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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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).

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.

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.

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.

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.

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.

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.

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.

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 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.