Noting that single mode fault diagnosis methods have limitations in complex fault detection, and single fault diagnosis models have low accuracy and robustness, this article proposes a multimode fault diagnosis method for rotating mechanical equipment based on feature-level dynamic fusion and decision-level improved Dempster–Shafer (DS) evidence theory. First, by introducing time-domain, frequency-domain, and time-frequency domain data, three fault diagnosis submodels: convolutional neural network, long short-term memory network, and random forest are constructed for extracting and processing three different modal input signals. Second, a dynamic fusion strategy is developed during feature-level fusion to gradually optimize the features of different modalities, to improve the robustness and accuracy of fault diagnosis. Preliminary fault classification results for each submodel are obtained through different feature-level fusion methods. Third, the improved DS evidence theory is used to fuse the fault classification information of each submodel, and the evidence is corrected from both the performance and fault type aspects of the submodels, to obtain the final fault diagnosis result after fusion. Finally, the superiority of the proposed method is verified through experiments.

Under varying operating conditions, the operating state of rotating equipment is influenced by multiple factors, presenting the characteristics of complex and changeable data distribution and high nonlinearity. Deep belief networks (DBN) possess powerful feature learning capabilities, making them suitable for fault diagnosis under such complex conditions. However, traditional DBNS have limitations such as structural design relying on experience and being prone to getting stuck in local optima. At the same time, the adaptability to the differences in distribution of data under different working conditions is insufficient, resulting in limited accuracy of fault diagnosis and model generalization ability. To cope with these issues, a fault diagnosis method based on improved DBN is presented in this paper. Firstly, a multiple kernel principal component analysis (MKPCA) is proposed. The radial basis function(RBF) kernel and the polynomial function kernel are combined, and the weights of the kernel functions are dynamically adjusted according to different characteristics to improve the processing ability of KPCA for complex data. Secondly, the Particle Swarm Optimization algorithm (PSO) is introduced to improve the network structure and parameters of the DBN. Then, the shortcomings of traditional DBN structure design that relies on experience and is prone to fall into local optimum is overcame, achieving adaptive optimization of network structure and parameters. In addition, considering the differences in the distribution of data under different working conditions, this paper combines semi-supervised domain adaptation with DBN and introduces the multiple kernel maximum mean difference (MK-MMD), forcing DBN to learn general features, reducing the distribution differences between domains, and transferring the knowledge learned in the source domain to the target domain, thus solving the problem of insufficient generalization ability of the model caused by changes in working conditions. Finally, through experimental verification, the results indicate that the method introduced in this paper significantly enhances the accuracy and generalization ability of fault diagnosis of rotating equipment under varying operating conditions.

This paper investigates the event-triggered guaranteed-performance security control problem for nonlinear systems subject to hybrid cyber-attacks (denial-of-service (DoS) attacks and deception attacks). First, a fuzzy-model-based description approach is employed to characterize the nonlinear system, effectively capturing its complex dynamic characteristics. Second, to alleviate the communication burden in bandwidth-constrained networks, a history-dependent event-triggering mechanism incorporating historical transmission data is designed, dynamically optimizing information transmission efficiency between sensors and controllers. Third, a security control framework with prescribed performance metrics is constructed. By integrating Lyapunov functional theory and matrix decomposition techniques, sufficient conditions ensuring system stability are rigorously derived. This guarantees that the proposed guaranteed-performance security control scheme can effectively counteract malicious impacts induced by cyber-attacks. Finally, comprehensive simulation case studies validate the effectiveness of the proposed security control method, demonstrating its robustness against hybrid attack patterns while maintaining desired control performance. The results show that, compared to the traditional event-triggered mechanism (ETM) and the dynamic event-triggered mechanism (DETM), the dynamic memory event-triggered mechanism (DMETM) proposed in this paper reduces the number of triggers by approximately 63.87$\%$and 18.49$\%$, respectively; Compared to the recent Adaptive Memory Event Triggering Mechanism (AMETM), it further reduces communication overhead by approximately 8.12$\%$. Furthermore, the system maintains exponential mean-square stability under mixed attacks and achieves the specified$H\_{\infty }$performance level.

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.

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 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.

Amidst the burgeoning advancements in deep learning, traditional neural networks have demonstrated significant achievements in unimodal tasks such as image recognition. However, the handling of multimodal data, especially in visual question answering (VQA) tasks, presents challenges in processing the complex structural relationships among modalities. To address this issue, this article introduces a dynamic heterogeneous hypergraph neural network (HGNN) model that utilizes a Transformer-based combined attention mechanism and designs a hypergraph representation imaging network to enhance model inference without increasing parameter count. Initially, image scenes and textual questions are converted into pairs of hypergraphs with preliminary weights, which facilitate the capture of complex structural relationships through the HGNN. The hypergraph representation imaging network further aids the HGNN in learning and understanding the scene image modalities. Subsequently, a transformer-based combined attention mechanism is employed to adapt to the distinct characteristics of each modality and their intermodal interactions. This integration of multiple attention mechanisms helps identify critical structural information within the answer regions. Dynamic updates to the hyperedge weights of the hypergraph pairs, guided by the attention weights, enable the model to assimilate more relevant information progressively. Experiments on two public VQA datasets attest to the model's superior performance. Furthermore, this article envisions future advancements in model optimization and feature information extraction, extending the potential of HGNNs in multimodal fusion technology.

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.

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.

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.

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.

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 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.

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.

In this article, a distributed observer-based fault-tolerant control strategy is proposed for interconnected systems, in which sensor faults, actuator faults, and disturbances are tackled. First, by augmenting the original system into a new descriptor system, a sliding mode observer (SMO) design scheme that considered the associated interconnection information among subsystems is proposed. Then, sensor faults, actuator faults, and disturbances are reconstructed, and the accuracy of the reconstruction of interconnected systems is improved. Second, based upon the proposed SMO, a distributed SMO-based fault-tolerant controller is developed to compensate sensor faults, actuator faults, and disturbances for considered interconnected systems. Then, the stabilization of the overall closed-loop interconnected systems can be guaranteed. Finally, a numerical example with two subsystems and the meta aircraft with multiple aircraft joined are utilized to demonstrate the effectiveness of the proposed theoretical results.

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.

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.

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.

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.

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.

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.

Threats of cyberattacks have penetrated from disclosing critical user information to destroying/manipulating industrial control systems. Study on data security during network transmission has raised increasing attention in the systems and control community, which is found very necessary and timely in the context of Industry 4.0. In most existing approaches, the protection of the transmitted data from eavesdropping attacks and the detection of malicious integrity attacks are usually carried out separately. In this study, an integrated data-driven framework applicable at the control level is proposed to deal with secure transmission and attack detection simultaneously. In the framework, a secure correlation-based encryption/decryption approach and a trustworthiness judgement approach are proposed. Comprehensive discussions are made regarding the analysis of the sensitivity to attacks, the introduced time delay, and the design degree-of-free. Executable algorithms are presented, corresponding to which hardware is modularized and can work standalone independent from the configuration of the monitoring and control systems or any third-party authentication agencies. Evaluation results on a simulated two-area frequency-load control power grid system are provided to show the effectiveness and performance of the proposed approaches.

This article proposes a fault-tolerant compensation control approach against nonlinearity, simultaneous additive, and multiplicative actuator faults in Markov jump systems. In this article, we first exploit the fuzzy logic system (FLS) to approximate the nonlinear functions, which have no available knowledge. Then, by utilizing the adaptive backstepping technique, a FLS-based adaptive fault-tolerant compensation controller is proposed, which can completely compensate for the adverse effects, arising from the additive actuator faults, the multiplicative actuator faults, and the mismatched nonlinearity simultaneously. The stability of the closed-loop system can be guaranteed by the proposed FLS-based adaptive controller with the adaptation laws. The novelty of this article lies in the fact that the additive and multiplicative actuator faults, and mismatched nonlinearity are considered simultaneously. Besides, the renown sliding mode control approach has limitations to deal with the FTC problem considered in this article because the considered nonlinearity is a mismatched one. The proposed control approach can cope with the challenging case. Finally, a practical wheeled mobile manipulator system is used to demonstrate the effectiveness and validity of the proposed approach.

The fault-tolerant control (FTC) issue is considered in this article for Markovian jump systems (MJSs) in which both nonlinearity and actuator faults exist simultaneously. The existed nonlinearity in the considered MJSs means that there exist limitations to employ the renown sliding mode control (SMC) method directly. In this work, the radial basis function (RBF) neural network (NN) technique is exploited to model the nonlinearity on which no knowledge whatsoever is available. Then, with the help of the adaptive backstepping method, an NN-based FTC approach is proposed to overcome the considered challenging case. The adverse effects, arising from the nonlinearity and the actuator faults can be completely compensated by the proposed adaptive controller. With the proposed controller and the adaptation laws, the bounded stability of the considered closed-loop plant can be guaranteed. Furthermore, only two types of adaptive parameters are adopted in the proposed approach to achieve the purpose of FTC, and this reduces the computational burden and thus extends its applicability. Finally, the effectiveness of the developed approach is demonstrated on a practical system: a wheeled mobile manipulator.

In this paper, fault and state estimation issue for wheeled mobile manipulators with time delay, using a novel sliding mode observer (SMO) approach has been discussed. It is well-known that the traditional SMO method, i.e., the equivalent output error injection technique cannot be simply employed to Markov jump systems (MJSs) to estimate actuator faults. In this paper, we propose a novel SMO to reconstruct the actuator and sensor faults for MJSs with time delay. First, we decouple the actuator faults from the first subsystem by utilizing coordinate transformation technique. Then, construct an augmented plant for the new system and propose a novel reduced-order SMO. By the proposed novel SMO, the state and fault can be reconstructed simultaneously. Finally, an illustrative wheeled mobile manipulator example is given to show the effectiveness of the proposed approach.

This work focuses on the fault estimation (FE) problem for Markov Jump Systems (MJS) with sensor and actuator faults, and a novel reduced-order observer-based FE method is proposed. Firstly, an augmented plant in standard form is considered and a new theorem is derived to decouple the augmented fault vectors $d(t)$ from $\bar{x}_{1^{(1)(t)}}$ which is the state vector after the first time coordinate transformation. Then, the novel reduced-order observer is investigated and the Theorem 2 is derived to ensure the asymptotically reconstruction of $x(t)$. Compared with other existing observer-based method for MJS with faults, the advantage is that the FE and state estimation can be obtained directly without any supplementary design. Finally, simulations are provided to demonstrate the effectiveness of the proposed observer approach.

This paper focuses on the fault-tolerant control problem of Markov jump systems (MJS) with Itô stochastic process and output disturbances. Such a problem widely exists in practical systems such as mobile manipulator systems. Since MJS can suitably describe mobile manipulator systems, in this paper, a new approach based on the MJS model is proposed. First, a proportional-derivative sliding mode observer (SMO) and an observer-based controller are designed and synthesized. Two new theorems are derived to ensure the close-loop stochastic stability and the reachability of the sliding mode surface. Compared with the existing works, the system model is more general, which could describe a larger variety of plants or processes. The controller design procedure is simplified by solving the sliding mode parameters and the controller gain simultaneously with only one linear matrix inequality problem. In addition, the augmented fault vector can be reconstructed by employing a descriptor SMO. Simulations are provided to demonstrate the validity of the derived theorems and the effectiveness of the proposed algorithm.

This paper presents an adaptive neural network (NN)-based fault-tolerant control approach for the compensation of actuator failures in nonlinear systems with time-varying delay. The novelty of this paper lies in the fact that both the lock in place and loss of effectiveness faults, unmodeled dynamics, and dynamic disturbances are catered for simultaneously. Furthermore, this is achieved by the adaptation of only one parameter, which simplifies the computation of the control effort, and therefore extends its applicability. In the approach, the Razumikhin lemma and a dynamic signal are employed. It is shown that the output of the system converges to a neighborhood of the reference signal and the semiglobal boundedness of all signals is guaranteed. A simulation example is used to illustrate the validity and efficacy of the approach.

In this paper, an approximated-based adaptive fuzzy control approach with only one adaptive parameter is presented for a class of single input single output strict-feedback nonlinear systems in order to deal with phenomena like nonlinear uncertainties, unmodeled dynamics, dynamic disturbances, and unknown time delays. Lyapunov-Krasovskii function approach is employed to compensate the unknown time delays in the design procedure. By combining the advances of the hyperbolic tangent function with adaptive fuzzy backstepping technique, the proposed controller guarantees the semi-globally uniformly ultimately boundedness of all the signals in the closed-loop system from the mean square point of view. Two simulation examples are finally provided to show the superior effectiveness of the proposed scheme.