradient method and the improved recursive least squares method are employed to adjust network parameters to obtain accurate network output. Finally, the output accuracy and prediction accuracy of the investigated model are verified by simulation and comparison experiments.

This paper deals with sideslip angle estimation problems of autonomous ground vehicles that repeatedly perform the specific tasks in the absence of model knowledge for their lateral dynamics. By designing appropriate estimators, the equivalence between estimator auxiliary input synthesis and output feedback stabilization along the iteration axis is established. Moreover, we propose an innovative data-based output feedback stabilization framework that leverages insufficient sampled data to formulate an output feedback controller without the need of identification. To be specific, with the application of some helpful linear matrix inequality (LMI) techniques, the data-based synthesis of required output feedback controller is transformed into solving the equivalent LMI conditions. By employing the proposed data-based estimation strategy and partial lateral dynamics information of ground vehicles, accurate estimation of sideslip angles over the entire estimation duration can be achieved even in the presence of disturbances. Experiments on an Ackermann steering intelligent vehicle are provided to demonstrate the effectiveness of the proposed estimation strategy.

Type-2 fuzzy neural networks (T2FNNs) are particularly effective in dealing with nonlinear systems. However, they inevitably suffer from multicollinearity problems caused by the significant overlaps of the footprint uncertainty (FOU), which leads to generalization biases. To solve this challenge, a self-organizing stacked T2FNN with rule generalization (RG-SOST2FNN) is developed to boost its overall performance. First, a stacked technique with cosine smart priority is designed for T2FNN fusion. This technique employs multivariable cosine similarity to obtain sparse inputs, which selectively stacks multiple T2FNNs with non-collinear inputs to reduce collinearity dependence. Second, a dynamic stacked framework with a rule cluster generation mechanism is developed to achieve individual and batch rule adjustment. Then, a stacked structure with diversity is obtained to alleviate collinearity among rules by eliminating the singularity of the parameter matrix of FOUs. Third, a stacked risk mitigation algorithm is proposed to shape the fuzzy rule clusters (FRCs). Then, the parameters of FRCs are optimized using sparse gradient learning, which avoids the updating of collinear features to reduce the variance of parameter estimation. Finally, the simulation tests show that RG-SOST2FNN can achieve state-of-the-art performance even at high multicollinearity in complex systems.

Fuzzy neural network (FNN) is a structured learning technique that has been successfully adopted in nonlinear system modeling. However, since there exist uncertain external disturbances arising from mismatched model errors, sensor noises, or unknown environments, FNN generally fails to achieve the desirable performance of modeling results. To overcome this problem, a self-organization robust FNN (SOR-FNN) is developed in this article. First, an information integration mechanism (IIM), consisting of partition information and individual information, is introduced to dynamically adjust the structure of SOR-FNN. The proposed mechanism can make itself adapt to uncertain environments. Second, a dynamic learning algorithm based on the -divergence loss function ( -DLA) is designed to update the parameters of SOR-FNN. Then, this learning algorithm is able to reduce the sensibility of disturbances and improve the robustness of Third, the convergence of SOR-FNN is given by the Lyapunov theorem. Then, the theoretical analysis can ensure the successful application of SOR-FNN. Finally, the proposed SOR-FNN is tested on several benchmark datasets and a practical application to validate its merits. The experimental results indicate that the proposed SOR-FNN can obtain superior performance in terms of model accuracy and robustness.

Feature pyramids are widely adopted in visual detection models for capturing multiscale features of objects. However, the utilization of feature pyramids in practical object detection tasks is prone to complex background interference, resulting in suboptimal capture of discriminative multiscale foreground semantic features. In this article, a foreground capture feature pyramid network (FCFPN) for multiscale object detection is proposed, to address the problem of inadequate feature learning in complex backgrounds. FCFPN consists of a foreground dual attention (FDA) module and a pathway aggregation (PA) structure. Specifically, the FDA mechanism activates top-down foreground channel responses and lateral spatial foreground location features, so that channel and spatial foreground features are adequately captured. Then, the PA module adaptively learns the fusion weights of multiscale features at different levels of the feature pyramid, which enhances the complementarity of semantic information between different levels of the foreground feature maps. Since the fusion weights are learned adaptively based on different pyramid levels, the detection model accordingly retains the gained information of feature sizes and suppresses the conflicting information. The evaluations on public datasets and the self-built complex background dataset demonstrate that the detection average precision (AP) and the feature learning performance of the proposed method are superior compared with other FPNs, which proves the effectiveness of the proposed FCFPN.

The presence of sparse samples poses a formidable challenge for neural networks (NNs) in shaping representative patterns due to the limited coverage of concentrative activation range in NNs. To address this issue, a robust reconstructed NN, based on spectral elastic activation (SEA-RRNN), is developed in this article. Primarily, a spectral elastic activation (SEA) is designed to broaden the original activation of NNs, which embeds a spectral increment scaled by the estimated outlier degree on the activation boundary. It enables SEA-RRNN to stretch the boundary of SEA to cover the features of sparse samples. Then, an adaptive robust gradient descent (ARGD) algorithm is introduced to update the parameters of SEA. By tuning the loss between error and correntropy with the estimated outlier degree, the ARGD algorithm establishes two loss functions with complementary distance sensitivity for different parameters of SEA, which alleviates the construction conflict of robust center and precise boundary in SEA-RRNN. Furthermore, the theoretical analysis of SEA-RRNN is provided to validate its convergence and robustness. Finally, the experimental results demonstrate that SEA-RRNN exhibits superior robustness compared to other NN models.

External disturbances can render constrained multiagent systems (MASs) unstable and affect their convergence speed. To address this issue, the cooperative control strategy for MASs based on a predefined time (PT) disturbance observer (PTDOB) is proposed in this article. First, the original time-varying constrained states of MASs, which are influenced by external disturbances and have a coupled communication topology, are transformed into unconstrained states using the nonlinear transformed function (NTF). This transformation ensures that the limitations of various physical states for agents are not exceeded. Second, the transformed unconstrained states are used to construct the PTDOB for fast observation of external disturbances. Then, based on the proposed PTDOB and the backstepping control technique, an adaptive fuzzy PT cooperative controller is designed. This controller not only ensures the convergence of MASs within PT but also prevents the states from exceeding the time-varying bounds. Finally, the effectiveness of the proposed control strategy is demonstrated through its application to multiple single-link robotic arms as illustrative examples.

In wastewater treatment processes (WWTPs), data and knowledge are employed to build an effective model for monitoring its operation. Unfortunately, they are difficult to be fused due to their heterogeneity, which struggles to provide a united and reliable solution. To solve this issue, a data-knowledge-driven inductive learning (DKIL) method is introduced to WWTPs. First, a fuzzy-based expression strategy is introduced to describe the operational status of WWTPs. This strategy captures the available data, constraint knowledge and semantic knowledge for the modeling process. Second, a heterogeneous assimilation mechanism is designed to integrate data and knowledge. This mechanism supports their interaction to form a unified scheme through fusion operations. Third, a collaborative optimization algorithm is developed to extract the operational features of WWTPs. This algorithm updates the parameters using both error information and semantic knowledge, which enhances the modeling performance. In the experiment, the results have verified that DKIL can efficiently model WWTPs.

Model predictive control (MPC) is a practical method for addressing control issues in constrained systems. System identification and constrained optimization are two key problems that affect MPC performance. In this work, a self-organizing MPC (SOMPC) strategy is proposed for constrained nonlinear systems with unknown dynamics to achieve constraint satisfaction and improve control performance. First, the generalized multiplier method is introduced into the MPC framework to redesign the objective function. In this way, the constrained optimal control problem is reconstructed into an easily solvable unconstrained optimal problem. Second, a self-organizing fuzzy neural network (SOFNN) is adopted to identify unknown nonlinear system. Then, the performance of SOFNN is optimized by parameter updating and structure self-organization to provide accurate prediction output. Third, the gradient descent algorithm is utilized to solve nonlinear optimization problem of MPC to obtain control input. To ensure practical application, the convergence of SOFNN, the feasibility and stability of SOMPC strategy are proved. Finally, the proposed SOMPC strategy is demonstrated by a numerical experiment and an industrial process control simulation experiment, and the results show that it exhibits outstanding control performance and constraint satisfaction ability.

In industrial processes, the optimization and control processes operate on different time scales. Neglecting the multitime scale characteristics can lead to an optimized control law that fails to guarantee the control performance of the controlled nonlinear system. To address this problem, a data-knowledge-driven multitime scale integrated optimal control (DK-MTSIOC) strategy is proposed for the nonlinear system in this article. First, a multitime scale integrated optimal control (MTSIOC) framework, including a TSCOF, is established. Then, multitime scales of nonlinear systems are coordinated to the fast time scale to ensure real-time optimization and control. Second, to address the problem of low accuracy in predicting fast time scale model driven by the slow time scale data information, a data-knowledge-driven prediction model is introduced to predict the future dynamics of the system at the fast time scale. Furthermore, a knowledge compensation strategy is designed to supplement missing fast time scale specific information. Third, a COA is utilized to solve the setpoints and control laws simultaneously. Besides, the convergence of the data and knowledge-driven prediction model and stability of DK-MTSIOC are proved. Finally, the proposed DK-MTSIOC is tested on a conventional nonlinear system and a benchmark example of the wastewater treatment process to validate its effectiveness.

Due to its demonstrated efficacy, optimal control has extensive application in nonlinear systems. However, in the optimal control process, the time delays in the optimization objectives makes the optimization problem difficult to solve. To improve the optimal control performance, a coevolution-based robust optimal control (C-TDROC) method is designed. First, a data-driven estimation strategy is proposed to approximate the optimal objectives of nonlinear systems. Then, the approximation errors caused by time delays are described as uncertain representations of system states. Second, a coevolution-based robust optimization (CRO) algorithm is developed to solve the optimal set points of system states. This algorithm generates two coevolutionary particle swarms in robust time delay intervals to improve the robustness of optimal set points. Third, an adaptive time delay controller is proposed for tracking the optimal set points. Then, the Lyapunov-Krasovskii functionals are employed to ensure the stability of C-TDROC. The experiments on a time-delay nonlinear system and a time-delay biochemical reaction process are carried out to prove the availability of C-TDROC.

The optimal control of nonlinear systems is crucial to improve system performance. However, the uncertainties of cost functions and systems dynamics make it difficult to solve the optimal control laws. To cope with this problem, a hierarchical learning-based integrated robust optimal control (HL-IROC) method is proposed in this article. The merits of the proposed HL-IROC method are three aspects: First, a hierarchical learning-based integrated optimal control (HL-IOC) scheme, contains a system dynamic learning layer and a cost function learning layer, is designed to transform the original optimal control problem into an integrated optimization problem with control laws as decision variables. Then, the relationships between cost functions and control laws are captured to overcome the difficulties brought by uncertainties in the optimal control process. Second, a global-local cooperative robust evolutionary optimization (GL-CREO) algorithm is proposed to obtain the optimal control laws. Then, a global-local robust searching strategy is employed to deal with two types of uncertainties for improving the robustness of control laws. Third, the convergence analysis of HL-IOC and GL-CREO is discussed in theory. In the experiments, the effectiveness of HL-IROC is illustrated with a nonlinear system and a wastewater treatment process.

Distributed learning-based high-dimensional temporal modeling for the Industrial Internet of Things (IIoT) has become a prevailing trend. However, traditional distributed learning inefficiently extracts information by straightforward architects, resulting in low modeling accuracy and high communication costs. We propose a distributed hierarchical temporal graph learning (DHTGL) approach. In terminal equipment, we construct an adaptive hierarchical dilation convolutional network to dynamically capture spatiotemporal features by adjusting the dilation factor at each layer. Next, we construct adaptive graphs according to the connection similarity between dimensions to capture implicit connections. In the edge device, we design a node-edge graph distance calculation based on Gromov-Wasserstein distance to group feature graphs and construct representative cluster feature graphs. Edge devices upload cluster feature graphs to reduce communication costs while minimizing information loss. In the central server, we incorporate graph attention networks into graph neural networks for edge updating in training models on clustered feature graphs. Experiments using public IIoT datasets and the self-built IIoT platform demonstrate the effectiveness of DHTGL in comparison with common distributed learning approaches. The results confirm that DHTGL consumes fewer communications while achieving higher accuracies.

Multi-objective optimal control is widely applied in wastewater treatment processes (WWTPs) to ensure the security and stability of the operation processes. However, for the existing stepwise multi-objective optimal control (SMOC) algorithms, the unknown disturbances will further influence the obtain of set-points and the design of control laws, which may degrade the control performance and operation performance of WWTPs. Aim at the above-mentioned problem, this study presents a multi-objective integrated robust optimal control (MIROC) method for WWTPs. The merits of MIROC are three folds. First, a model approximator is designed to capture the nonlinear dynamics of WWTPs. Second, a disturbance observer is utilized to describe the disturbances of WWTPs. Then, based on the model approximator and disturbance observer, a more accurate prediction model of WWTPs with disturbances is established. Third, under the framework of multi-objective model predictive control (MMPC), a MIROC structure with a cooperative cost function (CCF) and a gradient-based multi-objective optimization algorithm (GMOA) is developed to coordinate optimization and control solution of WWTPs with unknown disturbances. Finally, the stability analysis of MIROC is provided in theory. Meanwhile, the results on the benchmark simulation platform demonstrate that MIROC can improve the performance of WWTPs. Note to Practitioners—The SMOC algorithms may degrade the performance of WWTPs with the unknown disturbances. In the paper, a MIROC scheme is presented for WWTPs with the unknown disturbances. Three key parts are contained, the model approximator, the disturbance observer and the MIROC structure. A prediction model of WWTPs with disturbances is established with the model approximator and the disturbance observer. Then, the model approximator and the disturbance observer are applied to improve modeling accuracy of MIROC. Based on the prediction model of WWTPs, a MIROC structure is designed to comprehensively analyze the optimization process and control process of WWTPs with the unknown disturbances. Then, MIROC structure is composed of a CCF and a GMOA. Finally, the results on an industrial application of WWTPs demonstrate that MIROC can achieve optimal operation of WWTPs.

Model predictive control (MPC) has been successfully applied to multivariable nonlinear systems with operational constraints. However, the control performance of MPC is hindered by the different time scales of controlled variables. A two-time scale MPC (TTSMPC) strategy is developed to address the challenge caused by two-time scale characteristics, and ultimately improve the control accuracy. Two-time scale models based on fuzzy neural network (FNN), including slow-sampling FNN (S-FNN) with time scale conversion mechanism and fast-sampling FNN (F-FNN), are constructed to model the two-time scale nonlinear system. Then, the predicted outputs of all controlled variables are obtained at the fast time scale. On this basis, the multiobjective optimal control problem (MOCP) is also solved at the fast time scale to improve control accuracy. Besides, the corresponding convergence and stability conditions of TTSMPC are proved in theory. Finally, the experiment results on the benchmark example of wastewater treatment process (WWTP) illustrate that TTSMPC can achieve satisfactory operation performance at the fast time scale.Note to Practitioners—The motivation of this paper is to overcome the negative impact of two-time scales on MPC in terms of control accuracy. Considering the scenario of an unknown nonlinear system with two-time scales, a TTSMPC scheme is put forward to improve the control accuracy. The implementation of TTSMPC scheme includes four steps. First, establish an FNN-based fast sampling model to compute the predicted output of the fast-sampling controlled variable at the fast time scale. Second, construct a S-FNN with time scale conversion mechanism to calculate the predicted output of the slow-sampling controlled variable at the fast time scale. Third, solve the MOCP on the fast time scale to obtain the control input and apply it to the controlled system. Fourth, correct the parameters of S-FNN and F-FNN at the sampling instants of slow-sampling controlled variable and fast-sampling controlled variable, respectively. Finally, experiments on the benchmark platform of WWTP show the superiority of TTSMPC in terms of control accuracy.

Wastewater treatment process is a complex industrial process with disturbance and strong nonlinearity, and it is difficult to accurately track the pre-designed dissolved oxygen (DO) concentration in finite time. In this paper, a self-organizing fuzzy terminal sliding mode (SOFTSM) control strategy is proposed to solve this problem. First, a terminal sliding mode controller (TSMC) is designed to obtain a control law and achieve the finite time tracking of the pre-designed DO concentration. Second, a self-organizing fuzzy neural network (SOFNN) is utilized to estimate the nonlinear term. Then, the pruning strategy without pre-setting pruning threshold is designed to improve the approximation accuracy and further ensure the accuracy of control performance. Third, an adaptive law and robust control term are designed to reduce the influence of uncertainty and approximation error. Moreover, the stability of SOFTSM and the characteristic of finite time convergence are proved. Finally, the proposed method is tested on the benchmark simulation model no. 1 (BSM1). In contrast to other existing methods, SOFTSM can realize accurate control of DO concentration in finite time.Note to Practitioners—The nonlinear and strong disturbance characteristics of wastewater treatment process will reduce the control accuracy of dissolved oxygen (DO) concentration in infinite time. To realize the finite time precise control of DO concentration, a self-organizing fuzzy terminal sliding mode (SOFTSM) control strategy is designed in this paper. The strategy mainly includes three parts: First, a terminal sliding mode controller (TSMC) is designed to obtain the specific expression of control law and realize the finite time tracking of pre-designed DO concentration. Second, the self-organizing fuzzy neural network (SOFNN) without pre-setting pruning threshold is used to estimate the nonlinear term. The pruning strategy without pre-setting pruning threshold is designed to improve the approximation accuracy. Third, adaptive law and robust control term are designed to reduce the influence of uncertainty and approximation error. Finally, the effectiveness of SOFTSM is verified by industrial applications of wastewater treatment processes. The simulation results show that SOFTSM can achieve precise control of DO concentration in finite time.

The severe influence of external disturbances makes it difficult to keep the tracking error of the wastewater treatment process (WWTP) within a given range. Therefore, it is a challenging task to design the controller to realize robust bounded tracking control for WWTP. To solve this problem, a robust type-2 fuzzy neural control (RT2FNC) strategy is designed in this paper. The main contributions of the proposed RT2FNC strategy are threefold. First, an estimation model of interval type 2 fuzzy neural network (IT2FNN) with adaptive update strategy in RT2FNC is developed to identify the unknown dynamics of WWTP. Then, the high robustness of the IT2FNN estimation model is utilized to achieve accurate estimation of WWTP within external disturbances. Second, a type 2 fuzzy neural control algorithm based on nonlinear mapping (NM) method is proposed to consider the transformation of the aeration and denitrification processes into an unconstrained problem. Then, the tracking errors of dissolved oxygen and nitrate nitrogen can be guaranteed to be within the specified range. Third, the stability of the RT2FNC strategy is analyzed and demonstrated. Then, the successful application of the developed method is guaranteed. Finally, the simulation results tested on benchmark simulation model 1 (BSM1) verify the effectiveness of the proposed RT2FNC strategy with good robust bounded tracking performance within external disturbances.Note to Practitioners—The motivation of this paper is to overcome the influence of external disturbances of WWTP on the control accuracy. We propose a robust type-2 fuzzy neural control (RT2FNC) strategy to ensure that the tracking errors of dissolved oxygen (DO) and nitrate nitrogen (NO$_3$-N) of WWTP under external disturbances can be maintained within a certain range. In this paper, a critical analysis and discussion on the improvement of the control accuracy is provided and we present a successful implementation of the RT2FNC strategy on performance evaluation, which can be regarded as a significant attempt for engineering practice. Considering the complexity and uncertainty of the controlled objects in WWTP, the implementation of the RT2FNC method consists of three aspects: First, an adaptive type-2 fuzzy neural network identifier is established to achieve accurate estimation of WWTP dynamics. Then, a type-2 fuzzy neural control algorithm based on nonlinear mapping is proposed to ensure the boundedness of tracking control by using the transformation error. Third, a robust compensator is designed to overcome external disturbances and ensure the stability. Finally, the experiments on the WWTP benchmark platform verify that the RT2FNC strategy has high control accuracy and robustness under external disturbances, meanwhile helping practitioners improve the reliability of WWTP operation.

The high tracking control precision and fast finite-time convergence for nonlinear systems is a significant challenge due to complex nonlinearity and unknown disturbances. To address this challenge, a dynamic surface intelligent robust control strategy with fixed-time sliding-mode observer (DSIRC-SMO) is proposed to improve the tracking control performance in a finite time. First, adaptive fuzzy neural network based on a predictor (P-AFNN) is designed to imitate the complex nonlinearity. In particular, the weight adaptive law is formulated by utilizing the prediction error information, which improves the accuracy of approximating the nonlinear system. Second, the fixed-time sliding-mode observer (SMO) is integrated into the dynamic surface control technique to deal with unknown disturbances and modeling errors in a fixed time. This integration allows for timely updates the dynamic surface using observation information, thereby enhancing the system's anti-interference capability. Then, the fixed-time convergence of SMO is proven. Third, the proposed DSIRC-SMO can be effectively implemented and the finite-time convergence of DSIRC-SMO is proven in detail based on the fixed-time convergence of SMO. Finally, numerical simulation and actual wastewater treatment processes simulation are conducted to validate the effectiveness of DSIRC-SMO.

External disturbances and packet dropouts will lead to poor control performance for the wastewater treatment process (WWTP). To address this issue, a robust model-free adaptive predictive control (RMFAPC) strategy with a packet dropout compensation mechanism (PDCM) is proposed for WWTP. First, a dynamic linearization approach (DLA), relying only on perturbed process data, is employed to approximate the system dynamics. Second, a predictive control strategy is introduced to avoid a short-sighted control decision, and an extended state observer (ESO) is used to attenuate the disturbance effectively. Furthermore, a PDCM strategy is designed to handle the packet dropout problem, and the stability of RMFAPC is rigorously analyzed. Finally, the correctness and effectiveness of RMFAPC are verified through extensive simulations. The simulation results indicate that RMFAPC can significantly reduce IAE by 0.0223 and 0.1976 in two scenarios, regardless of whether the expected value remains constant or varies. This comparison to MFAPC demonstrates the superior robustness of RMFAPC against disturbances. The ablation experiment on PDCM further confirms its capability in handling the packet dropout problem.

Optimal control is developed to guarantee nonlinear systems run in an optimum operating state. However, since the operation demands of systems are dynamically changeable, it is difficult for optimal control to obtain reliable optimal solutions to achieve satisfying operation performance. To overcome this problem, a knowledge-data driven optimal control (KDDOC) for nonlinear systems is designed in this article. First, an adaptive initialization strategy, using the knowledge from historical operation information of nonlinear systems, is employed to dynamically preset parameters of KDDOC. Then, the initial performance of KDDOC can be enhanced for nonlinear systems. Second, a knowledge guide-based global best selection mechanism is used to assist KDDOC in searching for the optimal solutions under different operation demands. Then, dynamic optimal solutions of KDDOC can be obtained to adapt to flexible changes in nonlinear systems. Third, a knowledge direct-based exploitation mechanism is presented to accelerate the solving process of KDDOC. Then, the demand response speed of KDDOC can be improved to ensure nonlinear systems with optimal operation performance in different states. Finally, the performance of KDDOC is validated on a simulation and a practical process. Several experimental results illustrate the effectiveness of the proposed optimal control for nonlinear systems.

The wastewater treatment process (WWTP) is characterized by unknown nonlinearity and external disturbances, which complicates the tracking control of dissolved oxygen concentration (DOC) within operational constraints. To address this issue, a data-driven tube-based robust predictive control (DTRPC) strategy is proposed to achieve stable tracking control of DOC and satisfy the system constraints. First, a tube-based robust predictive control (TRPC) strategy is designed to deal with system constraints and external disturbances. Specifically, a nominal controller is designed to ensure that the nominal output accurately tracks the set-point under tightened constraints, while an auxiliary feedback controller is designed to suppress disturbances and restore the nominal performance of the disturbed WWTP. Second, two fuzzy neural network identifiers are employed to provide accurate predictive outputs for the control process, overcoming the challenges of modeling the WWTP with strong nonlinearity and unknown dynamics. Third, the generalized multiplier method is utilized to solve the constrained optimization problem to obtain the nominal control law, and the gradient descent algorithm is used to obtain the auxiliary control law. The implementation of this composite controller ensures the satisfaction of the system constraints and the effective suppression of disturbances. Finally, the feasibility and stability of the proposed DTRPC strategy are guaranteed through rigorous theoretical analysis, and its effectiveness is demonstrated through the simulations on the benchmark simulation model No.1.

With the escalating severity of environmental pollution caused by effluent, the wastewater treatment process (WWTP) has gained significant attention. The wastewater treatment efficiency and effluent quality are significantly impacted by effluent scheduling that adjusts the hydraulic retention time. However, the sequential batch and continuous nature of the effluent pose challenges, resulting in complex scheduling models with strong constraints that are difficult to tackle using existing scheduling methods. To optimize maximum completion time and effluent quality simultaneously, this article proposes a restructured set-based discrete particle swarm optimization (RS-DPSO) algorithm to address the WWTP effluent scheduling problem (WWTP-ESP). First, an effective encoding and decoding method is designed to effectively map solutions to feasible schedules using temporal and spatial information. Second, a restructured set-based discrete particle swarm algorithm is introduced to enhance the searching ability in discrete solution space via restructuring the solution set. Third, a constraint handling strategy based on violation degree ranking is designed to reduce the waste of computational resources. Fourth, a Sobel filter based local search is proposed to guide particle search direction to enhance search efficiency ability. The RS-DPSO provides a novel method for solving WWTP-ESP problems with complex discrete solution space. The comparative experiments indicate that the novel designs are effective and the proposed algorithm has superior performance over existing algorithms in solving the WWTP-ESP.

Multiobjective particle swarm optimization (MOPSO) has been proven effective in solving multiobjective problems (MOPs), in which the evolutionary parameters and leaders are selected randomly to develop the diversity. However, the randomness would cause the evolutionary process uncertainty, which deteriorates the optimization performance. To address this issue, a robust MOPSO with feedback compensation (RMOPSO-FC) is proposed. RMOPSO-FC provides a novel closed-loop optimization framework to reduce the negative influence of uncertainty. First, Gaussian process (GP) models are established by dynamically updated archives to obtain the posterior distribution of particles. Then, the feedback information of particle evolution can be collected. Second, an intergenerational binary metric is designed based on the feedback information to evaluate the evolutionary potential of particles. Then, the particles with negative evolutionary directions can be identified. Third, a compensation mechanism is presented to correct the negative evolution of particles by modifying the particle update paradigm. Then, the compensated particles can maintain the positive exploration toward the true PF. Finally, the comparative simulation results illustrate that the proposed RMOPSO-FC can provide superior search capability of PFs and algorithmic robustness over multiple runs.

Optimal control methods have gained significant attention due to their promising performance in nonlinear systems. In general, an optimal control method is regarded as an optimization process for solving the optimal control laws. However, for uncertain nonlinear systems with complex optimization objectives, the solving of optimal reference trajectories is difficult and significant that might be ignored to obtain robust performance. For this problem, a double-closed-loop robust optimal control (DCL-ROC) is proposed to maintain the optimal control reliability of uncertain nonlinear systems. First, a double-closed-loop scheme is established to divide the optimal control process into a closed-loop optimization process that solves optimal reference trajectories and a closed-loop control process that solves optimal control laws. Then, the ability of the optimal control method can be improved to solve complex uncertain optimization problems. Second, a closed-loop robust optimization (CL-RO) algorithm is developed to express uncertain optimization objectives as data-driven forms and adjust optimal reference trajectories in a close loop. Then, the optimality of reference trajectories can be improved under uncertainties. Third, the optimal reference trajectories are tracked by an adaptive controller to derive the optimal control laws without certain system dynamics. Then, the adaptivity and reliability of optimal control laws can be improved. The experimental results demonstrate that the proposed method can achieve better performance than other optimal control methods.

Ant colony optimization (ACO) algorithm is widely used in the instant delivery order scheduling because of its distributed computing capability. However, the order delivery efficiency decreases when different logistics statuses are faced. In order to improve the performance of ACO, an adaptive ACO algorithm based on real-time logistics features (AACO-RTLFs) is proposed. First, features are extracted from the event dimension, spatial dimension, and time dimension of the instant delivery to describe the real-time logistics status. Five key factors are further selected from the above three features to assist in problem modeling and ACO designing. Second, an adaptive instant delivery model is built considering the customer's acceptable delivery time. The acceptable time is calculated by emergency order mark and weather conditions in the event dimension feature. Third, an adaptive ACO algorithm is proposed to obtain the instant delivery order schedules. The parameters of the probability equation in ACO are adjusted according to the extracted key factors. Finally, the Gurobi solver in Python is used to perform numerical experiments on the classical datasets to verify the effectiveness of the instant delivery model. The proposed AACO-RTLF algorithm shows its advantages in instant delivery order scheduling when compared to the other state-of-the-art algorithms.

The problem of sampled-data$H_{\infty}$dynamic output-feedback control for networked control systems with successive packet losses (SPLs) and stochastic sampling is investigated in this article. The aim of using sampled-data control techniques is to alleviate network congestion. SPLs that occur in the sensor-to-controller (S-C) and controller-to-actuator (C-A) channels are modeled using a packet loss model. Additionally, it is assumed that stochastic sampling follows a Bernoulli distribution. A model is established to capture the stochastic characteristics of both the SPL model and stochastic sampling. This model is crucial as it allows us to determine the probability distribution of the sampling interval between successive update instants, which is essential for stability analysis. An exponential mean-square stability condition for the constructed equivalent discrete-time stochastic system, which also guarantees the prescribed$H_{\infty}$performance, is established by incorporating probability theory. The desired controller is designed using a step-by-step synthesis approach, which may offer lower design conservatism compared to some existing methods. Finally, our designed approach using a networked F-404 engine system model is validated and its merits relative to existing results are discussed. The proposed method is finally validated by employing a networked model of the F-404 engine system. Furthermore, the advantages of our method are presented in comparison to previous results.

In practical applications, sampled-data systems are often affected by unforeseen physical constraints that cause the sampling interval to deviate from the expected value and fluctuate according to a certain probability distribution. This probability distribution can be determined in advance through statistical analysis. Taking into account this stochastic sampling interval, this article focuses on addressing the leader-following sampled-data consensus problem for linear multiagent systems (MASs) with successive packet losses. First, the relationship of the equivalent sampling interval between two successive update instants is established, taking into account the double randomness introduced by both SPLs and stochastic sampling. Then, the equivalent discrete-time MAS is obtained, and the overall leader-following consensus problem is formulated as a stochastic stability problem of the equivalent system by incorporating the sampled-data consensus protocol and properties of the Laplacian matrix. Based on the equivalent the discrete-time system, a consensus criterion is derived under a directed graph by using the Lyapunov theory and leveraging a vectorization technique. By the introduction of a matrix reconstruction approach, the mathematical expectation of a product of three matrices, including the system matrix and its transpose, can be determined. Then, the consensus protocol gain is designed. Finally, an example is provided to validate our theoretical results.

Evolutionary multitasking optimization (EMTO) has capability of performing a population of individuals together by sharing their intrinsic knowledge. However, the existed methods of EMTO mainly focus on improving its convergence using parallelism knowledge belonging to different tasks. This fact may lead to the problem of local optimization in EMTO due to unexploited knowledge on behalf of the diversity. To address this problem, in this article, a diversified knowledge transfer strategy is proposed for multitasking particle swarm optimization algorithm (DKT-MTPSO). First, according to the state of population evolution, an adaptive task selection mechanism is introduced to manage the source tasks that contribute to the target tasks. Second, a diversified knowledge reasoning strategy is designed to capture the knowledge of convergence, as well as the knowledge associated with diversity. Third, a diversified knowledge transfer method is developed to expand the region of generated solutions guided by acquired knowledge with different transfer patterns so that the search space of tasks can be explored comprehensively, which is favor of EMTO alleviating local optimization. Finally, the performance of the proposed algorithm is evaluated in comparison with some other state-of-the-art EMTO algorithms on multiobjective multitasking benchmark test suits, and the practicality of the algorithm is verified in a real-world application study. The results of experiments demonstrate the superiority of DKT-MTPSO compared to other algorithms.

The main goal of multitask optimization (MTO) is the parallel optimization of multiple different tasks. However, since different tasks in the MTO problem usually have heterogeneous characteristics, it is difficult to realize the positive knowledge transfer among tasks, resulting in poor convergence. To cope with this problem, a multi-task particle swarm optimization with a heterogeneous domain adaptation strategy (MTPSO-HDA) is proposed to transfer positive knowledge among heterogeneous tasks. First, a nonlinear mapping between the source task and the target task is constructed based on the adaptive kernel function. Then, source tasks are mapped to the target task space to reduce the differences among heterogeneous tasks. Second, a multi-source domain adaptive strategy based on fitness landscape similarity is designed to implement domain adaptation. Then, the importance of each source domain is quantitatively described to reduce the differences between multiple source domains and a target domain and achieve domain adaptation among heterogeneous tasks. Third, a heterogeneous multitask particle swarm optimization mechanism is introduced to facilitate positive knowledge transfer among heterogeneous tasks. Then, an appropriate evolutionary mechanism is designed according to the fitness landscape similarity to achieve positive knowledge transfer. Finally, to assess the effectiveness of the MTPSO-HDA algorithm, some experiments are designed based on some benchmark problems and real-world application of wastewater treatment process. The results demonstrate that the proposed MTPSO-HDA algorithm can promote positive knowledge transfer among heterogeneous tasks to improve convergence.

In practical applications, sampled-data systems are often affected by unforeseen physical constraints that may cause deviations in the sampling interval from the expected value and result in fluctuations in a probabilistic way, where the probability distribution of stochastic sampling intervals is often time-varying and unknown. How to design a stable tracking controller for sampled-data control systems affected by unknown stochastic sampling probability is a challenging task. A stochastic sampled-data model predictive control (SSDMPC) strategy for T-S fuzzy systems (TSFSs) is proposed to overcome this challenge. First, based on the input delay approach, the considered system is modeled as a continuous-time TSFS with stochastic input delay. Then, the stochastic nature of the sampling interval is effectively mapped to the input delay within the TSFS. Second, considering the unknown characteristic of the sampling interval, a Q-learning-based online estimation algorithm is developed to acquire the sampling probability, and an event-triggered mechanism is designed to reduce the computational burden of the estimation algorithm. Furthermore, the mapped stochastic input delay probability can be obtained. Third, to achieve stable tracking control of the abovementioned continuous-time TSFS with stochastic input delay, a predictive controller is designed to obtain the control law. Finally, the stability of SSDMPC is analyzed theoretically to ensure its reliability. Additionally, the effectiveness of SSDMPC is confirmed through numerical simulations.

The complex dynamics and strong nonlinearity characteristics will bring obstacle for the accurate and stable tracking control performance of unknown nonlinear systems. To solve this problem, a predictor-based self-organizing control (PSOC) method is designed to improve the control performance in this article. The merits of PSOC are three aspects. First, a self-organizing fuzzy neural network (SOFNN) is designed to adaptively approximate the strong nonlinearity of the system. Then, the self-organizing strategy, based on rule similarity and validity, is studied to adjust the number of fuzzy rules in SOFNN to improve the approximate accuracy. Second, a dynamic surface control scheme is designed to describe the system dynamics. Then, the dynamic surface control law is obtained to achieve the stable control. Third, a state predictor is developed to predict the state variable accurately. Then, the prediction error is utilized to design the adaptive law of PSOC to reduce the variation range of tracking control errors and further improve the control accuracy. Finally, the numerical simulations and a detailed comparison study are given to evaluate the efficiency of the proposed PSOC method.

For the uncertain nonlinear systems, the disturbance caused by external factors can affect the accuracy of tracking control. To solve this issue, a hierarchical self-organizing fuzzy control (HSOFC) strategy is proposed to improve the tracking control performance. First, the self-organizing fuzzy neural network is employed as a fuzzy approximator to estimate the unknown nonlinear function. Specifically, a hierarchical strategy is designed to improve the estimation accuracy by preventing the wrong pruning of rules, without setting the pruning threshold based on rule density and significance. Second, an additional robust control component based on sliding mode surface is designed to suppress the influence on the control performance by external disturbances and the approximation error. Furthermore, to further improve the robust control performance and reduce computational complexity, an adaptive allocation strategy is studied to set the parameters of HSOFC. Finally, the stability of HSOFC is proven. The simulation results show that HSOFC can reduce computational complexity and obtain accurate tracking control performance.

The model bias caused by input outliers is a dramatic obstacle to the application of models in industrial processes. To cope with this problem, this article proposes a robust modeling method based on frequency reconstructed fuzzy neural network (FRFNN) for industrial process. The robust modeling consists of two parts: One is feature extraction, where a Fourier-based filter is developed with input data denoising. It enables the model to suppress high-frequency input noises and burst outliers. The other one is feature representation that is realized with a FRFNN. The soft margins of membership functions of FRFNN are designed with Fourier estimation of outliers, which have the capability of outlier-tolerant for filtered-residual outliers. Moreover, an adaptive gradient descent algorithm is introduced to update the model parameters. Based on the adaptive learning rate decaying with outliers, this algorithm is insensitive to the bias effect of outliers and also maintains convergence. Finally, the proposed robust modeling method is tested on two real-world industrial datasets with input outliers. The experimental results demonstrate that the proposed robust modeling method can strengthen robustness and achieve superior performance over other previous methods.

Fuzzy neural network (FNN) is regarded as a prominent approach in application of time-series modeling. With the capability of fuzzy reasoning, FNN can capture temporal patterns from the time-series samples. However, the existing FNNs may suffer from the temporal pattern distortion because possibly multiscale features cannot be explored sufficiently. To address this problem, a time-aware fuzzy neural network, based on the frequency-enhanced modulation mechanism (FEM-TAFNN), is developed for time-series prediction in this article. First, a Fourier-based decoder is established to extract the multiscale features. This decoder employs the frequency-domain model to orthogonally separate the time-scale features with different frequencies into independent temporal patterns based on the Fourier basis, which prevents the overlap of temporal patterns using time-domain analysis. Second, a frequency-enhanced modulation mechanism is designed to shape fuzzy rules of FNN based on the contribution of different temporal patterns in the frequency spectrum. It enables FEM-TAFNN to modulate out the realistic multiscale temporal patterns. Finally, the proposed FEM-TAFNN is tested on four multiscale time-series datasets. The empirical results confirm its superior prediction performance than other methods.

The control of the wastewater treatment processes (WWTPs) is considered as an adaptive robust control problem due to the presence of high nonlinearity and disturbances. In this article, an adaptive robust fuzzy sliding mode control (ARFSMC) strategy for WWTPs is proposed to guarantee the operational performance. First, considering the high nonlinearity of the WWTPs, a fuzzy neural network (FNN) is employed to identify the system dynamics. And the identification results are directly used for controller design. To address the effect of disturbances on identification accuracy, a sliding mode observer has been designed, where the observation error is utilized to adjust the adaptive law of the FNN identifier. Second, a variable parameters disturbance observer is devised to accurately estimate time-varying disturbances in the WWTPs. The observer is used to build a dynamic model by estimating the state, thereby obtaining disturbance as an additional state. And the parameters within the observer are dynamically adjusted using a state estimation error-based parameter adjustment law. Third, an adaptive switching gain sliding mode controller, combined with the disturbance observer, is designed to improve the stability of the system. Specifically, the switching gain is determined by subtracting the disturbance observer output from the estimated disturbance upper bound. Finally, the experimental results on the BSM1 demonstrate that ARFSMC has superior control performance compared to existing methods.

The key focus in this paper is to develop an adaptive fuzzy function constraint control method for nonlinear systems with actuator and sensor faults. The effectiveness indicators of actuator and sensor are considered as the unknown functions with the bounded time-varying bias fault existing in actuator. Because system states are not applied to design controller, how to achieve constraints on the system states is a significant challenge. In order to cope with this challenge, the constraint target transformation is introduced to convert the constraints on real states to measurement variables. Then, the nonlinear statedependence mapping is used to ensure tracking error and system states remain within the given function constrain ranges. In contrast to the existing time-dependence constraint methods, this paper consider that the constraint boundaries are related not only time but also state variables, which extends the application fields for practical systems. Moreover, the deferred transformation function is employed to remove the restrictive condition that the initial values of system states must be within the constraint regions. Finally, the effectiveness of the developed method is confirmed by two simulation examples including the numerical example and wastewater treatment process (WWTP).

Neural network control has been developed into an efficient strategy to guarantee the safe and steady operation of wastewater treatment process (WWTP). However, due to the complex mechanism and serious damage of sludge bulking in WWTP, it is significant for neural network control to achieve the timely self-helaing of operation. Therefore, the goal of this article is to devise a knowledge-guided adaptive neuro-fuzzy self-healing control (KG-ANFSHC) for sludge bulking. The originality of KG-ANFSHC is threefold. First, a knowledge evaluation strategy is introduced to consider the correlation and differentiation between the normal operation condition and sludge bulking to obtain available information. Then, the proposed strategy can provide a guide for control to take remedial actions. Second, a KG-ANFSHC based on a knowledge transfer mechanism, which makes full use of knowledge and data to dynamically adjust its parameters, is designed to eliminate the sludge bulking. Then, KG-ANFSHC can timely and precisely regulate manipulated variables to realize the self-healing of operation. Third, the Lyapunov stability theorem is employed to ensure the stability of KG-ANFSHC. Then, the proof of stability can assist its effective application. Finally, the proposed control is applied to Benchmark Simulation Model No. 2 to verify its advantages. Several results demonstrate that KG-ANFSHC can own satisfying self-healing performance to guarantee the operation recovered from sludge bulking.

The aim of this article is to address the modeling and control problems of discrete-time Takagi–Sugeno (T-S) fuzzy systems that are affected by stochastic packet dropouts. To describe the stochastic behavior of packet dropout between the sensor–controller and controller–actuator, a consecutive packet dropout model is employed. By treating consecutive packet dropouts (CPDs) as an extension of the transmission interval, the considered T-S system is transformed into a stochastic system with bounded stochastic input delay. In addition, a novel equivalent model for the closed-loop system is proposed, which captures the nonuniform distribution of the input delay caused by CPDs. Using the obtained equivalent model, it is possible to evaluate the probability distribution of each stochastic input delay value using the formula for total probability. This approach allows us to fully consider the probability information of CPDs in subsequent stability analysis and controller design. Based on this model, delay-probability dependent stability conditions are derived using stochastic Lyapunov functionals, and controller design conditions are also provided. Finally, the correctness and conservatism reduction of the proposed design method are demonstrated using numerical examples of two physical systems described by T-S fuzzy models.

This article is concerned with the stabilization problem of nonlinear networked control systems (NCSs) subject to successive packet losses (SPLs), probabilistic sampling (PS), and input dynamic quantization. Specifically, the Takagi–Sugeno (T–S) fuzzy system is used to approximate the nonlinear plant, and the model of SPLs is used to describe packet losses occurring in the sensor-to-controller and controller-to-actuator channels, while PS is represented by a Bernoulli distribution. First, by considering the double randomness of both the SPL model and PS, a unified model is proposed to evaluate the probability of the sampling interval between two successive update times. Second, by introducing probability knowledge and using the exact-time discrete approach, the stochastic stability condition is established for the constructed equivalent discrete-time T–S fuzzy system in the presence of input dynamic quantization. Third, based on the established stability condition, the fuzzy controller is designed. Finally, the networked mass-spring mechanical system is given to show the validity of the proposed approach, and the merits of the proposed design approach are discussed in comparison to existing results.

Sample property drift is an essential issue for interval type-2 fuzzy neural networks (IT2FNNs). When the samples with fresh properties appear, IT2FNN invariably suffers from catastrophic forgetting due to the modification of its numerous parameters. To solve this problem, an antiforgetting incremental learning algorithm is proposed to update IT2FNN. First, a double-displacement indicator (DDI) is designed to detect when catastrophic forgetting occurs caused by property drift. It integrates the indicators from the feature and target spaces to avoid missing detection of property breakpoints. Second, a multilevel learning objective is developed to perceive catastrophic forgetting. The convergence, diversity, and stability criteria of fuzzy rules are embedded into the objective to improve the compatibility of IT2FNN for different properties. Third, an adaptive hierarchical update strategy (AHUS) is proposed to update the parameters of IT2FNN. With AHUS, the parameters are shared among samples with different properties, which can alleviate catastrophic forgetting. Finally, some experiments have verified that the performance of the presented method is superior to other methods in dynamic system identification.

Interval type-2 fuzzy neural network (IT2FNN) has extensive applications for modeling nonlinear systems with multidimensional structured data. However, the traditional IT2FNN based on the structured topology struggles to identify nonlinear systems using semistructured and unstructured data. To tackle this issue, a multimodal learning-based IT2FNN (ML-IT2FNN) is developed for joint learning of the multimodal data. First, an encoding layer with a multimodal perception strategy is designed to identify the multimodal information. The parameterized modalities are utilized to map the features of the semistructured and unstructured data into the structured spaces. Second, a multimodal representation mechanism is introduced to extract the features of multiple modalities from the structured spaces. In this mechanism, type-2 fuzzy sets with soft boundaries are used to intricate coupling relationships among modalities by adapting to the nuances of multimodal data. Third, a constrained hybrid learning algorithm, combining parallel and sequential updating frameworks, is presented to optimize the parameters of ML-IT2FNN. The type-2 fuzzy parameters and the coupling parameters with constraints are updated adaptively to facilitate the intramodal identification performance and cross-modal interaction performance. Finally, a series of examples in nonlinear systems are introduced to verify ML-IT2FNN. Empirical results demonstrate that ML-IT2FNN surpasses the cutting-edge approaches with accuracy.

Water quality prediction is an indispensable task in water environment and source management. The existing predictive models are mainly designed by data-driven artificial neural networks (ANNs), especially deep learning models for large-scale water quality prediction. However, the state of water environment is a dynamic process where the stationarity of water quality data suffers from time variation and human activities, which leads to a poor prediction accuracy because ANNs receive whole water quality data passively, including abnormal conditions. We consider such a tough problem in this article and propose an event-triggered deep fuzzy neural network (ET-DFNN) to pursue the better performance of water quality prediction in the complex water environment. First, a deep pretraining model is constructed to extract the effective features from raw water quality data. Second, we construct a DFNN model where the extracted effective features are considered as the input variables. Third, some events are defined to characterize the abnormal conditions of state evolution in water quality. The DFNN is trained and updated using different learning strategies only when the corresponding events are triggered, otherwise it ignores the current data sample and directly goes to the next data sample. The practical data-based experimental results show that the ET-DFNN achieves better prediction performance in accuracy and efficiency than its peers. Especially, the training efficiency of ET-DFNN is improved by 57.94% on total phosphorus prediction and 48.31% on biochemical oxygen demand prediction, respectively.

Set-point optimization of wastewater treatment process (WWTP) is critical for energy savings but is challenging due to complex nonlinear mechanisms and measurement noises. To address this optimization problem, a mechanism-data-driven multiobjective optimization method is developed to alleviate deficiencies in mechanisms and process data. First, a mechanism-data-driven model is established to describe the relationships between effluent quality, energy consumption, and key process variables. Then, the mechanisms and process data can be collaboratively leveraged to alleviate the inaccuracy of mechanism models and suppress measurement noises. Second, a weighted indicator-based multiobjective particle swarm optimization algorithm is proposed to suppress uncertainties introduced by measurement noises. Then, the set-points with noise robustness are obtained to improve optimization performance under real restricted conditions. Third, the proposed method is applied to the benchmark simulation model No. 1 to evaluate its capability. The results demonstrate that this method can improve the optimization performance of WWTP.

In wastewater treatment process (WWTP), abnormal data seriously reduce data quality rendering the application techniques impractical. The implementation of abnormal data detection is challenging due to the nonlinear nature of WWTP. Typically, constructing an accurate anomaly detector requires large amounts of labeled data, which is difficult in practice. Thus, a self-supervised memory enhanced deep clustering method (SMEL) is proposed to detect abnormal data without using any labels. First, a self-supervised deep clustering network, combining stacked autoencoders and the clustering algorithm, leverages unlabeled data to extract nonlinear features and capture the normal pattern. Second, an adaptive weight objective function, jointly optimizing the reconstruct error and clustering error, is designed to obtain a robust clustering structure. Third, double memory enhanced modules, consisting of a centroid memory and a score memory, are presented to enhance training stability and detection accuracy. Finally, experiments on three WWTP datasets show that SMEL achieves the highest detection accuracy.

The increasing complexity and scale of the wastewater treatment process (WWTP) demand more and more safety and stability. However, due to the unavoidable existence of external disturbance, sludge bulking is commonly encountered, which can result in risks for the efficient and stable operation of WWTP. To address this problem, a knowledge-data-driven robust fault-tolerant control (KDD-RFTC) is proposed in this article. First, a robustness evaluation strategy (RES) is constructed to extract the response and fluctuation characteristics of KDD-RFTC. Then, the antijamming ability of KDD-RFTC can be obtained in the presence of sludge bulking. Second, an adaptive knowledge transfer strategy (AKTS), based on RFTC, is designed to suppress the sludge bulking with the knowledge from the results of RES and the process data. Then, the proposed KDD-RFTC can readjust the manipulated variable to ensure a safe and stable operation. Third, the stability proof of KDD-RFTC is verified by the Lyapunov theory. Then, the successful application of KDD-RFTC can be guaranteed. Finally, KDD-RFTC is employed in the benchmark simulation model no. 1 (BSM1) to verify its merits. The experimental results illustrate that the proposed KDD-RFTC method can obtain excellent control performance and inhibit sludge bulking.

Wastewater treatment process (WWTP) is one of the most means to achieve the water resource protection and sustainable utilization. Dissolved oxygen and nitrate are main factors limiting effluent quality, which are involved with carbon consumption, nitrification and denitrification. To achieve efficacious control of dissolved oxygen and nitrate concentrations under actuator faults and saturation, a nonlinear mapping-based adaptive neural fault-tolerant control method is developed in this article for WWTP. The coordinate transformation is employed to boil down the constrained denitrification and aeration processes to unconstrained issues. To obtain the appointed steady-state tracking performance, nonlinear mapping is incorporated into the adaptive fault-tolerant controller, because of many categories of physical, chemical, and biological phenomena existing in associated and treatment zones, radial basis function neural networks are used to approximate the uncertain dynamics in WWTPs. The proposed control scheme is verified via the benchmark simulation model 1.

Missing values frequently appearing in the wastewater treatment process are automatically replaced by zero to ensure the implementation of downstream applications. These meaningless zero values bias data distribution and decrease data quality. However, the existing imputation methods treat all values equally without considering the existence of meaningless zero values, affecting the performances of imputation and downstream models. Thus, an attention-guided position-sensitive multiple imputation (APMI) method is proposed. First, a position-sensitive localization attention module selectively focuses on the most informative values, enhancing the ability for observed data utilization. Second, a masked attention multiple imputation module focuses on the observed values and fuses multiple candidate estimations as the final result to improve imputation performance. Third, a joint optimization objective function is designed to ensure the consistency of localization and imputation tasks. The extensive experimental results show that the proposed APMI outperforms existing method imputation performance under different missing rates.

The optimization control of nonlinear systems is crucial to improve system performance. However, uncertain disturbances of cost functions and system states make it difficult to solve optimal set points and realize stability control. For this problem, a disturbance-estimation-based robust optimization control (DERO-C) scheme is designed. First, a data-driven disturbance distribution evaluation strategy is proposed to detect the deviations in cost functions caused by disturbances. Then, the deviations are employed to approximate the distribution of uncertain disturbances. Second, an adaptive robust evolutionary algorithm is designed to solve the optimization problem. Then, the adaptive robustness indexes, derived from the disturbance distribution, are designed to guide the evolutionary process to improve the robustness of optimal set points. Third, a sliding mode controller with an adaptive reaching law is employed to track the optimal set points Finally, the optimal control performances of DERO-C are tested in the wastewater treatment process.

Fuzzy neural networks (FNNs) hold the advantages of knowledge leveraging and adaptive learning, which have been widely used in nonlinear system modeling. However, it is difficult for FNNs to obtain the appropriate structure in the situation of insufficient data, which limits its generalization performance. To solve this problem, a data-knowledge-driven self-organizing FNN (DK-SOFNN) with a structure compensation strategy and a parameter reinforcement mechanism is proposed in this article. First, a structure compensation strategy is proposed to mine structural information from empirical knowledge to learn the structure of DK-SOFNN. Then, a complete model structure can be acquired by sufficient structural information. Second, a parameter reinforcement mechanism is developed to determine the parameter evolution direction of DK-SOFNN that is most suitable for the current model structure. Then, a robust model can be obtained by the interaction between parameters and dynamic structure. Finally, the proposed DK-SOFNN is theoretically analyzed on the fixed structure case and dynamic structure case. Then, the convergence conditions can be obtained to guide practical applications. The merits of DK-SOFNN are demonstrated by some benchmark problems and industrial applications.

Interval type-2 fuzzy neural network (IT2FNN) is widely used to model nonlinear systems. Unfortunately, the gradient descent-based IT2FNN with uncertain variances always suffers from low convergence speed due to its inherent singularity. To cope with this problem, a nonsingular gradient descent algorithm (NSGDA) is developed to update IT2FNN in this article. First, the widths of type-2 fuzzy rules are transformed into root inverse variances (RIVs) that always satisfy the sufficient condition of differentiability. Second, the singular RIVs are reformulated by the nonsingular Shapley-based matrices associated with type-2 fuzzy rules. It averts the convergence stagnation caused by zero derivatives of singular RIVs, thereby sustaining the gradient convergence. Third, an integrated-form update strategy (IUS) is designed to obtain the derivatives of parameters, including RIVs, centers, weight coefficients, deviations, and proportionality coefficient of IT2FNN. These parameters are packed into multiple subvariable matrices, which are capable to accelerate gradient convergence using parallel calculation instead of sequence iteration. Finally, the experiments showcase that the proposed NSGDA-based IT2FNN can improve the convergence speed through the improved learning algorithm.

Various constraints commonly exist in most physical systems; however, traditional constraint control methods consider the constraint boundaries only relying on constant or time variable, which greatly restricts applying constraint control to practical systems. To avoid such conservatism, this study develops a new adaptive neural controller for the nonlinear strict-feedback systems subject to state-dependent constraint boundaries. The nonlinear state-dependent mapping is employed in each step of backstepping procedure, and the prescribed transient performance on tracking error and the constraints on system states are ensured without repeatedly verifying the feasibility conditions on virtual controllers. The radial basis function neural network (NN) with less parameters approach is introduced as an identifier to estimate the unknown system dynamics and reduce computation burden. For removing the effect of unknown control direction, the Nussbaum gain technique is integrated into controller design. Based on the Lyapunov analysis, the developed control strategy can ensure that all the closed-loop signals are bounded, and the constraints on full system states and tracking error are achieved. The simulation examples are used to illustrate the effectiveness of the developed control strategy.

Wastewater treatment process (WWTP), consisting of a class of physical, chemical, and biological phenomena, is an important means to reduce environmental pollution and improve recycling efficiency of water resources. Considering characteristics of the complexities, uncertainties, nonlinearities, and multitime delays in WWTPs, an adaptive neural controller is presented to achieve the satisfying control performance for WWTPs. With the advantages of radial basis function neural networks (RBF NNs), the unknown dynamics in WWTPs are identified. Based on the mechanistic analysis, the time-varying delayed models of the denitrification and aeration processes are established. Based on the established delayed models, the Lyapunov-Krasovskii functional (LKF) is used to compensate for the time-varying delays caused by the push-flow and recycle flow phenomenon. The barrier Lyapunov function (BLF) is used to ensure that the dissolved oxygen (DO) and nitrate concentrations are always kept within the specified ranges though the time-varying delays and disturbances exist. Using Lyapunov theorem, the stability of the closed-loop system is proven. Finally, the proposed control method is carried out on the benchmark simulation model 1 (BSM1) to verify the effectiveness and practicability.

The study of aperiodic sampling has witnessed enormous interest due to the ubiquitous presence of digital controllers in relevant application domains. Most existing aperiodic sampled-data control methods assume that the model of the system is known or obtainable, though it is unknown and unavailable in reality. The idealized assumption will limit the application of these methods. To address this problem, a data-driven model predictive control (DMPC) strategy is designed to stabilize the aperiodic sampled-data unknown nonlinear systems (ASUNSs). The main contributions of the proposed DMPC are threefold. First, a linearized polytopic approximation dynamic (LPAD), based on the local linear approximation, is constructed to approximate the dynamics of ASUNSs. Then, the aperiodic sampling information of ASUNS is able to be contained. Second, a data-driven model predictive controller is designed to solve the optimal steady-state problem and the optimal control problem (OCP) successively. Then, the desired output reference can be tracked online. Third, the stability of DMPC is analyzed in theory. Then, the corresponding stability conditions are given to ensure its successful applications. Finally, some experimental studies have been performed on the online control of a general unknown nonlinear system (GUNS) with aperiodic sampling and wastewater treatment process (WWTP) with aperiodic sampling to verify its effectiveness.

Sampled-data systems (SDSs) have received extensive attention due to their wide application in industrial processes. However, for SDSs characterized by complex nonlinear dynamics, it is still a great challenge to achieve stable tracking control when they are affected by stochastic sampling. To deal with this situation, a data-based adaptive model predictive control (DAMPC) method is developed to stabilize the stochastic sampled-data complex nonlinear systems (SSDCNSs). First, an equivalent system with stochastic time-varying delay is constructed to describe SSDCNS. Then, the sampling interval variation of SSDCNS is equivalently converted into the stochastic time-varying delay, whose transfer probability can be gained by the activation frequencies of stochastic sampling intervals. Second, a fuzzy neural network (FNN)-based multistep predictive model with an adaptive prediction horizon (APH) is established. Then, APH is adaptively adjusted according to the stochastic time-varying delay and its transfer probability, and the necessary predictive information can be provided for the controller. Third, an optimal control problem (OCP) is solved to stabilize the SSDCNS. Especially, an attenuation learning rate (ALR) is designed for the controller to reduce excessive control increments. Then, the control action can be calculated to realize stable tracking control. Finally, the stability of the proposed scheme is analyzed in theory, and the effectiveness of the designed method is assessed by a numerical simulation system and an industrial application in the wastewater treatment process (WWTP).

For the data-driven multimodal multiobjective optimization problems (MMOPs), the inevitable uncertainties will lead to distortion of multiple peak landscapes, thus causing slow convergence in complex landscapes. To solve this problem, a robust multimodal multiobjective particle swarm optimization (RMMPSO) is designed to alleviate slow convergence. There are three novelties in RMMPSO. First, a perturbation observer is proposed to detect perturbation in the fixed point of variance to evaluate the influences of disturbed recording position on convergence. Second, an adaptive adjustment mechanism, based on the perturbation observer, is designed to obtain reasonable search ranges and suppress the abnormal changes in convergence, so as to improve convergence performance. Third, a Lipschitz-based exploitation strategy is designed to search for reliable solutions, which reduces the optimal offset caused by uncertainties. Finally, the effectiveness of RMMPSO is demonstrated in terms of multiobjective multimodal benchmark problems with uncertain components and wastewater treatment simulation platform. The results of experiments demonstrate the superiority of RMMPSO in solving data-driven MMOPs compared to state-of-the-art multimodal multiobjective algorithms.

Multiobjective optimal control (MOC) optimize multiple performance indices of nonlinear systems to obtain setpoints, and design the controller to track the setpoints. However, if the feasibility of the controller is not considered, untraceable setpoints may be obtained. Furthermore, the performance of data-driven MOC may be degraded due to insufficient data. To address this problem, a data-knowledge-driven multiobjective integrated optimal control (DK-MIOC) method is proposed in this article. First, an integrated optimal control (IOC) framework is designed that integrates a cost function for both system performance and tracking error. Then, the feasibility of the controller can be considered simultaneously while solving for the optimal setpoints. Second, a data-knowledge-driven model is incorporated into this framework to predict future dynamics. Then, the performance indices can be accurately predicted even with insufficient data. Third, a collaborative optimization algorithm is implemented to determine setpoints and control laws. Consequently, the operational control performance of the nonlinear system is enhanced. Furthermore, the stability of the DK-MIOC strategy is also analyzed. Finally, DK-MIOC is tested on a conventional nonlinear system and a wastewater treatment process (WWTP) to validate its effectiveness.

For a category of nonlinear systems subject to time-varying constraints on tracking error and full states and unknown control directions, this article develops an adaptive neural control strategy using nonlinear mapping and double-layer constraint structure. Radial basis function neural network is applied to identify the unknown system dynamics. The dynamic surface control with less learning parameters is employed to eliminate “explosion of complexity” and reduce online computation burden. The Nussbaum gain technique is employed to deal with the unknown control direction. The nonlinear mapping is applied to ensure the satisfaction of the multiple constraints on state variables and remove feasibility conditions on virtual control signals. Double-layer constraint boundaries are incorporated into controller design process, the inside boundaries are utilized to cope with the multiple state constraints, and the outside boundaries are used into controller and adaptive law design. Hence, the singularity problem caused by the system state approaching the bound boundary is completely solved. The numerical example is used to deduce the availability of developed control approach.

This paper is concerned with the asynchronous control problem of multi-rate sampled-data nonlinear systems. To solve this problem, the data-driven multi-model predictive control (DMMPC) strategy is proposed. First, a multi-model predictive control structure is designed such that each state variable of the multi-rate sampled-data nonlinear system can be controlled synchronously at all sampling instants. In this structure, the fuzzy neural network (FNN) is introduced to build the multi-model. Then, the prediction outputs of each state variable at all sampling instants are obtained to provide control information for the controller. Specially, the objective function with adaptive weight matrix (AWM) is designed to reduce the influence of the prediction error caused by nonlinear fitting on control performance. Then, the optimal control laws are calculated to improve the control precision. Finally, the convergence and stability of DMMPC are proved in detail. The numerical example and industrial application reveal that the proposed DMMPC can obtain considerable control performance for the multi-rate sampled-data nonlinear systems.Note to Practitioners—The asynchronous control problem of the multi-rate sampled-data nonlinear system (MRSNS) may degrade the operation performance of closed-loop system. In this paper, a data-driven multi-model predictive control (DMMPC) strategy is designed for MRSNS without mechanism model. The strategy mainly consists of three parts: First, a multi-model prediction structure based on fuzzy neural network (FNN) is established to obtain the prediction output of all variables at each sampling point. The parameters of FNNs are corrected at each sampling point to ensure prediction accuracy. Second, an objective function with an adaptive weight matrix (AWM) is designed to compute the control law, in which AWM is used to reduce the influence of prediction error on control performance. Third, the effectiveness of DMMPC is verified by a numerical example and an industrial application of the wastewater treatment process. The experimental results show that DMMPC can achieve satisfied operation performance in control accuracy.

Wastewater treatment process (WWTP) is operated with multiple conditions. Accurately identify these conditions and satisfy the different requirements are the keys to guarantee the optimal operation of WWTP. To solve this problem, a dynamic optimal control (DOC) strategy is designed in this paper. First, with the aid of the predicting models by adaptive fuzzy neural network for effluent nitrate and total nitrogen, different operating conditions can be identified. Corresponding to each condition, changing number of operating objectives are formulated to match the different requirements. Second, due to the changeable operating objectives can cause the expanded/contracted dimension of Pareto-optimal set, a dynamic multi-objective particle swarm optimization algorithm is developed. In this algorithm, self-adjusting mechanism of population size and global optimal solution are designed to derive the optimal solutions of control variables. Third, fuzzy controllers, matched with the different conditions, are designed to trace these optimal solutions. Finally, the effectiveness of DOC strategy is tested on a real WWTP. The results demonstrate that this proposed DOC strategy enables to achieve promising operating performance.Note to Practitioners—This article aims to develop an optimal control strategy to match the multiple conditions and improve the operating performance. To achieve this goal, a dynamic optimal control (DOC) strategy, with the consideration of different operating conditions, is designed. Two key points are contained, the identification of multiple operating conditions and the satisfaction of different requirements. Due to each condition confronts with different requirements, it is important to accurately identify the conditions and construct the corresponding operating objectives. Based on the obtained operating data, changeable operating objectives are established to describe the different conditions. In addition, to satisfy the operating requirements, it is necessary to optimize the changeable objectives, but the changes in the number of objectives can cause the expanded/ contracted of Pareto-optimal set. A dynamic multi-objective particle swarm optimization algorithm, with self-adjusting mechanism of population size and global optimal solution, is designed to deal with this kind of optimization problem. The effectiveness and applicability of the proposed DOC strategy are evaluated on a pilot platform of a real WWTP, showing the improvement on the operating performance. These advantages can be valuable for transplanting this strategy to other real wastewater treatment plants to realize the optimal operation.

The multiobjective optimal control method optimizes the performance indexes of nonlinear systems to obtain setpoints, and designs a controller to track the setpoints. However, the stepwise optimal control method that independently analyzes the optimization process may obtain unfeasible and difficult to track setpoints, which will reduce the operation and control performance of the systems. To solve this problem, a multiobjective integrated optimal control (MIOC) strategy is proposed for nonlinear systems in this article. The main contributions of MIOC are threefold. First, in the framework of multiobjective model predictive control, an integrated control structure with a comprehensive cost function and a collaborative optimization algorithm is designed to achieve the coordinate optimal control. Second, for the time inconformity of setpoints and control laws caused by the characteristic of tracking control, the different prediction horizons are designed for the comprehensive cost function. Then, the collaborative optimization algorithm is proposed for the comprehensive cost function to achieve the integrated solution of setpoints and control laws to enhance the operation and control performance of nonlinear systems. Third, the stability and control performance analysis of MIOC is provided. Finally, the proposed MIOC method is applied for a nonlinear system to demonstrate its effectiveness.

Multiobjective differential evolution (DE) algorithm (MODE) has been widely used in multiobjective optimization problems. However, due to the complex feasible regions, the optimization efficiency of MODE may decrease when solving constrained multiobjective problems. It is challenging to promote the evolution of population with few feasible solutions. In this article, a multistate-constrained MODE with variable neighborhood strategy (MSCMODE-VNS) is proposed to enhance the optimization effectiveness with complex feasible regions. First, a variable neighborhood DE strategy, based on a specially designed convergence indicator, is designed to accelerate the generation of feasible solutions. Second, a multistate population updating strategy with a comprehensive solution evaluation mechanism is devised to update the population of the next generation to improve the performance of solutions. Third, the convergence analysis, based on the probability theory, is derived to verify the effectiveness of the proposed MSCMODE-VNS algorithm. Finally, experimental results indicate that MSCMODE-VNS can achieve a satisfactory performance on three benchmark test suites and two real-world-constrained multiobjective problems.

In this article, the consensus problem of multiagent systems (MASs) affected by input and communication delays is investigated. A predictor-based state feedback protocol is used to reach the consensus of linear MASs by delay compensation. In order to analyze the maximum delay under the predictor-based protocol, the overall MASs are equivalent to the feedback interconnection system, including a linear time-invariant system and a time-delay operator, in view of the characteristic of the Laplacian matrix. Then, the maximum delay corresponding to the predictor-based protocol is evaluated by using the small gain theorem (SGT). Finally, two numerical examples are given to verify the effectiveness of the obtained consensus condition.

Multitask optimization aims to solve multiple optimization problems in parallel utilizing a single population. However, if the computing resources are limited, allocating the same computing resources to different tasks will cause resource waste and make complex tasks difficult to converge to the optimal solution. To address this issue, a multitask particle swarm optimization with a dynamic on-demand allocation strategy (MTPSO-DA) is proposed to dynamically allocate computing resources. First, a task complexity index, based on convergence rate and contribution rate, is designed to evaluate the difficulty of solving different tasks. Then, the complexity of different tasks can be evaluated in real time. Second, the skill factor of the particle is extended to a time-varying matrix according to the task complexity index. Then, the recently captured feedback is stored to determine the computational resource demands of the task. Third, an on-demand allocation strategy, based on the time-varying matrix, is developed to obtain the skill factor probability vector utilizing the attenuation accumulation method. Then, computing resources can be allocated dynamically among different tasks. Finally, some comparative experiments are conducted based on the benchmark problem to evaluate the superiority of the MTPSO-DA algorithm. The results indicate that the proposed MTPSO-DA algorithm can achieve dynamic resource allocation.

Order scheduling is an important part of the e-waste recycling process, which can influence the quantity and efficiency of the recycling. With the sustainable development of e-waste recycling, low-carbon order scheduling becomes a significant and challenging reverse logistics scheduling problem. However, it is difficult to obtain an effective low-carbon order schedule considering the conflicting interests of the multiple stakeholders, including enterprises, drivers, customers, and governments. To address this issue, a multiobjective order scheduling model (MOOSM) and a multiobjective differential evolution algorithm balancing multiple stakeholders (MODE-MS) are proposed in this article. First, to embody the interests of different stakeholders, three time-dependent key variables are calculated by the road congestion and vehicle load, including the velocity, traveling time, and carbon emission. Second, with the above key variables, a five-objective order scheduling model is formulated to describe the low-carbon order scheduling problem in e-waste recycling. Third, for solving the MOOSM, a multiobjective differential evolution algorithm based on an adaptive evolutionary search strategy is developed to obtain the low-carbon and stakeholders satisfied scheduling schemes. The experimental results validate the feasibility of MOOSM and the effectiveness of MODE-MS. By comparing with four state-of-the-art algorithms, the advantages of the proposed MODE-MS are further demonstrated in solving the low-carbon order scheduling.

Covariate shift is a critical issue of interval type-2 fuzzy neural networks (IT2FNNs) due to the distribution discrepancy between training and testing samples. In this situation, IT2FNNs usually struggle to identify potential features from samples with explicit inductive biases. To address this problem, a self-organizing IT2FNN with an adaptive discriminative strategy (ADS-SOIT2FNN) is developed to maintain the identification performance in the presence of covariate shift. First, a granularity-based metric (GM), using higher order statistics of local samples, is designed to distinguish the distribution discrepancy caused by covariate shift. The multiple kernels incorporated into GM are able to cover the sample features of the whole Hilbert space. Second, a self-organizing strategy, associated with GM-based discriminative information, is presented to alleviate the structural bias by growing and pruning fuzzy rules. Then, a compact structure of ADS-SOIT2FNN is achieved to adapt to the covariate shift of samples and further strengthen its inductive ability. Third, an adaptive risk mitigation learning algorithm (RMLA) is introduced to update the parameters of ADS-SOIT2FNN. RMLA can regulate the derivatives of parameters with arbitrary distribution samples, which is beneficial for maintaining the global accuracy by relieving the risk of parameter biases. Finally, the effectiveness of ADS-SOIT2FNN is verified by some experiments for identifying nonlinear systems with covariate shift.

Due to the existence of strong nonlinearity and external disturbances, the controller design of complex nonlinear systems is a challenging problem. Therefore, it is necessary to design an effective robust predictive controller for this issue. In this article, based on a fuzzy neural network, an iterative learning model predictive control (FNN-ILMPC) is designed for complex nonlinear systems. First, a dynamic linearization technique is used to establish a data-driven model, which only relies on input and output data. Since the established model contains an unknown disturbance term that may have an impact on the control performance, an FNN is used to evaluate the disturbance so that the uncertainty of the system is captured. Subsequently, based on the above data-driven model, an FNN-ILMPC strategy, considering the impact of external disturbances, is developed to eliminate the influence of disturbances. Then, it is proved that the designed controller can make both modeling error and tracking error decrease gradually and ensure the closed-loop system stability. Finally, the experimental results verify the effectiveness and superiority of the designed controller.

Decision making is essential to utilize the operation information of wastewater treatment process (WWTP) to provide the inhibition strategy for sludge bulking. However, since majority of decision-making models focus solely on knowledge or data resources, avoiding the interrelations and dependencies between the operation information, these models are difficult to obtain comprehensive and precise solutions. Thus, to solve this problem, a knowledge-aided and data-driven fuzzy decision-making (KD-FDM) model is designed for sludge bulking. First, a recursive reconstruction contribution (RRC) method is proposed to analyze the operation data to diagnose the fault of sludge bulking. Then, the fault information can be recorded as valid knowledge to assist in decision making. Second, a knowledge internalization mechanism is developed to make use of the knowledge from the results of RRC and the expert experience of sludge bulking to construct the initial condition of KD-FDM model. Then, the KD-FDM model can obtain the precision parameters and compact structure in the initialization phase. Third, the KD-FDM model using a knowledge-aided fuzzy broad learning system is employed to determine suppression strategies for sludge bulking. Then, the KD-FDM model can obtain fast and accurate strategies to mitigate the detrimental impact on the process performance. Finally, the KD-FDM model is tested in a real WWTP to confirm its effectiveness. The experimental results demonstrate that the proposed model can achieve outstanding performance.

This article investigates the security control problem of sampled-data Takagi–Sugeno (T–S) fuzzy systems subject to cyberattacks and successive packet losses. The cyberattack considered in this article is a stochastic deception attack. The packet losses under consideration occur in the sensor-to-controller and controller-to-actor channels, both of which are modeled as two independent Bernoulli processes. On this basis, a novel successive packet loss modeling method is proposed with some basic assumptions. By the exact discrete-time model approach, a discretized sampled-data T–S fuzzy model is first established by considering the probability characteristic of the deception attacks and successive packet losses in a unified framework. Based on the established mode, the sufficient conditions to guarantee the security degree are derived by the Lyapunov function approach. Furthermore, the fuzzy security controller is designed in view of linear matrix inequalities. Finally, a benchmark example is given to show the validity of the proposed approach.

The phenomenon of sludge bulking, which can be classified as slight or serious abnormal operating conditions according to sludge volume index (SVI), is a widespread problem in wastewater treatment process. In this article, a piecewise sliding-mode control (PSMC) strategy is developed to overcome the adverse effects and furthermore improve the operating performance for wastewater treatment process under different operating conditions of sludge bulking. First, a soft sensing model of SVI based on fuzzy neural network is established. Then, it can online determine the state of sludge and whether sludge bulking has occurred. Second, in view of the specific operating condition of sludge, a piecewise sliding-mode controller is designed. Then, the sludge bulking can be eliminated by regulating the concentration of dissolved oxygen and nitrate nitrogen. Third, the boundary condition of PSMC is evaluated. Then, the stability of the control system is proved on the basis of ensuring the boundary condition of PSMC. Finally, the performance of PSMC is verified in the benchmark simulation platform. The results further demonstrate the effectiveness of the proposed control method.

To achieve the excellent operational performance of the wastewater treatment process, optimal control has been considered a reliable method. However, there is a time-delay response of the operation performances to the process variables, leading to uncertainties of operational optimal objectives. It is difficult to obtain the optimal set-points due to the uncertain operational optimal objectives. Therefore, a kernel-density-estimation-based robust optimal control (KDE-ROC) method is proposed. First, a data-driven prediction strategy is developed to construct the uncertain operational optimal objectives. Based on the time-delay intervals, the uncertainties between process variables and operational optimal objectives are expressed. Second, a kernel-density-estimation-based robust optimization algorithm is designed to solve the uncertain operational optimal objectives. Then, the optimal set-points of process variables are obtained depending on the robustness index to reduce the influence of uncertainties. Third, an adaptive neural network controller is developed to track the optimal set-points of process variables. Finally, the proposed KDE-ROC is applied in benchmark simulation model No.1. In the experimental results, the optimal control performance of KDE-ROC is compared with some effective optimal control strategies to demonstrate its effectiveness.

Self-healing control plays a crucial role in taking remedial action to minimize the adverse impacts of sludge bulking in wastewater treatment process (WWTP). However, since sludge bulking is a strong nonlinear and complex process with multiple fault conditions, the conventional self-healing control is difficult to obtain reliable performance. Thus, the purpose of this article is to design a broad learning-based self-healing predictive controller (BL-SHPC) for sludge bulking in WWTP. The main innovations of the proposed controller are threefold. First, a dynamic fuzzy broad learning system with an adaptive expansion strategy is used to identify the fault conditions of sludge bulking. Then, the fault features of sludge bulking can be comprehensively extracted with desirable performance. Second, a prioritized multiobjective optimization algorithm-based predictive control, which considers the objective correlation and preference of fault conditions, is presented to obtain the optimal solutions to achieve self-healing. Then, the proposed controller can feasibly and precisely readjust manipulated variables to eliminate the sludge bulking. Third, the stability of the developed controller is proved by the Lyapunov stability theorem. Then, the stability analysis can ensure the successful application of BL-SHPC. Finally, the proposed BL-SHPC is tested on the Benchmark Simulation Model No.2 to validate its merits. The simulation results indicate that the proposed controller can obtain superior self-healing ability for sludge bulking in WWTP.

For prognostics and health management of industrial systems, machine remaining useful life (RUL) prediction is an essential task. While deep learning-based methods have achieved great successes in RUL prediction tasks, large-scale neural networks are still difficult to deploy on edge devices owing to the constraints of memory capacity and computing power. In this article, we propose a lightweight and adaptive knowledge distillation (KD) framework to alleviate this problem. First, multiple teacher models are compressed into a student model through KD to improve the industrial prediction accuracy. Second, a dynamic exiting method is studied to enable an adaptive inference on the distilled student model. Finally, we develop a reparameterization scheme to further lessen the student network. Experiments on two turbofan engine degradation datasets and a bearing degradation dataset demonstrate that our method significantly outperforms the state-of-the-art KD methods and enables the distilled model with an adaptive inference ability.

Anomaly monitoring of key performance indicators (KPIs) is the core to guarantee the stable operation of wastewater treatment process (WWTP). One issue that has not been considered in WWTP is that KPIs can only be sporadically sampled, which is not conductive to the real-time monitoring. To solve this problem, a trend feature-based anomaly monitoring method is proposed. First, a fused multistep prediction strategy is designed to establish the nonlinear relationship between infrequent KPIs and the variables, with adaptive algorithm updating the parameters. Second, an autoregressive model is used to represent the variation trends, and a convex optimization problem, with the balance of small residuals and stable trends, is solved to extract trend features of KPIs. Third, the monitoring index, based on the$\ell _{2}$-norm of the trend features, is utilized to identify the abnormal KPIs. The operating data from WWTP are applied to demonstrate the effectiveness of the proposed monitoring method.

Missing data imputation is a critical data processing procedure in wastewater treatment process. However, the existing imputation methods cannot stand the missing data with high proportions that frequently happens due to unmaintained instruments or detection failures. Transfer Learning aims to learn much reliable information for the target domain with previous learned knowledge from a source domain, which provides a framework for solving such problem. This paper proposes a filter transfer learning algorithm (FTLA) for missing data imputation with high proportions. First, a knowledge acquisition strategy is developed to extract the source knowledge, including independent knowledge from historical datasets and parallel knowledge in terms of related datasets. The missing data is then interpreted through source knowledge comprehensively. Second, a filter transfer learning algorithm is designed to achieve target knowledge that mimics the tendency of the missing data. This algorithm can avoid serious negative transfer by using the extended Kalman filter to filtrate source knowledge. Third, a knowledge rolling mechanism is established to perform the imputation online with target knowledge, which can maintain the reliable imputation for missing data with high proportions. Finally, several comparative experiments of wastewater data are provided to demonstrate the merits of missing data imputation with FTLA.

One of the major challenges of transfer learning algorithms is the domain drifting problem where the knowledge of source scene is inappropriate for the task of target scene. To solve this problem, a transfer learning algorithm with knowledge division level (KDTL) is proposed to subdivide knowledge of source scene and leverage them with different drifting degrees. The main properties of KDTL are three folds. First, a comparative evaluation mechanism is developed to detect and subdivide the knowledge into three kinds-the ineffective knowledge, the usable knowledge, and the efficient knowledge. Then, the ineffective and usable knowledge can be found to avoid the negative transfer problem. Second, an integrated framework is designed to prune the ineffective knowledge in the elastic layer, reconstruct the usable knowledge in the refined layer, and learn the efficient knowledge in the leveraged layer. Then, the efficient knowledge can be acquired to improve the learning performance. Third, the theoretical analysis of the proposed KDTL is analyzed in different phases. Then, the convergence property, error bound, and computational complexity of KDTL are provided for the successful applications. Finally, the proposed KDTL is tested by several benchmark problems and some real problems. The experimental results demonstrate that this proposed KDTL can achieve significant improvement over some state-of-the-art algorithms.

Interval type-2 fuzzy neural networks (IT2FNNs) usually stack adequate fuzzy rules to identify nonlinear systems with high-dimensional inputs, which may result in an explosion of fuzzy rules. To cope with this problem, a self-organizing IT2FNN, based on the information aggregation method (IA-SOIT2FNN), is developed to avoid the explosion of fuzzy rules in this article. First, a relation-aware strategy is proposed to construct rotatable type-2 fuzzy rules (RT2FRs). This strategy uses the individual RT2FR, instead of multiple standard fuzzy rules, to interpret interactive features of high-dimensional inputs. Second, a comprehensive information evaluation mechanism, associated with the interval information and rotation information of RT2FR, is developed to direct the structural adjustment of IA-SOIT2FNN. This mechanism can achieve a compact structure of IA-SOIT2FNN by growing and pruning RT2FRs. Third, a multicriteria-based optimization algorithm is designed to optimize the parameters of IA-SOIT2FNN. The algorithm can simultaneously update the rotatable parameters and the conventional parameters of RT2FR, and further maintain the accuracy of IA-SOIT2FNN. Finally, the experiments showcase that the proposed IA-SOIT2FNN can compete with the state-of-the-art approaches in terms of identification performance.

In this article, an adaptive neural learning method is introduced for a category of nonlinear strict-feedback systems with time-varying full-state constraints. The two challenging problems of state constraints and learning capability are investigated and solved in a unified framework. To obtain the learning of unknown functions and satisfy full-state constraints, three main steps are considered. First, an adaptive dynamic surface controller (DSC) based on barrier Lyapunov functions (BLFs) is structured to implement that the closed-loop systems signals are bounded and full-state variables remain within the prescribed time-varying intervals. Moreover, the radial basis function neural networks (RBF NNs) are used to identify unknown functions. The output of the first-order filter, instead of virtual control derivatives, is used to simplify the complexity of the RBF NN input variables. Second, the state transformation is used to obtain a class of linear time-varying subsystems with small perturbations such that the recurrence of the RBF NN input variables and the partial persistent excitation condition are actualized. Therefore, the unknown functions can be accurately approximated, and the learned knowledge is kept as constant NN weights. Third, the obtained constant weights are borrowed into an adaptive learning scheme to achieve the batter control performance. Finally, simulation studies illustrate the advantage of the reported adaptive learning method on higher tracking accuracy, faster convergence rate, and lower computational expense by reusing learned knowledge.

Stochastic sampling is ubiquitous for the complex nonlinear systems, which may destroy the stability of the closed-loop system. Concerned with the sampled-data stabilization problem for the nonlinear systems with complex dynamics and stochastic sampling, a data-driven model-predictive control (DDMPC) strategy is proposed to control the system at each sampling instant. The main merits of DDMPC are threefold. First, a data-driven method based on the fuzzy neural network (FNN) is used to establish the mathematical model for the complex nonlinear system. Especially, considering the stochastic sampling characteristics of the system, a multimodel structure is constructed to predict the future system outputs at possible sampling instants. Second, the objective function is designed to deal with the stochastic sampling control problem. The reasonable control laws are computed to stabilize the nonlinear system with stochastic sampling. Finally, the stability of DDMPC is proved in theory, and the numerical simulation results and industrial application for the wastewater treatment process (WWTP) reveal that the proposed DDMPC can achieve a satisfactory control performance for the stochastic sampling nonlinear system (SSNS).

The broad learning system (BLS) has been identified as an important research topic in machine learning. However, the typical BLS suffers from poor robustness for uncertainties because of its characteristic of the deterministic representation. To overcome this problem, a type-2 fuzzy BLS (FBLS) is designed and analyzed in this article. First, a group of interval type-2 fuzzy neurons was used to replace the feature neurons of BLS. Then, the representation of BLS can be improved to obtain good robustness. Second, a fuzzy pseudoinverse learning algorithm was designed to adjust the parameter of type-2 FBLS. Then, the proposed type-2 FBLS was able to maintain the fast computational nature of BLS. Third, a theoretical analysis on the convergence of type-2 FBLS was given to show the computational efficiency. Finally, some benchmark and practical problems were used to test the merits of type-2 FBLS. The experimental results indicated that the proposed type-2 FBLS can achieve outstanding performance.

For nonlinear full-state-constrained systems with unmeasured states, an adaptive output feedback control strategy is developed. The main challenge of this article is how to avoid that the unmeasured states exceed the constrained spaces. To achieve a good tracking performance for the considered systems, a stable state observer is structured to estimate unmeasured states which are not available in the control design. In addition, the constraints existing in most practical engineering are the source of reducing control performance and causing the system instability. The main limitation of current barrier Lyapunov functions is the feasibility conditions for intermediate controllers. The nonlinear mappings are used to achieve the satisfaction of full-state constraints directly and avoid feasibility conditions for intermediate controllers. By the Lyapunov theorem, the closed-loop system stability is proven. Simulation results are given to confirm the validity of the developed strategy.

Particle swarm optimization algorithm has become a promising approach in solving multitask optimization (MTO) problems since it can transfer knowledge with easy implementation and high searching efficiency. However, in the process of knowledge transfer, negative transfer is common because it is difficult to evaluate whether knowledge is effective for population evolution. Therefore, how to obtain and transfer the effective knowledge to curb the negative transfer is a challenging problem in MTO. To deal with this problem, a self-adjusting multitask particle swarm optimization (SA-MTPSO) algorithm is designed to improve the convergence performance in this article. First, a knowledge estimation metric, combining the decision space knowledge and the target space knowledge for each task, is designed to describe the effectiveness of knowledge. Then, the effective knowledge is obtained to promote the knowledge transfer process. Second, a self-adjusting knowledge transfer mechanism, based on the effective knowledge and the self-adjusting transfer method, is developed to achieve effective knowledge transfer. Then, the ineffective knowledge is removed to solve the negative transfer problem. Third, the convergence analysis is given to guarantee the effectiveness of the SA-MTPSO algorithm theoretically. Finally, the proposed algorithm is compared with some existing MTO algorithms. The results show that the performance of the proposed algorithm is superior to most algorithms on negative transfer suppression and convergence.

This article is dedicated to studying realization issues of the stability performance-based nonlinear fault-tolerant control framework via Takagi–Sugeno (T–S)fuzzy models. To this end, the nonlinear fault-tolerant control strategy with an online fault detection system monitoring the system stability performance degradation induced by faults is first introduced by means of the stable image and kernel representations. On this basis, the T–S fuzzy models are applied to approximate the nonlinear system, and a design approach of the fuzzy observer-based controller is proposed for the system stabilization via the iterative linear matrix inequality method. With the controller gains, the fuzzy-model-based nominal stable image representation of the system is formulated, which leads to the generation of the input and output error signals. Then, with the reference signal and system input and output error signal data, a data-driven algorithm is given to online estimate the evaluation function defined in terms of system uncertainties and faults. By virtue of the$L_{2}$input–output stability of the controller stable kernel representation, a threshold calculation method is presented and, thus, the stability performance-based fault detection system based on fuzzy models is realized. Furthermore, for fault-tolerant purpose, the fault-tolerant controller design is discussed, which aims to retain the system stability. Two examples are provided in the end to illustrate the proposed results.

Transfer learning algorithm can provide a framework to utilize the previous knowledge to train fuzzy neural network (FNN). However, the performance of TL-based FNN will be destroyed by the knowledge over-fitting problem in the learning process. To solve this problem, an interactive transfer learning (ITL) algorithm, which can alleviate the negative transfer among different domains to improve the learning performance of FNN, is designed and analyzed in this article. This ITL-assisted FNN (ITL-FNN) contains the following advantages. First, a knowledge filter algorithm is developed to reconstruct the knowledge in source scene by balancing the matching accuracy and diversity. Then, the knowledge from source scene can fit the instance of target scene with suitable accuracy. Second, a self-balancing mechanism is designed to balance the driven information between the source and target scenes. Then, the knowledge can be refitted to reduce the useless information. Third, a structural competition algorithm is proposed to adjust the knowledge of FNN. Then, the proposed ITL-FNN can achieve compact structure to improve the generalization performance. Finally, some benchmark problems and industrial applications are provided to demonstrate the merits of ITL-FNN.

Owing to the possible existence of system failures and packet dropouts in the wastewater treatment process (WWTP), it is difficult to obtain sufficient data, which will result in data shortage. Therefore, it is a challenge to design an effective data-driven controller with the above data shortage issue for WWTP. To solve this problem, a syncretic fuzzy-neural controller (SFNC) was developed and analyzed in this article. First, the knowledge obtained from the operation conditions was made full use by a knowledge reconstruction mechanism to construct the initial condition of SFNC. Then, the proposed SFNC was able to obtain the accurate parameters and compact structure in the initialization phase. Second, a syncretic-form strategy (SFS) was designed to syncretize the knowledge from the fuzzy rules and the data from the operation process to optimize the structure of SFNC. Then, the adaptability of SFNC can be improved to achieve good control performance in the presence of insufficient data. Third, the stability of the developed SFNC was proved by using Lyapunov stability theorem. Then, the stability of SFNC was given to guarantee its successful application. Finally, the proposed controller was tested on the Benchmark Simulation Model No.1 to confirm its effectiveness. The results demonstrated that the proposed SFNC can achieve superior control performance than some other existing controllers.

The design of a fuzzy neural network (FNN) has long been a challenging problem since most methods rely on approximation error to train an FNN, which may easily result in overfitting phenomenon to degrade the generalization performance. To improve the generalization performance, an FNN with a multiobjective optimization algorithm (MOO-FNN) is proposed in this article. First, the multilevel learning objectives are designed around the generalization performance to guide the training process of an FNN. Then, the method utilizes the approximation error, the structure complexity, and the output smoothness indicators instead of a single indicator to improve the evaluation accuracy of generalization performance. Second, an MOO algorithm with continuous–discrete variables is developed to optimize the FNN. Then, MOO is able to use a novel particle update method to adjust both the structure and parameters rather than adjusting them separately, thereby achieving suitable generalization performance of the FNN. Third, the convergence of MOO-FNN is analyzed in detail to guarantee its successful applications. Finally, the experimental studies of MOO-FNN have been performed on model identification of nonlinear systems to verify the effectiveness. The results illustrate that MOO-FNN has a significant improvement over some state-of-the-art algorithms.

Driven by the rapid development of modern industrial processes, cyber-physical systems (CPSs), which tightly conjoin computational and physical resources, have become ever-more prevalent during recent years. However, due to the intrinsical vulnerability of the cyber layer, the system performances of CPSs are easily degraded by malicious false data injection (FDI) attacks, which are launched by adversary. In this article, the issue of secure reconstruction is considered for linear CPSs with simultaneous sparse actuator and sensor attacks. First, an adaptive counteraction searching strategy is proposed to identify the potential combinational attack mode. In this way, malicious FDI attacks are excluded. Second, by constructing a descriptor switched sliding mode observer, the sparse FDI attacks and the system state are reconstructed effectively. Meanwhile, sufficient conditions of the error convergence can be derived. Finally, a numerical simulation is utilized to illustrate the applicability of the proposed theoretical derivation.

To achieve excellent treatment performance of complex and time-varying characteristics, the operation of wastewater treatment process (WWTP) has been considered as a dynamic multiobjective control problem. In this paper, an optimal controller, based on a dynamic multiobjective particle swarm optimization (DMOPSO) algorithm, is developed to deal with the dynamic multiple conflicting criteria [i.e., effluent quality (EQ), operation cost, and operation stability]. The novelties and advantages of this proposed DMOPSO-based optimal controller (DMOPSO-OC) include the following two aspects. First, an integrated optimization framework, where the multiple objectives not only conflict with each other but also change over time, is able to catch more characteristics of WWTP than the existing works. Second, a DMOPSO algorithm, with an adaptive global best selection mechanism, is designed to solve the multiobjective optimization problem (MOP) for the proposed optimal controller, thus leading to a significant improvement of optimal synthesis for performance. Finally, the proposed DMOPSO-OC is tested in the benchmark simulation model No. 1 (BSM1) and implemented in a real WWTP to evaluate its effectiveness. The experimental results demonstrate that this proposed DMOPSO-OC can achieve a significant improvement in optimal control performance and obey the requirement of multiple conflicting criteria.

With the increasing complexity and scale of activated sludge process (ASP), it is quite challenging to coordinate the performance indices with different time scales. To address this problem, a cooperative optimal controller (COC) is proposed to improve the operation performance in this paper. First, a cooperative optimal scheme is developed for designing the control system, where the different time-scale performance indices are formulated by two levels. Second, a data-driven surrogate-assisted optimization (DDSAO) algorithm is provided to optimize the cooperative objectives, where a surrogate model is established for evaluating the feasibility of optimal solutions based on the minimum squared error. Third, an adaptive predictive control strategy is investigated to derive the control laws for improving the tracking control performance. Finally, the proposed COC is tested on benchmark simulation model No. 1 (BSM1). The results demonstrate that the proposed COC is able to coordinate the multiple time-scale performance indices and achieve the competitive optimal control performance.

Wastewater treatment process, including multiple biochemical reactions, is a complex industrial process with strong nonlinearity and time-varying dynamics. It is a challenge to design an effective controller for this kind of process. To solve this problem, a cooperative fuzzy-neural controller is proposed to improve the operation performance of wastewater treatment process in this article. The main advantages of cooperative fuzzy-neural controller contain the following three parts: first, a structure cooperative strategy is developed to adjust the number of fuzzy rules in the controller by coordinating the indexes of similarity and independent contributions. Then, the structure of cooperative fuzzy-neural controller with the balanced redundant degree and efficiency can be adapted to satisfy the different operation conditions of wastewater treatment process. Second, a parameter cooperative strategy is proposed to coordinate the global and local parameters of controller. Then, the parameters can be optimized together to meet the control requirements. Third, the stability of control strategy is given in details. Then, the corresponding stability conditions are shown to guide its application. Finally, the control performance is confirmed on the benchmark simulation model and real wastewater treatment process. The results demonstrate that the proposed cooperative fuzzy-neural controller can achieve superior control precision and low computational burden.

Membrane fouling has become a serious issue in membrane bioreactor (MBR) and may destroy the operation of the wastewater treatment process (WWTP). The goal of this article is to design a data-driven intelligent warning method for warning the future events of membrane fouling in MBR. The main novelties of the proposed method are threefold. First, a soft-computing model, based on the recurrent fuzzy neural network (RFNN), was proposed to identify the real-time values of membrane permeability. Second, a multistep prediction strategy was designed to predict the multiple outputs of membrane permeability accurately by decreasing the error accumulation over the predictive horizon. Third, a warning detection algorithm, using the state comprehensive evaluation (SCE) method, was developed to evaluate the pollution levels of MBR. Finally, the proposed method was inserted into a warning system to complete the predicting and warning missions and further tested in the real plants to evaluate its efficiency and effectiveness. Experimental results have verified the benefits of the proposed method.

Model predictive control (MPC) has been considered as a promising alternative for the control of nonlinear systems. However, this controller suffers from a challenge that it is difficult to deal with the complex nonlinear systems with incomplete datasets. To solve this problem, a novel MPC, by utilizing knowledge-data-driven model (KDDM), is designed and analyzed in this article. In comparison with the existing literatures, this knowledge-data-driven MPC (KDD-MPC) contains these following contributions. First, a systematic strategy is developed to reduce the online computational burden of KDD-MPC. Therefore, this KDD-MPC can own fast action to achieve favorable control performance. Second, the proposed KDDM intends to not only make full use of limited state information from the current model but also effectively leverage the knowledge from the reference model in the learning process. Therefore, it is more efficient for the complex nonlinear systems with insufficient data. Third, a novel transfer learning mechanism is designed to determine the optimal control sequence of KDD-MPC with strong adaptability. Therefore, it is suitable to achieve the desired control performance for engineering implementations. Finally, the benchmark problem and industrial application are provided to demonstrate the attractiveness and effectiveness of KDD-MPC.

Optimal control system has been considered as a valuable technique to enhance the reliability and security of wastewater treatment process (WWTP). However, due to the complex environments, it is difficult to realize the optimal control with changeable operational conditions in WWTP. To overcome this problem, an intelligent optimal control system with flexible objective functions (IOCS-FOF) was proposed in this paper. The main merits of this proposed IOCS-FOF were shown as follows. First, an optimal control system scheme was developed, where different time-scale operational objectives were detailed to describe the operational features. Second, a flexible objective strategy was designed to determine suitable objective functions, which could adapt to complex environments of WWTP. Third, a novel dynamic multiobjective optimization algorithm for flexible objectives (FO-DMOA) was developed to obtain the optimal solutions of IOCS-FOF. Finally, the proposed IOCS-FOF was applied in the benchmark simulation model No. 1 (BSM1) to confirm its technique capability. The results demonstrate that this proposed method can improve the operation performance of WWTP.

Many nonlinear dynamical systems are usually lack of abundant datasets since the data acquiring process is time consuming. It is difficult to utilize the incomplete datasets to build an effective data-driven model to improve the industry productivity. To overcome this problem, a data-knowledge-based fuzzy neural network (DK-FNN) was developed in this article. Compared with the existing methods, the proposed DK-FNN consists of the following obvious advantages. First, through the multilayered connectionist structure, this proposed DK-FNN could not only make full use of the data from the current scene, but also use the existing knowledge from the source scene to improve the learning performance. Second, an integrated-form transfer learning (ITL) method was developed to improve the learning performance of DK-FNN. This first reported ITL method was able to integrate the internal information from the datasets in the source scene and the knowledge from the current scene to offset the data shortage in the learning process. Third, a mutual attraction strategy (MAS) was designed to balance the difference of data distributions to reduce the identification errors of DK-FNN. Then, the proposed DK-FNN was able to satisfy the nonlinear dynamical systems. Finally, the effectiveness and the merit of DK-FNN were validated by applying it to several practical systems.

To comply with the effluent standards and growing demands for safety and reliability, the operation of wastewater treatment processes (WWTPs) has been considered as a multiobjective control problem. In this article, a data-driven multiobjective predictive control (MOPC) method is developed to deal with the conflicting control objectives to improve the operation performance of WWTPs. The main contributions of MOPC are three folds: first, a multiobjective control strategy is developed in the design of MOPC. And an adaptive fuzzy neural network identifier, using the relevant process data, is designed to catch the nonlinear behaviors of WWTPs. Second, a transfer multiobjective optimization algorithm (TMOOA) is developed to obtain the optimal solutions of the conflicting control objectives. The major advantage of TMOOA is its low computational cost, which is realized by avoiding the computation of Pareto fronts. Third, the stability of MOPC has been given in detail. Meanwhile, the benefits and feasibility of MOPC are confirmed on the benchmark simulation model no. 2. The results further demonstrate the effectiveness of the proposed control method.

In this paper, a novel robust sliding mode control with adaptive reaching law (RSMC-ARL) is developed for a class of second-order nonlinear systems. First, a novel adaptive reaching law (ARL), utilizing a time-varying sliding surface, is designed to achieve fast convergence as well as maintain high accuracy for RSMC-ARL. Second, an adaptive tuning approach is developed to adjust the control law without frequency switching and avoid undesired chattering phenomenon. Then, the global robustness can be obtained against the uncertainties and external disturbances for nonlinear systems. Third, by constructing the Lyapunov function, the reachability and stability of RSMC-ARL can be guaranteed. Finally, three different second-order nonlinear systems are used to test the effectiveness of RSMC-ARL. The results have demonstrated that the proposed method can achieve fast convergence and high accuracy in comparison with some existing methods.

One of the major obstacles in using radial basis function (RBF) neural networks is the convergence toward local minima instead of the global minima. For this reason, an adaptive gradient multiobjective particle swarm optimization (AGMOPSO) algorithm is designed to optimize both the structure and parameters of RBF neural networks in this paper. First, the AGMOPSO algorithm, based on a multiobjective gradient method and a self-adaptive flight parameters mechanism, is developed to improve the computation performance. Second, the AGMOPSO-based self-organizing RBF neural network (AGMOPSO-SORBF) can optimize the parameters (centers, widths, and weights), as well as determine the network size. The goal of AGMOPSO-SORBF is to find a tradeoff between the accuracy and the complexity of RBF neural networks. Third, the convergence analysis of AGMOPSO-SORBF is detailed to ensure the prerequisite of any successful applications. Finally, the merits of our proposed approach are verified on multiple numerical examples. The results indicate that the proposed AGMOPSO-SORBF achieves much better generalization capability and compact network structure than some other existing methods.

Intelligent computing technologies are useful and important for online data modeling, where system dynamics may be nonstationary with some uncertainties. In this paper, an efficient learning mechanism is developed for building self-organizing fuzzy neural networks (SOFNNs), where a second-order algorithm (SOA) with adaptive learning rate is employed, the network size and the parameters can be determined simultaneously in the learning process. First, all parameters of SOFNN are adjusted by using the SOA strategy to achieve fast convergence through a powerful search scheme. Second, the structure of SOFNN can be self-organized using the relative importance index of each rule. The fuzzy rules used in SOFNN with SOA (SOA-SOFNN) are generated or pruned automatically to reduce the computational complexity and potentially improve the generalization power. Finally, a theoretical analysis on the learning convergence of the proposed SOA-SOFNN is given to show the computational efficiency. To demonstrate the merits of our proposed approach for data modeling, several benchmark datasets, and a real world application associated with nonlinear systems modeling problems are examined with comparisons against other existing methods. The results indicate that our proposed SOA-SOFNN performs favorably in terms of both learning speed and prediction accuracy for online data modeling.

Fuzzy neural networks (FNNs), with suitable structures, have been demonstrated to be an effective tool in approximating nonlinearity between input and output variables. However, it is time-consuming to construct an FNN with appropriate number of fuzzy rules to ensure its generalization ability. To solve this problem, an efficient optimization technique is introduced in this paper. First, a self-adaptive structural optimal algorithm (SASOA) is developed to minimize the structural risk of an FNN, leading to an improved generalization performance. Second, with the proposed SASOA, the fuzzy rules of SASOA-based FNN (SASOA-FNN) are generated or pruned systematically. This SASOA-FNN is able to organize the structure and adjust the parameters simultaneously in the learning process. Third, the convergence of SASOA-FNN is proved in the cases with fixed and updated structures, and the guidelines for selecting the parameters are given. Finally, experimental studies of the proposed SASOA-FNN have been performed on several nonlinear systems to verify the effectiveness. The comparison with other existing methods has been made, and it demonstrates that the proposed SASOA-FNN is of better performance.

An adaptive gradient multiobjective particle swarm optimization (AGMOPSO) algorithm, based on a multiobjective gradient (stocktickerMOG) method and a self-adaptive flight parameters mechanism, is developed to improve the computation performance in this paper. In this AGMOPSO algorithm, the stocktickerMOG method is devised to update the archive to improve the convergence speed and the local exploitation in the evolutionary process. Meanwhile, the self-adaptive flight parameters mechanism, according to the diversity information of the particles, is then established to balance the convergence and diversity of AGMOPSO. Attributed to the stocktickerMOG method and the self-adaptive flight parameters mechanism, this AGMOPSO algorithm not only has faster convergence speed and higher accuracy, but also its solutions have better diversity. Additionally, the convergence is discussed to confirm the prerequisite of any successful application of AGMOPSO. Finally, with regard to the computation performance, the proposed AGMOPSO algorithm is compared with some other multiobjective particle swarm optimization algorithms and two state-of-the-art multiobjective algorithms. The results demonstrate that the proposed AGMOPSO algorithm can find better spread of solutions and have faster convergence to the true Pareto-optimal front.

In this paper, a self-organizing intelligent controller (SOIC) is proposed for a class of nonlinear systems. The basic idea of this study is to use a self-organizing fuzzy neural network to imitate control law directly, and then, appeal to obtain a compact structure of controller to further reduce the computational burden and enhance the control performance. First, an effective criterion, using the tracking performance and structure risk of controller, is developed to self-organize the control rules online for SOIC to improve the tracking performance. Second, the structure and parameters of SOIC are updated by an adaptive projection-type algorithm to reduce the heavy computational burden to speed up the control response. Third, the stability of SOIC is proved in the sense of Lyapunov and the guidelines for selecting the control parameters are given. Finally, the effectiveness of SOIC is illustrated with three nonlinear systems. It is shown that the proposed SOIC can achieve better control performance in comparison with some other control schemes.

In this paper, a self-organizing radial basis function (SORBF) neural network is designed to improve both accuracy and parsimony with the aid of adaptive particle swarm optimization (APSO). In the proposed APSO algorithm, to avoid being trapped into local optimal values, a nonlinear regressive function is developed to adjust the inertia weight. Furthermore, the APSO algorithm can optimize both the network size and the parameters of an RBF neural network simultaneously. As a result, the proposed APSO-SORBF neural network can effectively generate a network model with a compact structure and high accuracy. Moreover, the analysis of convergence is given to guarantee the successful application of the APSO-SORBF neural network. Finally, multiple numerical examples are presented to illustrate the effectiveness of the proposed APSO-SORBF neural network. The results demonstrate that the proposed method is more competitive in solving nonlinear problems than some other existing SORBF neural networks.

Multiobjective particle swarm optimization (MOPSO) algorithms have attracted much attention for their promising performance in solving multiobjective optimization problems (MOPs). In this paper, an adaptive MOPSO (AMOPSO) algorithm, based on a hybrid framework of the solution distribution entropy and population spacing (SP) information, is developed to improve the search performance in terms of convergent speed and precision. First, an adaptive global best (gBest) selection mechanism, based on the solution distribution entropy, is introduced to analyze the evolutionary tendency and balance the diversity and convergence of nondominated solutions in the archive. Second, an adaptive flight parameter adjustment mechanism, using the population SP information, is proposed to obtain the distribution of particles with suitable diversity and convergence, which can balance the global exploration and local exploitation abilities of the particles. Third, based on the gBest selection mechanism and the adaptive flight parameter mechanism, this proposed AMOPSO algorithm not only has high accuracy, but also attain a set of optimal solutions with better diversity. Finally, the performance of the proposed AMOPSO algorithm is validated and compared with other five state-of-the-art algorithms on a number of benchmark problems and water distribution system. The experimental results validate the effectiveness of the proposed AMOPSO algorithm, as well as demonstrate that AMOPSO outperforms other MOPSO algorithms in solving MOPs.

An echo-state network (ESN) is an effective alternative to gradient methods for training recurrent neural network. However, it is difficult to determine the structure (mainly the reservoir) of the ESN to match with the given application. In this paper, a growing ESN (GESN) is proposed to design the size and topology of the reservoir automatically. First, the GESN makes use of the block matrix theory to add hidden units to the existing reservoir group by group, which leads to a GESN with multiple subreservoirs. Second, every subreservoir weight matrix in the GESN is created with a predefined singular value spectrum, which ensures the echo-sate property of the ESN without posterior scaling of the weights. Third, during the growth of the network, the output weights of the GESN are updated in an incremental way. Moreover, the convergence of the GESN is proved. Finally, the GESN is tested on some artificial and real-world time-series benchmarks. Simulation results show that the proposed GESN has better prediction performance and faster leaning speed than some ESNs with fixed sizes and topologies.

A nonlinear model predictive control (NMPC) scheme is developed in this paper based on a self-organizing recurrent radial basis function (SR-RBF) neural network, whose structure and parameters are adjusted concurrently in the training process. The proposed SR-RBF neural network is represented in a general nonlinear form for predicting the future dynamic behaviors of nonlinear systems. To improve the modeling accuracy, a spiking-based growing and pruning algorithm and an adaptive learning algorithm are developed to tune the structure and parameters of the SR-RBF neural network, respectively. Meanwhile, for the control problem, an improved gradient method is utilized for the solution of the optimization problem in NMPC. The stability of the resulting control system is proved based on the Lyapunov stability theory. Finally, the proposed SR-RBF neural network-based NMPC (SR-RBF-NMPC) is used to control the dissolved oxygen (DO) concentration in a wastewater treatment process (WWTP). Comparisons with other existing methods demonstrate that the SR-RBF-NMPC can achieve a considerably better model fitting for WWTP and a better control performance for DO concentration.

A novel algorithm, bases on the adaptive resonance theory (ART), is proposed to design the structure of radial basis function (RBF) neural networks in this paper. Based on the concept of “similarity”, this proposed ART-like algorithm can be utilized to construct the RBF neural network. The number of the hidden nodes is able to be adjusted in the learning process. Meanwhile, the activity of each hidden node can be owned through the initial width design to make the structure compact. Finally, three examples are employed to test the effectiveness of the proposed ART-like RBF (ART-RBF) neural network. The results indicate that this ART-RBF neural network has better comparable generalization performance with compact structure and fast training time.

This paper is concerned with the problem of adaptive neural control for a class of uncertain or ill-defined nonaffine nonlinear systems. Using a self-organizing radial basis function neural network (RBFNN), a direct self-constructing neural controller (DSNC) is designed so that unknown nonlinearities can be approximated and the closed-loop system is stable. The key features of the proposed DSNC design scheme can be summarized as follows. First, different from the existing results in literature, a self-organizing RBFNN with adaptive threshold is constructed online for DSNC to improve the control performance. Second, the control law and adaptive law for the weights of RBFNN are established so that the closed-loop system is stable in the term of Lyapunov stability theory. Third, the tracking error is guaranteed to uniformly asymptotically converge to zero with the aid of an additional robustifying control term. An example is finally given to demonstrate the design procedure and the performance of the proposed method. Simulation results reveal the effectiveness of the proposed method.

This paper proposes a novel input-output clustering approach for structure identification of T-S fuzzy neural networks. This approach consists of two phases. Firstly, k-means clustering method is applied to the input data to provide the initial clusters of the input space. Secondly, check whether the sub-clustering is needed for each input cluster by considering the corresponding output variation and then apply the k-means method to further partition those input clusters needed sub-clustering. Applying the above process recursively leads to the structure identification of a T-S fuzzy neural network and then the parameter identification is completed by using the gradient learning algorithm. The experiments by applying the proposed method to several benchmark problems show better performance compared with many existing methods and then verify the effectiveness and usefulness of the proposed method.

In this paper, a spiking growing algorithm (SGA) is proposed for optimizing the structure of radial basis function (RBF) neural network. Inspired by the synchronous behavior of spiking neurons, the spiking strength (ss) of the hidden neurons is defined as the criteria of SGA, which investigates a new way to simulate the connections between hidden and output neurons of RBF neural network. This SGA-based RBF (SGA-RBF) neural network can self-organize the hidden neurons online, to achieve the appropriate network efficiency. Meanwhile, to ensure the accuracy of SGA-RBF neural network, the structure-adjusting and parameters-training phases are performed simultaneously. Simulation results demonstrate that the proposed method can obtain a higher precision in comparison with some other existing methods.

In this paper, a self-organizing fuzzy-neural-network with adaptive computation algorithm (SOFNN-ACA) is proposed for modeling a class of nonlinear systems. This SOFNN-ACA is constructed online via simultaneous structure and parameter learning processes. In structure learning, a set of fuzzy rules can be self-designed using an information-theoretic methodology. The fuzzy rules with high spiking intensities (SI) are divided into new ones. And the fuzzy rules with a small relative mutual information (RMI) value will be pruned in order to simplify the FNN structure. In parameter learning, the consequent part parameters are learned through the use of an ACA that incorporates an adaptive learning rate strategy into the learning process to accelerate the convergence speed. Then, the convergence of SOFNN-ACA is analyzed. Finally, the proposed SOFNN-ACA is used to model nonlinear systems. The modeling results demonstrate that this proposed SOFNN-ACA can model nonlinear systems effectively.

In this paper, a real-time model predictive control (RT-MPC) based on self-organizing radial basis function neural network (SORBFNN) is proposed for nonlinear systems. This RT-MPC has its simplicity in parallelism to model predictive control design and efficiency to deal with computational complexity. First, a SORBFNN with concurrent structure and parameter learning is developed as the predictive model of the nonlinear systems. The model performance can be significantly improved through SORBFNN, and the modeling error is uniformly ultimately bounded. Second, a fast gradient method (GM) is enhanced for the solution of optimal control problem. This proposed GM can reduce computational cost and suboptimize the RT-MPC online. Then, the conditions of the stability analysis and steady-state performance of the closed-loop systems are presented. Finally, numerical simulations reveal that the proposed control gives satisfactory tracking and disturbance rejection performances. Experimental results demonstrate its effectiveness.

Sludge bulking is one of the most serious problems in the Wastewater Treatment Plants (WWTPs) and brings about significant economic loss. Sludge Volume Index (SVI), a key sludge sedimentation performance evaluation index, is difficult to be obtained accurately online. To monitor the SVI value, a new soft sensor modeling method based on Principal Component Analysis (PCA) and Elman Neural Network (ElmanNN) is proposed in this paper. The final inputs of model are determined by PCA. Then, the SVI value is modeled by the Elman network in the WWTPs. Finally, compared with other neural networks, the experimental results show that Elman network is more efficient in modeling the SVI. The scale of network can be simplified and its capability of dealing with dynamic information can be strengthened.

A novel learning algorithm is proposed for nonlinear modelling and identification using radial basis function neural networks. The proposed method simplifies neural network training through the use of an adaptive computation algorithm (ACA). In addition, the convergence of the ACA is analyzed by the Lyapunov criterion. The proposed algorithm offers two important advantages. First, the model performance can be significantly improved through ACA, and the modelling error is uniformly ultimately bounded. Secondly, the proposed ACA can reduce computational cost and accelerate the training speed. The proposed method is then employed to model classical nonlinear system with limit cycle and to identify nonlinear dynamic system, exhibiting the effectiveness of the proposed algorithm. Computational complexity analysis and simulation results demonstrate its effectiveness.

This paper presents a repair algorithm for the design of a Radial Basis Function (RBF) neural network. The proposed repair RBF (RRBF) algorithm starts from a single prototype randomly initialized in the feature space. The algorithm has two main phases: an architecture learning phase and a parameter adjustment phase. The architecture learning phase uses a repair strategy based on a sensitivity analysis (SA) of the network's output to judge when and where hidden nodes should be added to the network. New nodes are added to repair the architecture when the prototype does not meet the requirements. The parameter adjustment phase uses an adjustment strategy where the capabilities of the network are improved by modifying all the weights. The algorithm is applied to two application areas: approximating a non-linear function, and modeling the key parameter, chemical oxygen demand (COD) used in the waste water treatment process. The results of simulation show that the algorithm provides an efficient solution to both problems.

A new growing and pruning algorithm is proposed for radial basis function (RBF) neural network structure design in this paper, which is named as self-organizing RBF (SORBF). The structure of the RBF neural network is introduced in this paper first, and then the growing and pruning algorithm is used to design the structure of the RBF neural network automatically. The growing and pruning approach is based on the radius of the receptive field of the RBF nodes. Meanwhile, the parameters adjusting algorithms are proposed for the whole RBF neural network. The performance of the proposed method is evaluated through functions approximation and dynamic system identification. Then, the method is used to capture the biochemical oxygen demand (BOD) concentration in a wastewater treatment system. Experimental results show that the proposed method is efficient for network structure optimization, and it achieves better performance than some of the existing algorithms.

A novel growing-and-pruning (GP) approach is proposed, which optimizes the structure of a fuzzy neural network (FNN). This GP-FNN is based on radial basis function neurons, which have center and width vectors. The structure-learning phase and the parameter-training phase are performed concurrently. The structure-learning approach relies on the sensitivity analysis of the output. A set of fuzzy rules can be inserted or reduced during the learning process. The parameter-training algorithm is implemented using a supervised gradient decent method. The convergence of the GP-FNN-learning process is also discussed in this paper. The proposed method effectively generates a fuzzy neural model with a highly accurate and compact structure. Simulation results demonstrate that the proposed GP-FNN has a self-organizing ability, which can determine the structure and parameters of the FNN automatically. The algorithm performs better than some other existing self-organizing FNN algorithms.

In this paper, a novel pruning algorithm is proposed for self-organizing the feed-forward neural network based on the sensitivity analysis, named novel pruning feed-forward neural network (NP-FNN). In this study, the number of hidden neurons is determined by the output's sensitivity to the hidden nodes. This technique determines the relevance of the hidden nodes by analyzing the Fourier decomposition of the variance. Then each hidden node can obtain a contribution ratio. The connected weights of the hidden nodes with small ratio will be set as zeros. Therefore, the computational cost of the training process will be reduced significantly. It is clearly shown that the novel pruning algorithm minimizes the complexity of the final feed-forward neural network. Finally, computer simulation results are carried out to demonstrate the effectiveness of the proposed algorithm.

A fast training and pruning algorithm is proposed for the feed-forward neural network (FNN) which consists of a fixed value subset-based training algorithm (FSBT) as well as a fast pruning algorithm (extended Fourier amplitude sensitivity test, EFAST) in this paper. The FNN is trained using FSBT, at each training iteration, only the weights of the independent nodes will be trained using the Levenberg-Marquardt (LM) algorithm, while keeping the weights of the dependent nodes unchanged. Meanwhile, the FNN is pruned using fast EFAST during training to remove redundant neurons in the hidden layer. In this way, the computational cost of the proposed EF-FNN will be reduced significantly. Experimental results suggest that the abilities of the final FNN are greatly improved. In the end, the proposed EF-FNN is used to predict the effluent water COD values; the results demonstrate the effectiveness of the proposed algorithm.

A new neural fuzzy algorithm based on the method of growing self-organizing network is proposed in this paper. Then the fuzzy rules can be changed on-line, it takes the experience out of the necessary side for the number of the fuzzy rules. A novel learning algorithm based on dynamic descent gradient is also presented. The main salient characters of the algorithm in this paper are: 1) a new method resolves the problem of the conventional neural network which can’t change the structure of the network; 2) the neurons of the neural network can be changed on-line; 3) a new method for the fast learning speed can be own. This new algorithm can be used to control the dissolved oxygenic in the wastewater treatment process. The results of the experiments prove the superiority of this algorithm compared with the conventional neural fuzzy algorithm.