Soft sensor modeling is the task of using measurable variables to predict target ones, which may involve nonlinearity and temporally dynamics. Despite significant progress, there is a relative lack of research on soft sensor-oriented Quantum Long Short-Term Memory (QLSTM) design and application. As a novel quantum soft sensor approach, a temporally-preserving QLSTM (TP-QLSTM) is proposed by integrating with multiscale attention mechanisms. Specifically, a temporally-preserving-based adaptive variational quantum circuit is designed by establishing entanglement across temporal inputs to improve the temporally learning capability of QLSTM. Moreover, multiscale attention mechanisms are designed in the input and output parts of TP-QLSTM to learn nonlinearities and temporal dynamics from different feature dimensions and temporal ones, as well as from historical hidden states and temporal outputs. In addition, a referential attention-based autoregressive forecasting strategy is proposed as output module of TP-QLSTM to predict the target results. Experiments on two soft sensor cases demonstrate the effectiveness and practicality of our method. Note to Practitioners—In industrial processes, soft sensors are critical for achieving comprehensive state awareness and predictive management. However, practical soft sensors often struggle with complex nonlinear and time-dependent relationships in dynamic processes. As an innovative attempt to enhance soft sensing from a quantum algorithm perspective, we propose a TP-QLSTM by integrating multiscale attention mechanisms. Through designing adaptive quantum circuits that preserve temporal correlations and incorporating multiscale attention mechanisms, our method effectively captures multiscale dynamics and nonlinearities from process data. This enables accurate and robust predictions of key variables in industrial settings. Experiments on real cases confirm that our method achieves high prediction accuracy while maintaining low computational latency—with an average inference time of less than 0.6 ms per sample. A current limitation is that the quantum algorithm is implemented using simulated quantum circuits, which restricts the full exploitation of quantum parallelism. Future work will focus on deploying the model to hardware platforms that support real quantum circuit computation, thus enabling efficient training and inference.

Many important physical systems belong to distributed parameter systems (DPSs), which require appropriate models for optimization, decision-making, and control. The modeling of DPSs is typically challenging due to their highly time-space coupled nature. Time/space separation-based modeling methods have attracted substantial attention due to their ability to decouple spatiotemporal dynamics. From a systematic perspective, we identify and clarify a developmental trajectory underlying these methods, which, to the best of our knowledge, has not been explicitly presented in prior surveys. Specifically, these methods have progressed through a trajectory from traditional physics-based methods, to physics-data hybrid methods, then to purely data-driven methods, and more recently to deep physics-informed learning methods. Motivated by this newly identified paradigm, this paper presents a comprehensive review of time/space separation-based modeling methods over the past 15 years. Furthermore, we systematically summarize uncertainty quantification that has been overlooked in existing related surveys. Building upon these findings, we reveal potential future research directions for this class of methods. In addition, several representative application examples are provided to offer practical guidance for researchers and practitioners.

This article presents an adaptive neural network (AdNN)-based fault detection framework for the thermal processes of lithium-ion (Li-ion) batteries governed by 2-D semilinear partial differential equations (PDEs) with partially-known dynamics. To address the challenges of unknown nonlinear heat generation and limited sensor measurements, a two-stage approach combining reduced-order modeling with adaptive neural observation is proposed. First, a computationally tractable reduced-order model is derived through spectral approximation techniques. An adaptive neural observer is then designed to simultaneously estimate battery states and unknown nonlinear dynamics using only available surface temperature measurements. For robust fault detection, a hybrid scheme is developed that integrates model-based residual generation with data-driven threshold generation. Experimental validation on a pouch-type battery demonstrates the effectiveness of the proposed method in reliably detecting thermal abnormalities.

Sensor drift, which is the deviation of measurements over time, can compromise controller performance and cause system instability. To address this challenge, this article proposes a proactive fault-tolerant control strategy for distributed parameter systems. The proposed strategy is based on a time-varying spatiotemporal model that captures system dynamics. The initial phase of this research involves designing an adaptive observer-based detector to identify the temporal and spatial locations of fault occurrences accurately. Subsequently, a joint state-and-fault estimator is developed to accurately reconstruct the fault profile, even in the presence of strong state-fault coupling. The controller provides real-time corrections based on the estimation results. A rigorous stability analysis of the closed-loop system is provided, and the effectiveness of the controller is validated through experiments involving two distinct fault scenarios.

Distributed parameter systems (DPS) are prevalent in industrial processes; yet, traditional modeling methods are inadequate for handling varying conditions. To address this, a spatiotemporal transfer learning method is proposed for DPS modeling based on time/space (T/S) separation. Within the T/S separation framework, we initially design spatial basis functions (SBFs) and utilize a gated recurrent unit network to capture temporal dynamics for a relatively stable condition (source domain). When the system shifts to a new condition (target domain), we directly share the SBFs and transfer the temporal model using a novel spatiotemporal loss function. After T/S synthesis, the constructed model demonstrates satisfactory performance under varying conditions. Furthermore, generalization and convergence analysis have been conducted, proving that the errors are bounded. Finally, a simulation study and real experiments on battery systems demonstrate the efficacy of the suggested approach.

Real-world dynamic systems often exhibit time-varying behavior. While state space models (SSMs) have shown great potential for sequence modeling, especially in capturing long-range dependencies, most previous studies have been limited to time-invariant dynamics. To overcome this limitation, we propose a neural network architecture based on time-varying SSMs with dynamics that evolve over time, called dynamic SSMs. To enhance scalability and efficiency, several techniques are introduced, including sparsification strategy via diagonalization and fast tensor convolution with quasi-linear complexity in sequence length. Extensive experiments on both synthetic and real-world datasets show that the proposed model consistently outperforms existing state-of-the-art methods. Moreover, the model achieves significantly lower time and space complexity compared to architectures such as Transformer and LSTM. This work advances the theoretical foundation of SSMs-based neural networks in deep learning and promotes their further development. Code is available at:https://github.com/leonty1/dssmhttps://github.com/leonty1/dssm.

Handling incomplete data in spatiotemporal systems is a critical challenge in scientific and engineering applications. This paper introduces a time/space twist-based spatiotemporal modeling framework to address incomplete sampling in distributed parameter systems (DPSs). By decomposing system dynamics into temporal basis functions and spatial coefficients, the proposed method reconstructs missing spatial information using neural networks while preserving physical principles. The framework integrates data-driven modeling with physical constraints, ensuring accurate reconstruction even under sparse observations. Experimental validation on a catalytic reaction process highlights the effectiveness and superiority of the approach compared to traditional methods, demonstrating its ability to capture complex spatiotemporal dynamics with limited data.

Although deep learning-based methods have shown great success in spatiotemporal predictive learning, the frameworks of those models are mainly designed by intuition. How to make spatiotemporal forecasting with theoretical guarantees is still a challenging issue. In this work, we tackle this problem by applying domain knowledge from the dynamical system to the framework design of deep learning models. An observer theory-guided deep learning architecture, called Spatiotemporal Observer, is designed for predictive learning of high dimensional data. The characteristics of the proposed framework are twofold: first, it provides the generalization error bound and convergence guarantee for spatiotemporal prediction; second, dynamical regularization is introduced to enable the model to learn system dynamics better during training. Further experimental results demonstrate that this framework could effectively model the spatiotemporal dynamics and make accurate predictions in both one-step-ahead and multi-step-ahead forecasting scenarios.

Many industrial processes are typically distributed parameter systems (DPSs) described by partial differential equations. Data-driven methods have become popular for spatiotemporal modeling of DPSs, which is crucial for system understanding, simulation, and control improvement. However, current data-driven methods rely heavily on data volume and fidelity. With limited high-fidelity data, they exhibit unsatisfactory long-term predictions for out-of-sample scenarios. To remedy this issue, a novel physics-enhanced separation framework (called PhysiT/S) is proposed. PhysiT/S is composed of a physics-enhanced spatiotemporal unit and a coefficient network. By enhancing physics utilization through the physics-enhanced spatiotemporal unit, PhysiT/S becomes less data-dependent while computationally efficient. Multi-fidelity learning of the coefficient network further alleviates the request for a large volume of high-fidelity data. As a result, PhysiT/S can accurately predict out-of-sample distributions, even when only limited high-fidelity data is available. PhysiT/S introduces a novel way of combining physics with multi-fidelity data for spatiotemporal modeling of DPSs. Extensive simulations on two benchmark DPSs and the thermal process of lithium-ion batteries demonstrate the merits of PhysiT/S. Note to Practitioners—This paper is motivated by the problem of data-driven spatiotemporal modeling of DPSs, which is also applicable to other prediction tasks for complex spatiotemporal systems. Existing data-driven approaches rely heavily on high-fidelity data, while physics-informed approaches struggle to extract coupled spatiotemporal features. These drawbacks limit their practical applications to engineering modeling. In this paper, we propose a new generic modeling framework that integrates physics with data through the theory of time/space separation. It aims to achieve accurate long-term predictions for out-of-sample scenarios by constructing spatiotemporal enhancement units and using multi-fidelity data to decrease reliance on high-fidelity datasets. We have applied the proposed method to the thermal processes of a catalytic rod and a cylindrical lithium-ion battery. Preliminary results show that this method is feasible with better predictions than others, but it is untested in production. Future research will address online modeling in practical engineering.

During the distributed thermal process, frequent model updates (MUs) and controller activations can lead to worse performance due to over-computation. To address this problem, a dual event-triggered spatial model predictive control (DET-SMPC) under a data-driven framework is investigated for distributed thermal processes to achieve good global performance. The spatiotemporal model is built utilizing the time/space theorem and updated to accommodate the time-varying system dynamics. Since the controller effect will be affected when the model is switched, it is necessary to identify the preferable switching mode. Therefore, an adaptive MU approach based on an error-triggered generator is proposed. Subsequently, ET-model predictive control (MPC), the controller activation threshold derived from the Lyapunov function, is introduced. The controller will only be activated when the threshold is triggered, resulting in better performance. The availability of the dual event-triggered spatial MPC (DET-SMPC) is confirmed through both simulation studies and oven experiments.

In this work, we introduce a fuzzy intermittent control method for nonlinear coupled delayed partial differential equation-ordinary differential equation (PDE-ODE) systems based on spatially averaged measurements (SAMs). First, the nonlinear coupled delayed PDE-ODE systems are accurately modeled by adopting the Takagi-Sugeno (T-S) fuzzy PDE-ODE model. Then, based on the T-S fuzzy PDE-ODE model, a switching lyapunov functional (LF) is given, and fuzzy intermittent controllers are designed to ensure the exponential stability of the closed-loop fuzzy delayed coupled systems. Sufficient conditions for the exponential stability of the system are expressed through by a set of space-dependent linear matrix inequalities (SDLMIs). Finally, the simulation results are used to verify the effectiveness of the proposed approach for controlling hypersonic rocket car (HRC).

This article considers the adaptive stability control of a class of linear hyperbolic PDE systems. The PDE model is subject to constant but in-domain and boundary unknown parameters. A novel adaptive controller is developed by leveraging the swapping design technique and composite parameter learning law. With swapping design, several linear and static combinations, including carefully designed filters, unknown parameters, and error terms, are constructed to express the system states. From the static combinations, a composite learning based forgetting-factor least squares law is introduced to guarantee exponential parameter convergence without the persistent excitation (PE). Although inaccurate parameter estimation in the adaptive backstepping control results in asymptotic stability of the system, accurate parameter estimation ensures the exponential convergence of closed-loop system and concomitantly improves the transient performance. Finally, a comparative numerical simulation is performed to validate the effectiveness and advantage of the developed adaptive control scheme.

In printed circuit board (PCB) production, uncertainty in the manufacturing stage and sampling uncertainty in the inspection stage have a great impact on product quality. This article proposes rotating angles based on the optimal detection of PCB defects under uncertainties. First, the principal features are extracted and factors of information concentration are designed to construct the reference template from the preprocessed clean dataset. After that, a rotation-angle-based feature extraction and concentration optimization are performed to select the better representative angles. Then, all optimized features are probabilistically synthesized and compared with the reference template for defect detection. Finally, extensive experiments are conducted on the bare PCB and high-resolution integrated PCB to demonstrate the proposed method is efficient and faster and requires fewer model parameters.

Accurately modeling the electrochemical process of large-scale lithium-ion batteries (LLBs), which involves estimating the electrochemical state distributions within the process, is crucial for the design and management of LLBs. A two-dimensional (2-D) physics-based model can describe the electrochemical process of LLBs accurately. However, due to the presence of complex partial differential equations (PDEs), solving the model becomes a challenging task. This article develops a physics-informed composite network (PICN) as a surrogate model of the 2-D physics-based model. Specifically, PICN consists of four deep neural networks (DNNs) to estimate the distributions of four key electrochemical states, respectively. Since the architecture of PICN is inspired by PDE characteristics, it can achieve high accuracies with four lightweight DNNs. Additionally, by incorporating physics and data, PICN achieves accurate estimations using limited data. It can even estimate the electrochemical state distributions that may not be measured directly. Moreover, PICN presents a low-frequency information-based pretraining strategy and a two-stage loss balance strategy to address the convergence failure and loss imbalance that may arise in the training of PICN. PICN is a new attempt to model the electrochemical process of LLBs by integrating physics with data. Extensive experiments show that it is better than state-of-the-art models.

Distributed parameter systems (DPS) are widely presented in various industrial fields. Time/space separation-based methods have proven to be effective modeling schemes for DPS. However, the sparse sensing environments in practical industrial scenarios inevitably result in incomplete data, posing significant challenges to the implementation of traditional modeling methods. In addition, the nonstationary spatiotemporal dynamics of the system pose another challenge for modeling. In this article, a sparse information completion-based incremental learning approach is proposed for modeling the complex DPS. First, a sparse information completion module is designed to reconstruct the nonsensor data, which takes spatial coupling effects into account. Then, the spatial basis functions are incrementally constructed to capture the systematic spatial variation. Finally, the temporal learning model is also incrementally developed to track temporal dynamics. Two case studies of sparse sensing in industrial processes demonstrate the superiority of the proposed modeling approach.

Numerous industrial thermal processes and fluid dynamics systems can be described by distributed parameter systems (DPSs), where the inputs, outputs, and process variables vary in space and time. In this research, a continuous feature reconstruction-based spatiotemporal modeling method is introduced for DPSs under limited sensing scenarios. Initially, a discrete space completion approach is created to recuperate the spatiotemporal patterns of nonmonitored locations by limited sensors. Then, a continuous feature reconstruction method is designed for deriving continuous spatial basis functions (SBFs), which are the intrinsic characteristics of DPSs. The identification and adjustment of the nonlinear temporal model are carried out via the long short-term memory neural network. Eventually, the amalgamation of the derived SBFs and the temporal model results in a spatially continuous representation. The proposed method reduces the reliance of traditional first-principle methods on governing equations and minimizes the need for extensive sensor arrays in purely data-driven approaches. Experimental tests conducted on a pouch-type Li-ion battery demonstrate the effectiveness and superiority of the proposed spatiotemporal modeling method under limited sensing.

Many industrial processes can be described by distributed parameter systems (DPSs) governed by partial differential equations (PDEs). In this research, a spatiotemporal network is proposed for DPS modeling without any process knowledge. Since traditional linear modeling methods may not work well for nonlinear DPSs, the proposed method considers the nonlinear space-time separation, which is transformed into a Lagrange dual optimization problem under the orthogonal constraint. The optimization problem can be solved by the proposed neural network with good structural interpretability. The spatial construction method is employed to derive the continuous spatial basis functions (SBFs) based on the discrete spatial features. The nonlinear temporal model is derived by the Gaussian process regression (GPR). Benefiting from spatial construction and GPR, the proposed method enables spatially continuous modeling and provides a reliable output range under the given confidence level. Experiments on a catalytic reaction process and a battery thermal process demonstrate the effectiveness and superiority of the proposed method.

This article introduces a novel time/space separation-based physics-informed machine learning (T/S-PIML) modeling method by making full use of the complementary strengths of the physics-informed neural network (PINN) and the time/space separation methodology. T/S-PIML is the first attempt to seamlessly integrate structural (including spatial and temporal) physical information with data for effective spatiotemporal modeling of distributed parameter systems (DPSs). With the help of the spectral method, spatial basis functions are first extracted to capture spatial physical information. Subsequently, a reduced-order system is derived to characterize the corresponding temporal physical information. Upon the structural physical information, PINN is developed for temporal modeling. Following the time/space synthesis, a small amount of sensing data is utilized to calibrate system errors. Experiments on a benchmark DPS and the thermal process of a lithium-ion battery demonstrate the effectiveness of T/S-PIML.

This study presents an adaptive event-triggered control methodology for flexible manipulator systems with prescribed performance and input backlash. To reduce the communication burden between the controllers and actuators, we consider a relative threshold event-triggered mechanism. Then, an adaptive inverse function is applied to eliminate the input backlash of the actuator, and a neural network is adopted to handle the system uncertainty. It is proven that the proposed control approach not only ensures the tracking error converges to a small region close to zero within the prescribed time but also significantly reduces overshoot by using Lyapunov’s direct method. Furthermore, the efficacy of the scheme proposed is demonstrated through numerical simulations and experiments.

This paper proposed a learning-enabled approach for adaptive spatiotemporal modeling of industrial distributed processes. Within the framework of Karhunen-Loéve (KL) separation, the spatial basis functions (SBF) are updated online in a forgetful learning mode to capture spatial dynamics. Then, the temporal model is also updated iteratively in a forgetting mode to adjust temporal dynamics. Finally, the predicted spatiotemporal state is obtained via Time/Space synthesis. This dual forgetting mechanism embedded in the model can adaptively track the spatiotemporal dynamic changes, thus achieving better modeling effects. The experimental validation of distributed thermal processes in battery operation demonstrates the modeling efficacy of the designed learning approach.

This study focuses on the novel reinforcement learning control strategy of a nonlinear two-degrees-of-freedom (2-DOF) helicopter system for tracking the desired trajectory while minimizing the tracking error. First, gradient descent algorithm is incorporated in the context of the reinforcement learning control scheme to obtain the adaptive laws. Subsequently, considering the uncertainties in the nonlinear system, radial basis function (RBF) neural networks (NNs) are exploited to approximate the unknown internal dynamics. In contrast to the previous studies, aiming at accelerating the convergence in reinforcement learning control, a barrier Lyapunov function is constructed to constrain the states to ensure that the tracking error rapidly converges to a neighborhood of zero. Under the proposed control strategy, the states of the closed-loop system are proven to be semi-globally uniformly ultimately bounded through rigorous Lyapunov analyses, and the state constraints are satisfied. Furthermore, the simulations and experiments conducted on a Quanser laboratory platform reveal that the proposed control functions are suitable and effective. Note to Practitioners—This paper is motivated by designing a reinforcement learning control strategy to enhance online learning capability and control performance of the controller for a nonlinear 2-DOF helicopter system. The control framework is divided into the design of the critic and actor NNs, responsible primarily for evaluating the control performance and approximating uncertainties in the system separately. Unlike the adaptive NN control, the actor NN weights are updated by combining information of states and inputs from the critic NN. In addition, aiming at accelerating the convergence, a barrier Lyapunov function is constructed to constrain the states to ensure that the tracking error rapidly converges to a neighborhood of zero. Finally, the proposed control strategy is validated in simulation and experiment on the Quanser laboratory platform.

Physics-informed machine learning (PIML) has proven to be a valuable approach for overcoming data scarcity challenges by incorporating physical models into machine learning methods. However, PIML faces limitations in handling complex spatial relationships, as its process information is obtained from disordered collocation points. Fuzzy systems, based on expert knowledge, can provide an interpretable way for tackling strong process nonlinearities. This article proposes a brand-new physics-informed spatial fuzzy system framework (PiFuz) to capture the essential system information of complex distributed parameter systems. PiFuz utilizes spatial membership functions to transform collocation points into a 3-D fuzzy input. This input is processed by the inference mechanism, leveraging its 3-D nature to produce fuzzy outputs with distinctive spatial characteristics. A feature fusion module is utilized to integrate these characteristics and generate the distributed system state. Utilizing the known physical knowledge base, the proposed framework undergoes automatic tuning while preserving process interpretability, resulting in an optimal model that aligns with the actual physical process. A reliable prediction of strong spatial nonlinear behaviors is achieved without the dependency of process data. For modeling higher dimensional spatiotemporal problems, the extension, a multikernel PiFuz framework (MKPiFuz), is further developed to improve the representation of heterogeneous time-varying nonlinear behaviors. By incorporating spatial and wavelet kernels, MKPiFuz extracts underlying features from spatial and temporal dimensions, respectively. Experimental investigations on thermal process of the battery module demonstrate the good accuracy in modeling complex spatiotemporal systems.

In this article, the problem of output tracking via proportional-integral-derivative (PID) control scheme is discussed for a class of nonlinear infinite-dimensional spatiotemporal dynamic systems modeled by a semilinear parabolic partial differential equation (PDE) with collocated boundary control input and measurement output. To surmount the difficulty caused by the infinite-dimensional spatiotemporal nonlinear dynamics, a Takagi–Sugeno (T–S) fuzzy parabolic PDE model is first constructed to represent the nonlinear spatiotemporal dynamics, and then a fuzzy PID boundary output tracking control (BOTC) scheme is proposed via the obtained T–S fuzzy PDE model and the difference between the boundary measurement output and its desired constant reference signal to achieve the output tracking goal. Utilizing the Lyapunov technique combined with the inequality techniques, a systematic, conceptually simple yet effective parameter tuning method is developed for the fuzzy PID control scheme such that the suggested fuzzy PID-BOTC law drives the measurement output to asymptotically track the desired reference signal and ensures the boundedness of the resulting closed-loop system signals. Such parameter tuning is formulated as a feasibility problem subject to linear matrix inequality constraints. Moreover, two special cases of the proposed PID-BOTC design (i.e., fuzzy PI-BOTC scheme and fuzzy integral BOTC one) are also provided in this article. Extensive simulation results for a numerical example and a chemical axial dispersion tubular reactor are presented to show the effectiveness of the proposed fuzzy PID-BOTC scheme and its merit in the fast response of the preset reference signal and the less overshot is also illustrated by comparing with the fuzzy PI control law and the fuzzy integral one.

Modeling the temperature distribution of a battery is critical to its safe operation. Data-based modeling methods are computationally efficient, but require a large number of sensors, whereas physics-based modeling methods have better generalization, but the unknown dynamics of the actual scene are ignored. A physics-dominated neural network is presented to integrate electric–thermal mechanism of the battery and data information through a weight adaptive function. The electric–thermal coupling equation of the battery under complex conditions is taken as the prior knowledge to update parameters of the network, whereas the characteristic data obtained by the unique sensor are used to compensate the unknown disturbance in the actual scene. A well-trained model can predict the temperature distribution of the battery over entire space with a single sensor, and can also provide reasonable predictions for longer periods of time under extreme conditions. Experiments show that the proposed method outperforms traditional methods that rely only on pure data or pure physics.

Distributed parameter systems (DPS) widely exist in many industrial processes. Traditional modeling methods are not suitable for complex DPS under time-varying boundary conditions. To handle dynamics at different scales in the spatial and temporal domains, a dual-scale incremental learning approach is proposed for the efficient modeling of the complex time-varying DPS. Under the space/time separation framework, spatial basis functions (SBF) are first designed and updated incrementally at a slow scale over a long period of time. Under the given SBF, the temporal model will be incrementally iterated in real time (fast scale). An optimal choice of the fast/slow ratio can further improve the modeling performance by better coordinating the dynamics at different scales. The experiments on the curing oven thermal process can demonstrate the effectiveness of the proposed method for modeling complex time-varying dynamics of DPS.

The charging process design is crucial for optimizing the performance of lithium-ion batteries by identifying protocols that meet diverse demands. The main challenges include: 1) the high costs of battery experiments; 2) the multiple user preferences associated with the demands; and 3) the intricate high-dimensional search space of charging protocols. In light of this, this article presents a Gaussian process-accelerated multiobjective evolutionary design method for effective charging process design. To resolve the first concern, an electrochemical-thermal-aging model is constructed to evaluate charging protocols precisely, substituting the need for expensive battery experiments. Besides, the Gaussian process is applied to accelerate the evaluation process further. Regarding the second issue, a Gaussian process-accelerated two-archive evolutionary algorithm (GPA-TAEA) is developed to efficiently search for a set of optimal charging protocols that satisfy multiple user preferences. To address the third challenge, differential evaluation—an evolutionary algorithm proven effective for large-scale optimization—is employed to enhance the search process. The simulation results demonstrate that: 1) the proposed method effectively reduces the time required for charging process design, yielding a collection of optimal charging protocols that includes 530 solutions within 1000 simulations; 2) compared with five other multiobjective optimization algorithms, GPA-TAEA exhibits superior convergence and diversity; and 3) compared with fixed preference-based methods, GPA-TAEA demonstrates greater efficiency, saving 54% in simulation evaluations and 70% in time when considering seven user preferences.

Temperature is a key factor affecting the safety of the Lithium-ion (Li-ion) battery. Therefore, real-time thermal fault diagnosis is becoming more and more prominent, as battery faults can lead to local overheating and thermal runaway in severe cases. This article proposes a Chebyshev–Galerkin-based thermal fault detection and localization framework for the pouch-type Li-ion battery under limited sensing. First, the Chebyshev function is used to construct the spatial basis functions with global and orthonormal properties. Under the time–space (T-S) separation framework, the time coefficients can be derived through the Galerkin method using six sensors. Then, by decomposing the time coefficients using the independent component analysis, the temporal and spatial reference statistics can be formed for real-time fault detection. Finally, considering the detected fault snapshots, the thermal fault location can be identified by finding the maximum contributed position through T-S synthesis. Simulations and experiments demonstrate the effectiveness of the proposed method.

Fault detection for distributed parameter systems (DPSs) generally requires the complete model information to be known so far. However, for numerous industrial applications, it is common that accurate first-principles physical models are extremely difficult to obtain. Hence, the applicability of traditional model-based methods is being restricted. To pave the way, an adaptive neural network (AdNN) is constructed to simultaneously estimate the state variable and the unknown nonlinearity for a class of partially known nonlinear DPSs. Moreover, considering that full-state measurement is unrealistic in applications, the proposed adaptive neural observer is based on a reduced-order model, which also increases the computation efficiency. Then, the residual generation and evaluation are conducted using the output estimation error of the proposed adaptive neural observer. Bearing the effects of the neglected fast dynamics in mind, a data-driven threshold generation scheme is proposed. Extensive experimental results are presented and analyzed to validate the effectiveness of the proposed method.

Defect detection is an essential part of quality management for industrial processes. Existing vision-based detection methods are inefficient when uncertainty exists in the industrial image. This paper proposes a systematic methodology for defect detection of uncertain industrial images. It consists of adaptive convolution and confidence learning. First, a convolution model adaptively fuses multiple kernel prediction results, which is employed to learn image defect variation. After that, a confidence learning method is developed to filter the label noise and fine-tune the adaptive convolution model. Finally, experimental studies indicate the proposed method can achieve satisfactory detection accuracy and robustness.

Recently, with the development of the marine economy, marine risers have garnered increasing attention as they present facile and reliable methods for oil and gas transportation. However, these risers are susceptible to vibrations, which can lead to system performance degradation and fatigue damage. Therefore, effective vibration control strategies are required to address this issue. In this study, a novel adaptive fault-tolerant control (FTC) strategy is adopted to suppress the vibrations of a 3-D riser-vessel system against the effects of actuator failures, backlash-like hysteresis, and external disturbances. A barrier-based Lyapunov function is merged to eliminate the time-varying output constraints of the system. Adaptive FTC laws with projection mapping operators are designed to compensate for parameter uncertainties and consider input nonlinearities to improve system robustness. Finally, a rigorous Lyapunov analysis and numerical simulations are performed to verify the validity of the proposed controller and guarantee uniformly bounded stability of the system.

For nonlinear delayed parabolic partial differential equation (PDE) systems, this article addresses fault-tolerant stochastic sampled-data (SD) fuzzy control under spatially point measurements (SPMs). Initially, a T–S fuzzy PDE model is given to accurately describe the nonlinear delayed parabolic PDE system. Second, in consideration of possible actuator failure, a fault-tolerant SD fuzzy controller with stochastic sampling under SPMs is designed for nonlinear delayed parabolic PDE system, where two sampling periods are considered whose occurrence probabilities are given constants and satisfy the Bernoulli distribution. Then, by constructing a novel time-dependent Lyapunov functional, sufficient conditions that guarantee the mean square exponential stability of closed-loop delayed PDE system are obtained based on linear matrix inequalities. Last, three examples are given to illustrate the designed approach.

In this article, a spatio-temporal inference system is proposed to detect and locate thermal abnormalities of battery systems. The proposed spatio-temporal inference system consists of three modules: spatio-temporal processing module, abnormality inference module, and spatial inference module. Based on the distributed temperatures on the battery system, the monitoring statistic can be developed in the spatio-temporal processing module. The abnormality inference module is constructed to detect the abnormality based on the derived statistic index. Then, the spatial Bayes model is designed to estimate the abnormality location. The Bayes risk analysis indicates that the proposed method has a bounded error. Experiments on a lithium-ion (Li-ion) battery cell and a battery pack demonstrate that the proposed spatio-temporal inference system can detect and locate the internal short circuit fault before it develops into a thermal runaway.

Control-oriented thermal models are essential for onboard temperature monitoring of lithium-ion batteries in automobile applications. This work develops a Galerkin-spectral model for the 3-D thermal diffusion in pouch cells. First, a full-order model that depicts the battery thermal phenomenon is introduced from a physical point of view. Considering different physical properties in each area, we apply a space decomposition approach to decouple the interactive thermal effects between the cell core and tabs. Then, mild approximations are made to generate a more succinct model governed by the partial and ordinary differential equations. Finally, a low-order representation is extracted from the original infinite-dimensional system by employing spectral expansion on the spatiotemporal variable. Experimental and simulation studies indicate satisfactory reduced-order performance and practical validity of the proposed model.

This article proposes an adaptive control for a flexible manipulator (FM) under the influence of distributed disturbances, unknown dead zones, and input quantization. First, the hybrid effect of the unknown dead zone and input quantization is formulated and represented based on some essential transformations. Then, an adaptive robust quantized control with online updating laws is developed to address the uncertainty of the dead zone, ensure robustness and angle position, and dampen the vibration in the FM system. Subsequently, the Lyapunov theoretical analysis is employed to ensure the bounded stability of the system. Finally, numerical simulations and experiments with a Quanser platform are given to further verify the feasibility and superiority of the designed scheme.

In this article, we propose a new adaptive fuzzy fault-tolerant control (FTC) for a three-dimensional riser-vessel system with unknown backlash nonlinearity. A model for the smooth inverse dynamics of the backlash is introduced; then, the control input is divided into an expected input and a compensation error. Considering the imprecision of system modeling and unknown external disturbances, we employ a fuzzy adaptive technology to achieve compensation. By incorporating the actuator fault term and backlash error, the adaptive FTC is developed to resolve loss faults in the actuator and compensate for the unknown backlash to some extent. The direct Lyapunov method is used to demonstrate the system’s bounded stability. Finally, simulation results demonstrate the effectiveness of the derived scheme.

Ultra-high-frequency radio-frequency-identification (UHF RFID)-based sensing technology with antenna-integrated sensor tags offers a cost-effective solution for Internet of Things (IoT) applications. A multidimensional differential measurement technique for eliminating the effect of the measurement setup, such as unknown mutual distance and orientation between the read/write device (RWD) and sensor tags, and line-of-sight obstruction, on acquiring information from multiple sensor tags simultaneously is proposed. The concept is based on 1) using a channel hopping mechanism to acquire multidimensional data sets and 2) conducting a dissimilarity analysis between offline and online data sets to extract sensor information. The differential measurement, which is activated by the channel hopping mechanism, mitigates the impact of the measurement setup, making the pattern of the multidimensional data sets tightly relate to the sensing state. A sensor tag for measuring the water-filling level of polyvinyl chloride (PVC) pipes is designed and fabricated. Experiments show that the proposed method can accurately acquire information from three sensor tags simultaneously under different measurement setups. The performances using data sets of different dimensions are compared. Results reveal that using low-dimensional data sets can still be capable of getting accurate information from the sensor tags, implying that the acquisition time can be reduced.

Due to the lightly damped resonance and intrinsic nonlinearities, it is difficult for the piezoactuated nanopositioning stage to realize high-bandwidth and high-accuracy control. To handle these limitations, in this work, a dual-loop control scheme based on state-feedback-based modal method is designed to both actively damp and stiffen the resonant mode and to suppress the effects of nonlinearities of the piezoactuated nanopositioning stage. In this scheme, the state-feedback-based modal controller is first designed in the inner loop to enlarge both the damping ratio and natural frequency of the first resonant mode. Then, a proportional–integral (PI) controller is utilized in the outer loop for eliminating the tracking errors caused by other disturbances and nonlinearities including hysteresis and creep. To maximize the control bandwidth of system under the proposed dual-loop scheme, an optimization method is thus proposed for simultaneously tuning the parameters of the inner and the outer loop controllers. Finally, to validate the proposed dual-loop control scheme, comparative experiments are carried out on a piezoactuated nanopositioning stage. Results demonstrate that the proposed control scheme improves the bandwidth of the system from 497 Hz (with PI control) and 1543 Hz (with a commonly used positive acceleration, velocity, and position damping control and a PI controller) to 6546 Hz, which is 664 Hz larger than the first resonant frequency of the original system, validating the effectiveness of the proposed dual-loop scheme on high-bandwidth control. Note to Practitioners—The demand of high-bandwidth and high-accuracy piezoactuated nanopositioning stages increases rapidly. However, the lightly damped resonance of the mechanism and the intrinsic nonlinearities of the piezoelectric actuator limit the tracking performance of the stage. A dual-loop control structure is adopted in this work to improve the tracking performance of the nanopositioning stage. Different from most of the vibration control methods proposed in the literature which aimed only at improving the damping ratio, a state-feedback-based modal controller is designed in the inner-loop for improving both the damping ratio and the stiffness of the system. This task is realized by re-placing the resonant poles of the system to the optimized location. The outer-loop controller adopts the high-gain PI control for eliminating the tracking errors. More importantly, in order to realize the high-bandwidth and high-accuracy control, a numerical optimization method is proposed for simultaneously tuning the parameters of the controllers in inner and outer loops. The controller design is simple, and it can be applied to other systems with second or higher order in which the first resonant mode dominates the system dynamics.

Fault detection for distributed parameter processes (heat processes, fluid processes, etc.) is vital for safe and efficient operation. On one hand, the existing data-driven methods neglect the evolution dynamics of the processes and cannot guarantee that they work for highly dynamic or transient processes; on the other hand, model-based methods reported so far are mostly based on the backstepping technique, which does not possess enough redundancy for fault detection since only the boundary measurement is considered. Motivated by these considerations, we intend to investigate the robust fault detection problem for distributed parameter processes in a model-based perspective covering both boundary and in-domain measurement cases. A real-time fault detection filter (FDF) is presented, which gets rid of a large amount of data collection and offline training procedures. Rigorous theoretic analysis is presented for guiding the parameters selection and threshold computation. A time-varying threshold is designed such that the false alarm in the transient stage can be avoided. Successful application results on a hot strip mill cooling system demonstrate the potential for real industrial applications.

In this study, we propose an adaptive fuzzy event-triggered control scheme for an autonomous aerial refueling hose system involving uncertainty, an event-triggered mechanism, and actuator failures. The unknown nonlinear function is approximated using the designed fuzzy logic systems. Through introduction of the adaptive compensation scheme, the problem of an infinite number of actuator failures, including partial and complete failures, is solved. In addition, the event-triggered control strategy is designed to achieve vibration suppression while decreasing the communication burden between the controllers and actuators. The stability of the closed-loop system is demonstrated via the Lyapunov direct method. Finally, simulation examples are presented to confirm the validity of the proposed control scheme.

This study addresses adaptive fuzzy control for an axially moving slung-load cable system (AMSLCS) of a helicopter in the presence of an actuator fault, system uncertainty, and disturbances with the aid of a fuzzy logic system (FLS). The actuator fault considered is depicted by a more general faulty plant that includes an unknown actuator gain fault and a fault deviation vector. First, to compensate for system uncertainty and the fault deviation vector, a fuzzy control technique is adopted. Then, under the introduced FLS, a novel adaptive fuzzy control law is developed by employing a rigorous Lyapunov derivation. The closed-loop system of the AMSLCS is proved to be uniformly bounded even when considering the actuator fault, system uncertainty, and disturbances. Finally, a simulation is executed to expound the performance of the developed controller.

A spatial-construction-based fault diagnosis method is proposed to detect and locate the abnormality for unknown distributed parameter systems (DPSs). To accurately locate the abnormality, the continuous spatial basis functions (SBFs) are derived by the proposed spatial construction method from empirical data. Theoretical analysis proves that the B-spline curve is a proper solution to the spatial construction problem. Two new statistics are constructed based on the derived continuous SBFs and the improved independent component analysis algorithm. The abnormality can be timely detected according to the reference signals derived by the central limit theorem and hypothesis testing. With the continuous SBFs, the probability distribution of statistic contribution can be constructed to reveal the actual position of the abnormality. The proposed method can timely detect and locate the abnormality under fewer sensors without the knowledge of PDE and boundary conditions. The internal short circuit experiment on a lithium-ion battery demonstrates the effectiveness and superiority of the proposed method.

The thermal effect has a significant impact on the performance and durability of lithium-ion batteries. This article proposes a systematic approach for fast modeling of the distributed battery thermal process. In this method, the time/space (T/S) separation is adopted to decompose the spatio-temporal thermal dynamics. Under the T/S separation, an incremental-learning-based regulator is first employed for the recursive update of spatial basis functions, which can represent the most recent spatial complexity. Then, a corresponding temporal model with incremental adaptive characteristics is developed to capture the temporal nonlinearity. Under such a fully adaptive modeling pattern, the desired temperature distribution can be reconstructed with high efficiency and flexibility. Experimental studies indicate that the proposed method can achieve satisfactory modeling performance while its computational efficiency is outstanding compared to peer methods.

This article investigates the adaptive robust spatial vibration control for a flexible Timoshenko manipulator subject to input dead-zone nonlinearity characteristic. The “disturbance-like” terms and dead-zone nonlinearity are first incorporated into the context of control design, and the new boundary robust adaptive control laws are constructed to reduce the shear deformation and elastic oscillation, ensure the expected angle orientation, handle the input dead-zone, and estimate the upper bound of compound disturbances. The convergence of states and the stability of the system are analyzed and proven without simplifying the infinite dimensional dynamics. In the end, the effectiveness of the presented scheme is demonstrated by the result of simulation research.

Ultrahigh frequency radio-frequency identification (UHF RFID) technology using transducer-integrated antennas provides a cost-effective option for sensing. A novel setup-independent UHF RFID sensing system that can overcome challenges caused by the measurement setup with a priori unknown mutual distance and orientation between the tag and the read/write device (RWD) is proposed. The concept is based on using off-the-shelf radio-frequency identification (RFID) chips having self-tuning capability, which maximizes power transfer coefficient between RFID chip and RFID antenna. An ON-OFF differential (OOD) measurement is implemented to provide setup-independent sensing. The OOD parameters form a 3-D vector that can support more sensing states than prior art using single-dimensional information. Power transfer efficiency (PTE) and tag sensor efficiency (TSE) are defined, where PTE is the minimal power transfer coefficient in all sensing states and TSE is the minimal pairwise Euclidean distance of the OOD parameters. The RFID antenna layout is optimized by optimizing PTE and TSE simultaneously so as to offer sensing robustness without sacrificing communication performance in all sensing states. A water filling-level sensor has been designed and evaluated. Theoretical predications are favorably compared with experimental results under different measurement setups, having different relative distances and orientations between the tag and RWD.

The resonant controller (RC), as a promising candidate for high-speed nonraster nanopositioning applications, can track the sinusoidal reference with zero steady-state error. This article presents a controller composed of several RCs in parallel for tracking nonraster sequential scanning trajectories. The selection for each RC in the parallel array is based on two considerations: one is the spectrum of the reference signal and the other is the harmonics caused by the nonlinearities of the nanopositioning stage. The performance of RC is highly dependent on the accurate placement of the resonant poles, but unfortunately, many existing digital implementation methods could cause a deviation of the resonant poles from their initial locations. To address this problem, a modified Tustin (MTus) method is proposed in this article to implement the controller with better accuracy. Furthermore, the fractional-order (FO) calculus is introduced to improve the transient performance of the RCs. To validate the proposed methods, a comprehensive examination of several types of the nonraster sequential scanning trajectories with a wide frequency range has been carried out on a nanopositioning stage. The results have been compared with other methods, showing that the tracking errors are reduced significantly under the controller implemented by the MTus method especially in high-frequency conditions and that the application of the FO calculus reduces the settling time of the controller by more than 30% in most cases.Note to Practitioners—The demand for high-speed atomic force microscope (AFM) increases rapidly. However, the commonly used raster trajectory limits the achievable scan speed of the AFM. An effective way to improve the scanning and imaging speed of the AFM is the application of the sequential nonraster scanning methods. The trajectories of sequential nonraster scanning patterns mainly composed of few sinusoid signals with different frequencies. Therefore, the resonant controller (RC) is introduced in this article as it is capable to track the sinusoidal reference with zero steady-state error. Several RCs are selected first based on the spectrum analysis of the reference and the consideration of the harmonics caused by the system nonlinearities, and then, they are connected in parallel to form the controller for precise tracking of the reference. In order to realize the digital implementation of the designed controller, a modified Tustin discretization method is proposed, which ensures the accurate resonant pole placement of the RC and thus maintains the tracking performance of the RC. In addition, the fractional-order (FO) calculus is introduced to speed up the convergence of the designed controller while preserving the tracking accuracy, and this parallel-structure FO RC (PSFORC) design can be implemented to other systems that require high-speed and high-accuracy tracking of the periodic signals.

We propose, in this paper, a framework for time series and nonlinear system modeling, called the basis function matrix-based flexible coefficient autoregressive (BFM-FCAR) model. It has very flexible nonlinear structure. We show that many famous nonlinear time series models can be derived under this framework by choosing the proper basis function matrices. Some probabilistic properties (the conditions of geometrical ergodicity) of the BFM-FCAR model are investigated. Taking advantage of the model structure, we present an efficient parameter estimation algorithm for the proposed framework by using the variable projection method. Finally, we show how new models are generated from the proposed framework.

This paper introduces a fuzzy control (FC) under spatially local averaged measurements (SLAMs) for nonlinear-delayed distributed parameter systems (DDPSs) represented by parabolic partial differential-difference equations (PDdEs), where the fast-varying time delay and slow-varying one are considered. A Takagi-Sugeno (T-S) fuzzy PDdE model is first derived to exactly describe the nonlinear DDPSs. Then, by virtue of the T-S fuzzy PDdE model and a Lyapunov-Krasovskii functional, an FC design under SLAMs, where the membership functions of the proposed FC law are determined by the measurement output and independent of the fuzzy PDdE plant model, is developed on basis of spatial linear matrix inequalities (SLMIs) to guarantee the exponential stability for the resulting closed-loop DDPSs. Lastly, a numerical example is offered to support the presented approach.

This article considers the synchronization problem of delayed reaction-diffusion neural networks via quantized sampled-data (SD) control under spatially point measurements (SPMs), where distributed and discrete delays are considered. The synchronization scheme, which takes into account the communication limitations of quantization and variable sampling, is based on SPMs and only available in a finite number of fixed spatial points. By utilizing inequality techniques and Lyapunov-Krasovskii functional, some synchronization criteria via a quantized SD controller under SPMs are established and presented by linear matrix inequalities, which can ensure the exponential stability of the synchronization error system containing the drive and response dynamics. Finally, two numerical examples are offered to support the proposed quantized SD synchronization method.

Lithium-ion batteries are widely used as power sources in industrial applications. Electrochemical models and simulations are crucial to disclose many details that cannot be directly measured through experiments. Parameter identification of an accurate electrochemical model is much more cost-effective than direct and destructive measurement methods. However, the complex structure and strong nonlinearity of electrochemical models will make the parameter identification very difficult. Additionally, time-consuming electrochemical simulations can significantly limit the identification efficiency. This article proposes a surrogate-model-based scheme to achieve high-efficiency parameter identification of an electrochemical battery model. To be specific, the proposed method is implemented by the close integration of an evolutionary algorithm and a surrogate model. A sensitivity-based identification strategy is first designed to alleviate the difficulty of optimization. Then, a surrogate model is developed from historical data to gradually approach the objective function used for parameter evaluations. Finally, an evolutionary algorithm is employed to find promising solutions by minimizing the output of the surrogate model. Simulations and experimental studies demonstrate the effectiveness and high efficiency of the proposed method.

Identification of abnormal source hidden in distributed parameter systems (DPSs) belongs to the category of inverse source problems. It is important in industrial applications but seldom studied. In this article, we make the first attempt to investigate the abnormal spatio-temporal (S-T) source identification for a class of DPSs. An inverse S-T model for abnormal source identification is developed for the first time. It consists of an adaptive state observer for source identification and an adaptive source estimation algorithm. One major advantage of the proposed inverse S-T model is that only the system output is utilized, without any state measurement. Theoretic analysis is conducted to guarantee the convergence of the estimation error. Finally, the performance of the proposed method is evaluated on a heat transfer rod with an abnormal S-T source.

For complex distributed parameter systems (DPSs) with strong nonlinearities and time-varying dynamics, the conventional spatiotemporal modeling methods become ill-suited since the elementary assumption that the process data follow a unimodal Gaussian distribution usually becomes invalid. In this paper, a multimode method is proposed for modeling of such systems. First, the original operating space is partitioned along the time dimension into several subspaces via modified dissimilarity analysis. Each subspace represents the local spatiotemporal characteristics of the original system. Second, the Karhunen-Loève decomposition (KLD)-based spatiotemporal modeling approach is applied to approximate the local dynamics of each subspace. Finally, an ensemble model is obtained using the soft weighting sum of the local ones, where the corresponding weights are calculated by principal component regression. By properly decomposing the original space into several local parts, the ensemble model is capable of handling the strong nonlinearities and time-varying dynamics of the system. The validity and efficiency of the proposed method are verified on two representative applications: 1) a one-dimensional parabolic catalytic rod and 2) a two-dimensional curing thermal process. The experimental results show that the proposed method provides a superior performance regarding modeling accuracy compared to several baselines.

Pareto dominance-based multiobjective optimization has been successfully applied to constrained evolutionary optimization during the last two decades. However, as another famous multiobjective optimization framework, decomposition-based multiobjective optimization has not received sufficient attention from constrained evolutionary optimization. In this paper, we make use of decomposition-based multiobjective optimization to solve constrained optimization problems (COPs). In our method, first of all, a COP is transformed into a biobjective optimization problem (BOP). Afterward, the transformed BOP is decomposed into a number of scalar optimization subproblems. After generating an offspring for each subproblem by differential evolution, the weighted sum method is utilized for selection. In addition, to make decomposition-based multiobjective optimization suit the characteristics of constrained evolutionary optimization, weight vectors are elaborately adjusted. Moreover, for some extremely complicated COPs, a restart strategy is introduced to help the population jump out of a local optimum in the infeasible region. Extensive experiments on three sets of benchmark test functions, namely, 24 test functions from IEEE CEC2006, 36 test functions from IEEE CEC2010, and 56 test functions from IEEE CEC2017, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods.

A reinforcement learning-based method is proposed for optimal sensor placement in the spatial domain for modeling distributed parameter systems (DPSs). First, a low-dimensional subspace, derived by Karhunen-Loève decomposition, is identified to capture the dominant dynamic features of the DPS. Second, a spatial objective function is proposed for the sensor placement. This function is defined in the obtained low-dimensional subspace by exploiting the time-space separation property of distributed processes, and in turn aims at minimizing the modeling error over the entire time and space domain. Third, the sensor placement configuration is mathematically formulated as a Markov decision process (MDP) with specified elements. Finally, the sensor locations are optimized through learning the optimal policies of the MDP according to the spatial objective function. The experimental results of a simulated catalytic rod and a real snap curing oven system are provided to demonstrate the feasibility and efficiency of the proposed method in solving the combinatorial optimization problems, such as optimal sensor placement.

The construction of spatial basis functions (BFs) is critical to the time/space separation of the distributed parameter system (DPS). The spatial BFs constructed by traditional Karhunen-Loéve may not work satisfactorily for two spatial-dimensional (2-D) DPS, because of a distorted mapping of the original sensor array in the row-wise vectorization process. In this article, a novel time/space separation based method is proposed to construct dimension embedded BFs (DE-BFs) for modeling 2-D DPS. The DE-BFs are first formulated according to the spatial sensor array structure, and sequentially optimized with alternating least squares by minimizing the reconstruction error. The mapping relationship between the DE-BFs and the spatial sensor array is well preserved. In addition, the coupling across temporal and different spatial dimensions is sufficiently captured. A satisfactory model accuracy can be achieved by the DE-BFs, even with limited training data. Experiments of a 2-D curing thermal process are used to verify the effectiveness of the proposed method.

A novel data-driven approach is proposed to localize the abnormality for distributed parameter systems (DPSs) in this paper. The cross-correlation order of DPSs in the space domain is first obtained by the cumulants-based identification method. Then, a spatial augmented matrix of the spatial-temporal distribution data is formed and a dynamic spatial independent component analysis method is proposed for independent decomposition. The dominant spatial independent components will be extracted and the spatial residuals can be produced for spatial reference statistics. Through the kernel density estimation method, the confidence bounds of these statistics in normal condition (abnormality free) can be established as the spatial references. These unique two references will guarantee the reliable spatial localization of abnormality. Different from model-based methods that rely on an explicit system model of the process, the proposed approach is model free and only uses recorded process data. Experiments on two typical DPSs demonstrate the effectiveness of the proposed approach.

In this paper, a systematic incremental learning method is presented for reinforcement learning in continuous spaces where the learning environment is dynamic. The goal is to adjust the previously learned policy in the original environment to a new one incrementally whenever the environment changes. To improve the adaptability to the ever-changing environment, we propose a two-step solution incorporated with the incremental learning procedure: policy relaxation and importance weighting. First, the behavior policy is relaxed to a random one in the initial learning episodes to encourage a proper exploration in the new environment. It alleviates the conflict between the new information and the existing knowledge for a better adaptation in the long term. Second, it is observed that episodes receiving higher returns are more in line with the new environment, and hence contain more new information. During parameter updating, we assign higher importance weights to the learning episodes that contain more new information, thus encouraging the previous optimal policy to be faster adapted to a new one that fits in the new environment. Empirical studies on continuous controlling tasks with varying configurations verify that the proposed method achieves a significantly faster adaptation to various dynamic environments than the baselines.

Identifying reliable information from the information ocean is a natural talent of human being, which can be hardly formalized by machines. In this paper, we show how to measure the degree of uncertainty in terms of interpoint similarity. For applications under complex uncertainty, it is desirable that we provide a systematic way for users to identify reliable information. In our approach, the similarity uncertainty for different kinds of data sets is defined according to the Shannon entropy theory. Then, similarity constrained models are designed to guarantee superior learning performance under uncertainty. Experiments using both simulation data set and several public data sets, can clearly demonstrate significant improvements of the proposed method under large uncertainty.

This paper considers the estimator-based H sampled-data fuzzy control (SDFC) problem of nonlinear parabolic partial differential equation (PDE) systems. First, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is proposed to represent the nonlinear PDE system. Second, with the aid of the T-S fuzzy PDE model, an estimator-based SDFC design ensuring the exponential stability of the closed-loop fuzzy PDE system with an H performance is developed via a Lyapunov functional. The outcome of the estimator-based H∞SDFC problem is formulated as a bilinear matrix inequality optimization problem, which is solved by an iterative algorithm on the basis of the linear matrix inequalities. Finally, for demonstrating the effectiveness of the proposed method, simulation results are provided to control the diffusion equation and the FitzHugh-Nagumo equation.

In this paper, a novel incremental learning based subspace modeling method is developed for spatiotemporal modeling of distributed parameter systems (DPSs). First, the streaming snapshots are collected into small batches at a preset time interval in an online mode. The initial batch belongs to the first nominal subspace. Second, the dissimilarity analysis is further utilized to assign each new batch to one of the existing subspaces or a new subspace. Third, the local basis functions corresponding to the assigned subspace is updated or generated through incremental learning of the new batch data. Finally, all the local models are ensembled to approximate the system's dynamics over the whole time-space domain in real-time. The proposed method is tested on a hyperbolic advection system and a one-dimensional diffusion-reaction system. Results demonstrate that the proposed method is superior to the conventional global modeling, and achieves higher modeling accuracy for DPSs.

A tensor decomposition (TD) based method is proposed for modeling two spatial-dimensional (2-D) distributed thermal processes. Firstly TD is executed to the spatiotemporal tensor to accomplish time/space separation. Spatial basis functions (SBFs) and temporal coefficients are extracted. Then the least-squares support vector machine (LS-SVM) approach is used to learn the system dynamics in a low-dimensional temporal domain. Finally, the temperature distribution can be reconstructed by time/space synthesis. The proposed method well preserves the sensor array structure during constructing SBFs. The couplings across temporal and each spatial dimensions are also sufficiently captured. Experiments of a 2-D distributed thermal process inside of a curing oven are used to verify the effectiveness of the proposed method.

This paper presents a Lyapunov and partial differential equation (PDE)-based methodology to solve static collocated piecewise fuzzy control design of quasi-linear parabolic PDE systems subject to periodic boundary conditions. Two types of piecewise control, i.e., globally piecewise control and locally piecewise control are considered, respectively. A Takagi-Sugeno (T-S) fuzzy PDE model that is constructed via local sector nonlinearity method is first employed to accurately describe spatiotemporal dynamics of quasi-linear PDEs. Based on the T-S fuzzy PDE model, a static collocated piecewise fuzzy feedback controller is constructed to guarantee the locally exponential stability of the resulting closed-loop system. Sufficient conditions for the existence of such fuzzy controller are developed by applying vector-valued Poincaré-Wirtinger inequality and its variants and a linear matrix inequality (LMI) relaxation technique. These sufficient conditions are presented in terms of standard LMIs. Finally, the performance of the suggested fuzzy controller is illustrated by numerical simulation results of a nonlinear PDE system described by quasi-linear FitzHugh-Nagumo equation with periodic boundary conditions.

Data-based spatio-temporal modeling has rapidly developed over the past ten years. However, traditional spatio-temporal modeling methods will encounter some uncertainty caused by model reduction. In addition, the established model is complicated and short of linguistic interpretability. In this study, a novel three-dimensional (3-D) fuzzy modeling framework without model reduction is proposed and a new 3-D fuzzy modeling method based on clustering and support vector regression is developed. This method is based on a 3-D fuzzy system that naturally fuses time/space separation and time/space synthesis into a unified framework. Utilizing the machine learning algorithms (clustering and support vector regression), a 3-D fuzzy system is constructed for modeling an unknown nonlinear distributed parameter system. The advantages of the proposed modeling method over the traditional spatio-temporal modeling method are linguistic interpretability and no reliance on model reduction. The proposed modeling method consists of three steps. First, the nearest neighborhood clustering algorithm is used to learn initial structure model of antecedent sets of 3-D fuzzy rules. Then, similarity measure is used to simplify the initial structure via combining similar fuzzy sets and similar fuzzy rules. Finally, a support vector regression algorithm is applied to calculate spatial functions in the consequent sets of 3-D fuzzy rules. The simulation results demonstrate the effectiveness of the proposed modeling method.

Temperature monitoring is indispensable to the optimal and safe operation of a lithium-ion battery. In this paper, a spatio-temporal learning model designed by evolutionary algorithm is proposed to predict the thermal distribution. To formulate the multicharacteristic spatial dynamics, the chicken swarm optimization, based fusion of different dimensionality-reduction methods, is proposed for learning spatial basis functions. Through integration with the time/space separation based approach and equivalent circuit model based thermal model, the reduced-order model is derived. The related parameters of the reduced-order model are identified by integrating chicken swarm optimization with time/space separation based approach. A Bayesian-regularized neural-network based compensation model is developed to compensate for the model errors caused by the spatio-temporal coupled dynamics. Based on the Rademacher complexity, the generalization bound of the proposed model is analyzed. Simulations and comparisons demonstrate the superiority of the proposed model.

Time/space separation based spatiotemporal modeling methods have been proven to be effective and efficient for modeling a class of distributed parameter systems (DPSs). However, these conventional methods may not work satisfactorily for DPSs with time-dependent boundary conditions. A sliding window based dynamic spatiotemporal modeling method is proposed for this kind of DPSs. First, the sliding window is appropriately designed to capture the most recent spatiotemporal data. Then, the conventional Karhunen-Loève method can be used to construct the analytical model. Besides, a more general sliding window method can be achieved by using a forgetting factor to adjust different influence of the current and previous data. This analytical model can be utilized for online performance prediction. Simulation experiments on a benchmark and a battery with unknown boundary cooling have demonstrated the superior performance of the proposed method on the DPSs with time-dependent boundary conditions.

An incremental spatiotemporal learning scheme is proposed for online modeling of distributed parameter systems (DPSs). A novel incremental learning method is developed to recursively update the spatial basis functions and the corresponding temporal model based on the Karhunen-Loève decomposition for time-space separation. The time-space synthesis continually evolves by adding new increment data with more updated information and revising the existing parameters of the dynamic system. In this way, the spatiotemporal structure is inherited and updated efficiently as output data increases over time. The adaptive nature of this evolving structure makes it promising for online modeling of DPSs under streaming data environment. The proposed incremental modeling scheme is evaluated on the classical benchmark of a catalytic rod problem. The simulation results demonstrate the viability and efficiency of the proposed method for online modeling of DPSs.

When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the ε constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods.

Distributed parameter systems widely exist in many industrial thermal processes. Estimation of their temperature distribution in the entire operating area is not easy as the dynamics are time/space coupled, and there are only a few sensors available for measurement. In this paper, an effective spatiotemporal model is proposed for prediction of the temperature distribution. After the dominant spatial basis functions are obtained by the Karhunen-Loève method under the time/space separation, a kernel-based random vector functional-link network is developed for learning unknown temporal dynamics. After time/space synthesis, the spatiotemporal model can be constructed to effectively estimate the temperature distribution in high learning speed. The generalization performance of this model is discussed using Rademacher complexity. Simulations on two typical industrial thermal processes show that the proposed method has superior model performance than neural networks and least square support vector machine.

In this paper, a spatio/temporal separation based method is developed to detect fault and its spatial location for distributed parameter systems. Firstly, the original infinite-dimensional system is transformed into a finite-dimensional system by time/space separation and model reduction techniques. Then both independent component analysis and time/space synthesis methods are adopted to construct the monitoring model. Finally, experiments on a typical parabolic distributed parameter system are used to verify the effectiveness of the proposed approach.

A multi-task learning based spatiotemporal modeling method is proposed to construct analytical models of distributed thermal processes. Firstly, the time/space separation based framework is utilized to reduce a distributed thermal process into a finite-dimensional system, which is composed of a set of time series. Afterward, the multi-task learning based least squares support vector machine (ML-LS-SVM) is employed to model these time series which are related to each other. Finally, through time/space synthesis, the nonlinear spatiotemporal dynamics can be achieved. Experiments on a curing process have validated the effectiveness of the proposed method. The superiority of ML-LS-SVM over LS-SVM has also been demonstrated experimentally.

In this study, we propose an automated framework that combines diffusion tensor imaging (DTI) metrics with machine learning algorithms to accurately classify control groups and groups with cervical spondylotic myelopathy (CSM) in the spinal cord. The comparison between selected voxel-based classification and mean value-based classification were performed. A support vector machine (SVM) classifier using a selected voxel-based dataset produced an accuracy of 95.73%, sensitivity of 93.41% and specificity of 98.64%. The efficacy of each index of diffusion for classification was also evaluated. Using the proposed approach, myelopathic areas in CSM are detected to provide an accurate reference to assist spine surgeons in surgical planning in complicated cases.

The extreme learning machine (ELM) has been extensively studied in the machine learning field and has been widely implemented due to its simplified algorithm and reduced computational costs. However, it is less effective for modeling data with non-Gaussian noise or data containing outliers. Here, a probabilistic regularized ELM is proposed to improve modeling performance with data containing non-Gaussian noise and/or outliers. While traditional ELM minimizes modeling error by using a worst-case scenario principle, the proposed method constructs a new objective function to minimize both mean and variance of this modeling error. Thus, the proposed method considers the modeling error distribution. A solution method is then developed for this new objective function and the proposed method is further proved to be more robust when compared with traditional ELM, even when subject to noise or outliers. Several experimental cases demonstrate that the proposed method has better modeling performance for problems with non-Gaussian noise or outliers.

This paper employs a Takagi-Sugeno (T-S) fuzzy partial differential equation (PDE) model to solve the problem of sampled-data exponential stabilization in the sense of spatial ∥·∥∞for a class of nonlinear parabolic distributed parameter systems (DPSs), where only a few actuators and sensors are discretely distributed in space. Initially, a T-S fuzzy PDE model is assumed to be derived by the sector nonlinearity method to accurately describe complex spatiotemporal dynamics of the nonlinear DPSs. Subsequently, a static sampled-data fuzzy local state feedback controller is constructed based on the T-S fuzzy PDE model. By constructing an appropriate Lyapunov-Krasovskii functional candidate and employing vector-valued Wirtinger's inequalities, a variation of vector-valued Poincaré-Wirtinger inequality in one-dimensional spatial domain, as well as a vector-valued Agmon's inequality, it is shown that the suggested sampled-data fuzzy controller exponentially stabilizes the nonlinear DPSs in the sense of ∥·∥∞, if sufficient conditions presented in term of standard linear matrix inequalities (LMIs) are fulfilled. Moreover, an LMI relaxation technique is utilized to enhance exponential stabilization ability of the suggested sampled-data fuzzy controller. Finally, the satisfactory and better performance of the suggested sampled-data fuzzy controller are demonstrated by numerical simulation results of two examples.

The real-time monitoring of temperature distribution in lithium-ion batteries (LIBs) is crucial for their safety and optimal operation in electrical vehicles. An accurate and effective thermal model is needed for online temperature monitoring since limited sensors are available in vehicle application. In this paper, a data-based spatiotemporal modeling method is researched for online estimation of temperature distribution of LIBs. First, Isometric Mapping (ISOMAP) method is used for time/space separation and model reduction. Then, the low-dimensional representation can be obtained in terms of ISOMAP based mapping functions. The unknown temporal dynamics in the low-dimensional space can be approximated using neural network model with parameters trained using extreme learning machine (ELM) algorithm. Finally, the spatiotemporal model of the thermal process can be reconstructed by integrating the neural network model and the mapping functions. The generalization bound of the proposed spatiotemporal model can be analyzed using Rademacher complexity. Simulation results showed that the proposed modeling method can model the LIB thermal process very well.

This paper considers a least square regularized regression algorithm for multi-task learning in a union of reproducing kernel Hilbert spaces (RKHSs) with Gaussian kernels. It is assumed that the optimal prediction function of the target task and those of related tasks are in an RKHS with the same but with unknown Gaussian kernel width. The samples for related tasks are used to select the Gaussian kernel width, and the sample for the target task is used to obtain the prediction function in the RKHS with this selected width. With an error decomposition result, a fast learning rate is obtained for the target task. The key step is to estimate the sample errors of related tasks in the union of RKHSs with Gaussian kernels. The utility of this algorithm is illustrated with one simulated data set and four real data sets. The experiment results illustrate that the underlying algorithm can result in significant improvements in prediction error when few samples of the target task and more samples of related tasks are available.

Uncertain data clustering has been recognized as an essential task in the research of data mining. Many centralized clustering algorithms are extended by defining new distance or similarity measurements to tackle this issue. With the fast development of network applications, these centralized methods show their limitations in conducting data clustering in a large dynamic distributed peer-to-peer network due to the privacy and security concerns or the technical constraints brought by distributive environments. In this paper, we propose a novel distributed uncertain data clustering algorithm, in which the centralized global clustering solution is approximated by performing distributed clustering. To shorten the execution time, the reduction technique is then applied to transform the proposed method into its deterministic form by replacing each uncertain data object with its expected centroid. Finally, the attribute-weight-entropy regularization technique enhances the proposed distributed clustering method to achieve better results in data clustering and extract the essential features for cluster identification. The experiments on both synthetic and real-world data have shown the efficiency and superiority of the presented algorithm.

The temperature distribution in the curing oven is a typical distributed parameter system (DPS). Modeling of this kind of system is very difficult as only few sensors are available inside. Besides, thermal behaviors of the oven are time-varying in the directions of space and time. In this paper, an adaptive spatiotemporal modeling method is designed for the curing thermal process. Time-varying spatial basis functions are first obtained under adaptive time/space separation. An online sequential extreme learning machine (OS-ELM) is further developed for online modeling of the time-varying dynamics in time direction. Finally, the temperature distribution of the oven can be estimated by the adaptive spatiotemporal model. Simulation results demonstrate the superior of the proposed modeling method.

In this paper, a sampled-data fuzzy control problem is addressed for a class of nonlinear coupled systems, which are described by a parabolic partial differential equation (PDE) and an ordinary differential equation (ODE). Initially, the nonlinear coupled system is accurately represented by the Takagi-Sugeno (T-S) fuzzy coupled parabolic PDE-ODE model. Then, based on the T-S fuzzy model, a novel time-dependent Lyapunov functional is used to design a sampled-data fuzzy controller such that the closed-loop coupled system is exponentially stable, where the sampled-data fuzzy controller consists of the ODE state feedback and the PDE static output feedback under spatially averaged measurements. The stabilization condition is presented in terms of a set of linear matrix inequalities. Finally, simulation results on the control of a hypersonic rocket car are given to illustrate the effectiveness of the proposed design method.

The classification problem in the real-world applications always involves uncertainties in both stochastic and fuzzy nature. This paper proposes a classification framework based on the unified probabilistic fuzzy configuration for data with uncertainties in both stochastic and fuzzy nature. The design and tuning procedures are also developed in terms of probability-based performance measure for working in the complex environment. A theoretical analysis is conducted to derive its quantificational model and disclose the interesting features. In addition to a superior performance than the traditional fuzzy method, the proposed method generates probabilistic fuzzy rules that can help users to better understand how the classifier works. This explainable characteristic is crucial for the decision making. Finally, the effectiveness of the proposed classifier will be demonstrated on its application to the Pima Indians Diabetes data and low back pain diagnosis. The satisfactory classification and the explainable characteristic disclose its potential in classification of data with uncertainties.

This paper gives a membership-function-dependent approach to solve the design problem of fuzzy pointwise state feedback controller for a class of nonlinear distributed parameter systems modeled by semilinear parabolic partial differential equations (PDEs), where only a few actuators are discretely distributed in space. In the proposed design method, a Takagi-Sugeno (T-S) fuzzy PDE model obtained by using the sector nonlinearity method is first utilized to accurately describe the nonlinear spatiotemporal dynamics of the PDE system. As only the state information at some known specified points in the spatial domain (i.e., the pointwise state information) is available for the controller design, the favorable property offered by sharing all the same premises in the fuzzy PDE plant model and fuzzy controller cannot be employed to develop the fuzzy control design method. To overcome this drawback, a linear matrix inequality (LMI) relaxation technique is developed to enhance the stabilization ability of the fuzzy controller. Based on the T-S fuzzy PDE model, a membership-function-dependent fuzzy pointwise state feedback control design is then proposed by employing the Lyapunov technique, integration by parts, the vector-valued Wirtinger's inequality and the LMI relaxation technique, and presented in term of standard LMIs. Finally, the satisfactory and better performance of the proposed design method are demonstrated by the extensive numerical simulation results of two numerical examples.

The basic idea of most distance metric learning methods is to find a space that can optimally classify data points belong to different categories. However, current methods only learn one Mahalanobis distance for each data set, which actually fails to perfectly classify different categories in most real world applications. To improve the classification accuracy of k-nearest-neighbour algorithm, a multi-metric learning method is proposed in this paper to completely classify different categories by sequentially learning sub-metrics. The proposed algorithm is based on minimizing the Burg matrix divergence between metrics. The experiments on five UCI data sets demonstrate the improved performance of Multi-Metric learning when comparing with the state-of-the-art methods.

This paper presents a deep auto-encoder based model reduction method for large scale spatiotemporal process. This method includes three phases in order to find the near-optimal parameters of the reduced order model. The sequence of the phases is allocated according to the idea of greedy training which approximately minimizes the modeling error. This method also avoids including the spatial dimensionality into the model which enables it to handle large-scale model reduction. Two case studies are carried out to demonstrate the effectiveness of the method.

When solving constrained optimization problems by evolutionary algorithms, an important issue is how to balance constraints and objective function. This paper presents a new method to address the above issue. In our method, after generating an offspring for each parent in the population by making use of differential evolution (DE), the well-known feasibility rule is used to compare the offspring and its parent. Since the feasibility rule prefers constraints to objective function, the objective function information has been exploited as follows: if the offspring cannot survive into the next generation and if the objective function value of the offspring is better than that of the parent, then the offspring is stored into a predefined archive. Subsequently, the individuals in the archive are used to replace some individuals in the population according to a replacement mechanism. Moreover, a mutation strategy is proposed to help the population jump out of a local optimum in the infeasible region. Note that, in the replacement mechanism and the mutation strategy, the comparison of individuals is based on objective function. In addition, the information of objective function has also been utilized to generate offspring in DE. By the above processes, this paper achieves an effective balance between constraints and objective function in constrained evolutionary optimization. The performance of our method has been tested on two sets of benchmark test functions, namely, 24 test functions at IEEE CEC2006 and 18 test functions with 10-D and 30-D at IEEE CEC2010. The experimental results have demonstrated that our method shows better or at least competitive performance against other state-of-the-art methods. Furthermore, the advantage of our method increases with the increase of the number of decision variables.

The least squares support vector machine (LS-SVM) has emerged as a popular data-driven modeling method and been extensively studied in the machine learning community. However, the LS-SVM is sensitive to noisy data and may not be effective when the level of noise is high. In this paper, a probabilistic LS-SVM is proposed to have a more reliable performance. First, a distributed LS-SVM is constructed with parameters estimated from data samples. Due to distributed nature of multiple LS-SVM, the stochastic property of parameters can be easily obtained and processed. Using the distribution characteristics of these parameters, the final outcome is derived through the probabilistic inference and thus be evaluated statistically. Its parallel structure is also suitable for parallel computing to reduce computing time. Both simulations and experiments demonstrate the effectiveness of the proposed probabilistic LS-SVM.

This paper presents a deep learning-based model reduction method for distributed parameter systems (DPSs). The proposed method includes three phases. In phase I, numerical or experimental data of the spatiotemporal distribution is reduced into low-dimensional representations using the deep auto-encoder (DAE). In phase II, the low-dimensional representations are used to establish the reduced-order model. In phase III, the reduced model is then used to reconstruct the high-dimensional DPS. Experimental studies are conducted to validate the proposed method. The proposed method is compared with the classical proper orthogonal decomposition method and demonstrates better modeling accuracy and efficiency in the experiments.

Large-scale lithium-ion batteries (LLB) are crucial energy sources for hybrid electrical vehicles. Predicting their electrochemical states is critical in maintaining the safety and performance of LLB. Electrochemical behaviors of LLB have spatiotemporal dynamics. Their physical model is coupled partial differential equations which are not suitable for online states estimation. In this article, we present a space-time separation method to intelligently modeling the internal states distribution, including potential of electrodes and depth of discharge. The proposed models are validated by simulation.

In order to control the temperature distribution on the wafer in a rapid thermal processing system, we develop a learning control approach based on the dominant modes of the system state. Firstly, the dominant modes of the system state are extracted through the K-L method. Galerkin's method is utilized to construct the reduced model of the system from the dominant modes. Then learning control approach is designed based on this reduced model. Simulations are performed by heating the wafer from 300K to 1000K with the proposed control method. Simulation results show that the proposed control method has superb ability to reduce the temperature tracking error and improve the temperature uniformity among the wafer.

We propose a gradient radial basis function based varying-coefficient autoregressive (GRBF-AR) model for modeling and predicting time series that exhibit nonlinearity and homogeneous nonstationarity. This GRBF-AR model is a synthesis of the gradient RBF and the functional-coefficient autoregressive (FAR) model. The gradient RBFs, which react to the gradient of the series, are used to construct varying coefficients of the FAR model. The Mackey-Glass chaotic time series are used to evaluate the performance of the proposed method. It is shown that the GRBF-AR model not only achieves much more parsimonious structure but also much better prediction performance than that of GRBF network.

The radial basis function network-based autoregressive with exogenous inputs (RBF-ARX) models have much more linear parameters than nonlinear parameters. Taking advantage of this special structure, a variable projection algorithm is proposed to estimate the model parameters more efficiently by eliminating the linear parameters through the orthogonal projection. The proposed method not only substantially reduces the dimension of parameter space of RBF-ARX model but also results in a better-conditioned problem. In this paper, both the full Jacobian matrix of Golub and Pereyra and the Kaufman's simplification are used to test the performance of the algorithm. An example of chaotic time series modeling is presented for the numerical comparison. It clearly demonstrates that the proposed approach is computationally more efficient than the previous structured nonlinear parameter optimization method and the conventional Levenberg-Marquardt algorithm without the parameters separated. Finally, the proposed method is also applied to a simulated nonlinear single-input single-output process, a time-varying nonlinear process and a real multiinput multioutput nonlinear industrial process to illustrate its usefulness.

In the field of evolutionary computation, there has been a growing interest in applying evolutionary algorithms to solve multimodal optimization problems (MMOPs). Due to the fact that an MMOP involves multiple optimal solutions, many niching methods have been suggested and incorporated into evolutionary algorithms for locating such optimal solutions in a single run. In this paper, we propose a novel transformation technique based on multiobjective optimization for MMOPs, called MOMMOP. MOMMOP transforms an MMOP into a multiobjective optimization problem with two conflicting objectives. After the above transformation, all the optimal solutions of an MMOP become the Pareto optimal solutions of the transformed problem. Thus, multiobjective evolutionary algorithms can be readily applied to find a set of representative Pareto optimal solutions of the transformed problem, and as a result, multiple optimal solutions of the original MMOP could also be simultaneously located in a single run. In principle, MOMMOP is an implicit niching method. In this paper, we also discuss two issues in MOMMOP and introduce two new comparison criteria. MOMMOP has been used to solve 20 multimodal benchmark test functions, after combining with nondominated sorting and differential evolution. Systematic experiments have indicated that MOMMOP outperforms a number of methods for multimodal optimization, including four recent methods at the 2013 IEEE Congress on Evolutionary Computation, four state-of-the-art single-objective optimization based methods, and two well-known multiobjective optimization based approaches.

Nonlinear equation systems may have multiple optimal solutions. The main task of solving nonlinear equation systems is to simultaneously locate these optimal solutions in a single run. When solving nonlinear equation systems by evolutionary algorithms, usually a nonlinear equation system should be transformed into a kind of optimization problem. At present, various transformation techniques have been proposed. This paper presents a simple and generic transformation technique based on multiobjective optimization for nonlinear equation systems. Unlike the previous work, our transformation technique transforms a nonlinear equation system into a biobjective optimization problem that can be decomposed into two parts. The advantages of our transformation technique are twofold: 1) all the optimal solutions of a nonlinear equation system are the Pareto optimal solutions of the transformed problem, which are mapped into diverse points in the objective space, and 2) multiobjective evolutionary algorithms can be directly applied to handle the transformed problem. In order to verify the effectiveness of our transformation technique, it has been integrated with nondominated sorting genetic algorithm II to solve nonlinear equation systems. The experimental results have demonstrated that, overall, our transformation technique outperforms another state-of-the-art multiobjective optimization based transformation technique and four single-objective optimization based approaches on a set of test instances. The influence of the types of Pareto front on the performance of our transformation technique has been investigated empirically. Moreover, the limitation of our transformation technique has also been identified and discussed in this paper.

Highly dissipative nonlinear partial differential equations (PDEs) are widely employed to describe the system dynamics of industrial spatially distributed processes (SDPs). In this paper, we consider the optimal control problem of the general highly dissipative SDPs, and propose an adaptive optimal control approach based on neuro-dynamic programming (NDP). Initially, Karhunen-Loève decomposition is employed to compute empirical eigenfunctions (EEFs) of the SDP based on the method of snapshots. These EEFs together with singular perturbation technique are then used to obtain a finite-dimensional slow subsystem of ordinary differential equations that accurately describes the dominant dynamics of the PDE system. Subsequently, the optimal control problem is reformulated on the basis of the slow subsystem, which is further converted to solve a Hamilton-Jacobi-Bellman (HJB) equation. HJB equation is a nonlinear PDE that has proven to be impossible to solve analytically. Thus, an adaptive optimal control method is developed via NDP that solves the HJB equation online using neural network (NN) for approximating the value function; and an online NN weight tuning law is proposed without requiring an initial stabilizing control policy. Moreover, by involving the NN estimation error, we prove that the original closed-loop PDE system with the adaptive optimal control policy is semiglobally uniformly ultimately bounded. Finally, the developed method is tested on a nonlinear diffusion-convection-reaction process and applied to a temperature cooling fin of high-speed aerospace vehicle, and the achieved results show its effectiveness.

The safety, life, and performance of lithium ion batteries are all related to its thermal performance. The battery thermal process is a typical distributed parameter system which is spatiotemporal distributed. The online estimation of temperature distribution in vehicle battery systems is not easy as only few surface temperatures can be measured for the distributed parameter process. In this paper, a state observer is designed for lithium ion battery thermal process described by two dimensional partial differential equations. Based on the physical model of battery thermal process, a reduced order operational model suitable for online application is first obtained through Karhunen-Loeve decomposition. An adaptive observer is then designed based on the reduced order model. The whole temperature filed can then be reconstructed with the designed observer and measured voltage, current, and few surface temperature dates. Numerical simulation demonstrates the effectiveness of the designed observer.

We consider in this paper a class of nonlinear least squares problems in which the model can be represented as a linear combination of nonlinear functions. The variable projection algorithm projects the linear parameters out of the problem, leaving the nonlinear least squares problems involving only the nonlinear parameters. To implement the variable projection algorithm more efficiently, we propose a new variable projection functional based on matrix decomposition. The advantage of the proposed formulation is that the size of the decomposed matrix may be much smaller than those of previous ones. The Levenberg-Marquardt algorithm using finite difference method is then applied to minimize the new criterion. Numerical results show that the proposed approach achieves significant reduction in computing time.

This paper addresses the problem of fuzzy control design for a class of nonlinear distributed parameter systems represented by a cascaded model consisting of a Takagi-Sugeno (T-S) fuzzy ordinary differential equation and a linear first-order hyperbolic partial differential equation (PDE), where the control input affects the entire system through a boundary condition of the PDE. This characteristic makes the PDE subject to an inhomogeneous boundary condition. A state transformation is introduced to make the inhomogeneous boundary condition homogeneous, and a composite Lyapunov function that involves a fuzzy Lyapunov function and an entropy-like Lyapunov function is constructed for the transformed system. Based on this composite Lyapunov function, a sufficient condition for the closed-loop exponential stability of the cascaded system is presented in terms of a set of algebraic linear matrix inequalities in space. Using the sector bound approach and the finite spatial domain, a linear matrix inequality-based fuzzy control design procedure is developed from the obtained stability analysis result. Finally, simulation results on two numerical examples are provided to illustrate the effectiveness and merit of the proposed design method.

This paper deals with the problem of fuzzy boundary control design for a class of nonlinear distributed parameter systems which are described by semilinear parabolic partial differential equations (PDEs). Both distributed measurement form and collocated boundary measurement form are considered. A Takagi–Sugeno (T–S) fuzzy PDE model is first applied to accurately represent the semilinear parabolic PDE system. Based on the T–S fuzzy PDE model, two types of fuzzy boundary controllers, which are easily implemented since only boundary actuators are used, are proposed to ensure the exponential stability of the resulting closed-loop system. Sufficient conditions of exponential stabilization are established by employing the Lyapunov direct method and the vector-valued Wirtinger's inequality and presented in terms of standard linear matrix inequalities. Finally, the advantages and effectiveness of the proposed control methodology are demonstrated by the simulation results of two examples.

Due to privacy and security requirements or technical constraints, traditional centralized approaches to data clustering in a large dynamic distributed peer-to-peer network are difficult to perform. In this paper, a novel collaborative fuzzy clustering algorithm is proposed, in which the centralized clustering solution is approximated by performing distributed clustering at each peer with the collaboration of other peers. The required communication links are established at the level of cluster prototype and attribute weight. The information exchange only exists between topological neighboring peers. The attribute-weight-entropy regularization technique is applied in the distributed clustering method to achieve an ideal distribution of attribute weights, which ensures good clustering results. And the important features are successfully extracted for the high-dimensional data clustering. The kernelization of the proposed algorithm is also realized as a practical tool for clustering the data with “nonspherical”-shaped clusters. Experiments on synthetic and real-world datasets have demonstrated the efficiency and superiority of the proposed algorithms.

Effective thermal management is crucial to the optimal operation and health management of lithium-ion batteries. The online estimation of the temperature distribution in vehicle battery systems is not easy, as there are only a few sensors available on site. Furthermore, the thermal behaviors of batteries are difficult to predict, as their dynamics are strongly time-varying. In this paper, a hybrid model is developed for spatiotemporal estimation of temperature distribution in lithium-ion batteries. A simple but effective nominal model is first developed for real-time thermal management using a time/space separation method. Subsequently, a data-based neural model is proposed to compensate the model-plant mismatch caused by the spatial nonlinearity and other model uncertainties. The developed algorithm is simple and can be readily integrated into existing battery management systems. Simulation studies demonstrate the effectiveness of the proposed method.

The balance between exploration and exploitation is a key problem for reinforcement learning methods, especially for Q-learning. In this paper, a fidelity-based probabilistic Q-learning (FPQL) approach is presented to naturally solve this problem and applied for learning control of quantum systems. In this approach, fidelity is adopted to help direct the learning process and the probability of each action to be selected at a certain state is updated iteratively along with the learning process, which leads to a natural exploration strategy instead of a pointed one with configured parameters. A probabilistic Q-learning (PQL) algorithm is first presented to demonstrate the basic idea of probabilistic action selection. Then the FPQL algorithm is presented for learning control of quantum systems. Two examples (a spin-1/2 system and a Λ-type atomic system) are demonstrated to test the performance of the FPQL algorithm. The results show that FPQL algorithms attain a better balance between exploration and exploitation, and can also avoid local optimal policies and accelerate the learning process.

Effective thermal management is crucial to the optimal operation of lithium ion batteries and its health management. However, the thermal behaviors of batteries are governed by complex chemical process whose parameters will degrade over time and different environment. Furthermore, limited sensors exist for measurement of the spatiotemporal thermal process. In this paper, an intelligent model for online estimation of the temperature distribution in lithium ion battery systems is proposed. Due to the difficulty and high cost to identify the online operational model directly from practical experiment measurement, an integrated approach is developed to derive the approximate analytical model through hierarchical modeling from experiment, simulation, and intelligent learning. The proposed model could be easily added to the existing battery management system.

Traditional wavelet system is a two-domain (time and frequency domains) wavelet system (2DWS), which works only in time and frequency domains. The 2DWS is not able to treat time-frequency information and fuzziness simultaneously. For this reason, a three-domain (fuzzy, time, and frequency domains) fuzzy wavelet system (3DFWS) is proposed, where the three-domain mechanism provides a solution to handle fuzzy uncertainties and time-frequency information together. The major advantage of 3DFWS is able to use the prior knowledge via the novel fuzzy domain to analyze uncertain data and signals, which will enhance the potentials of 2DWS. Experimental and simulation studies show that the performance of the proposed 3DFWS is superior to the traditional one for simultaneous processing of time-frequency and fuzziness.

This paper proposes a least square regularized regression algorithm in sum space of reproducing kernel Hilbert spaces (RKHSs) for nonflat function approximation, and obtains the solution of the algorithm by solving a system of linear equations. This algorithm can approximate the low- and high-frequency component of the target function with large and small scale kernels, respectively. The convergence and learning rate are analyzed. We measure the complexity of the sum space by its covering number and demonstrate that the covering number can be bounded by the product of the covering numbers of basic RKHSs. For sum space of RKHSs with Gaussian kernels, by choosing appropriate parameters, we tradeoff the sample error and regularization error, and obtain a polynomial learning rate, which is better than that in any single RKHS. The utility of this method is illustrated with two simulated data sets and five real-life databases.

A data-driven 3-D fuzzy-logic controller (3-D FLC) design methodology based on support vector regression (SVR) learning is developed for nonlinear spatially distributed dynamic systems. Initially, the spatial information expression and processing as well as the fuzzy linguistic expression and rule inference of a 3-D FLC are integrated into spatial fuzzy basis functions (SFBFs), and then the 3-D FLC can be depicted by a three-layer network structure. By relating SFBFs of the 3-D FLC directly to spatial kernel functions of an SVR, an equivalence relationship of the 3-D FLC and the SVR is established, which means that the 3-D FLC can be designed with the help of the SVR learning. Subsequently, for an easy implementation, a systematic SVR learning-based 3-D FLC design scheme is formulated. In addition, the universal approximation capability of the proposed 3-D FLC is presented. Finally, the control of a nonlinear catalytic packed-bed reactor is considered as an application to demonstrate the effectiveness of the proposed 3-D FLC.

In the real world, uncertainty in the data is a frequently confronted difficulty problem for learning system. The performance of the learning method can be deteriorated by the uncertainty. To properly represent and handle the uncertainty problem becomes one of the key issues in the decision learning field. An intelligent learning model is presented in this paper to address the uncertainty problem. The noise-insensitive feature of the Naïve Bayesian classifier is used to enhance the noise-tolerant ability of probabilistic information based Support Vector Machine. The intelligent learning model conducts a flexible strategy to integrate the two models, based on the probabilistic decision information obtained from the two classifiers. Then, it gives the final decision. Furthermore, the intelligent learning model is evaluated on an artificial dataset for a classification task. The experiment results show good performance when compared with using only one technique in the noise environment.

This paper deals with the exponential stabilization problem for a class of nonlinear spatially distributed processes that are modeled by semilinear parabolic partial differential equations (PDEs), for which a finite number of actuators are used. A fuzzy control design methodology is developed for these systems by combining the PDE theory and the Takagi-Sugeno (T-S) fuzzy-model-based control technique. Initially, a T-S fuzzy parabolic PDE model is proposed to accurately represent a semilinear parabolic PDE system. Then, based on the T-S fuzzy model, a Lyapunov technique is used to design a continuous fuzzy state feedback controller such that the closed-loop PDE system is exponentially stable with a given decay rate. The stabilization condition is presented in terms of a set of spatial differential linear matrix inequalities (SDLMIs). Furthermore, a recursive algorithm is presented to solve the SDLMIs via the existing linear matrix inequality optimization techniques. Finally, numerical simulations on the temperature profile control of a catalytic rod are given to verify the effectiveness of the proposed design method.

A novel inference configuration is proposed to improve the computational efficiency and information loss in the probabilistic fuzzy inference process. The probabilistic inference and the fuzzy inference are unified in one operation based on the continuous form of the probabilistic fuzzy set. Besides the faster inference operation, it is able to produce fuzzy outputs in a complete probabilistic distribution that in turn will provide information about the approximation bound. The computational analyses of six different fuzzy systems demonstrate the inference efficiency of the proposed method. Its effectiveness can be further demonstrated on the application to modeling of an industrial curing process. The robust modeling performance discloses its potential in process modeling under complex environment.

This paper considers the problem of multiobjective fuzzy control design for a class of nonlinear spatially distributed processes (SDPs) described by parabolic partial differential equations (PDEs), which arise naturally in the modeling of diffusion-convection-reaction processes in finite spatial domains. Initially, the modal decomposition technique is applied to the SDP to formulate it as an infinite-dimensional singular perturbation model of ordinary differential equations (ODEs). An approximate nonlinear ODE system that captures the slow dynamics of the SDP is thus derived by singular perturbations. Subsequently, the Takagi–Sugeno fuzzy model is employed to represent the finite-dimensional slow system, which is used as the basis for the control design. A linear matrix inequality (LMI) approach is then developed for the design of multiobjective fuzzy controllers such that the closed-loop SDP is exponentially stable, and an${\rm L}_{2}$performance bound is provided under a prescribed${\rm H}_{\infty}$constraint of disturbance attenuation for the slow system. Furthermore, using the existing LMI optimization technique, a suboptimal fuzzy controller can be obtained in the sense of minimizing the${\rm L}_{2}$performance bound. Finally, the proposed method is applied to the control of the temperature profile of a catalytic rod.

Generation of wind is a very complicated process and influenced by large numbers of unknown factors. A probabilistic fuzzy system based prediction model is designed for the short-term wind speed prediction. By introducing the third probability dimension, the proposed prediction model can capture both stochastic and the deterministic uncertainties, and guarantee a better prediction in complex stochastic environment. The effectiveness of this intelligent wind speed prediction model is demonstrated by the simulations on a group of wind speed data. The robust modeling performance further discloses its potential in the practical prediction of wind speed under complex circumstance.

In this paper, a distributed fuzzy control design based on Proportional-spatial Derivative (P-sD) is proposed for the exponential stabilization of a class of nonlinear spatially distributed systems described by parabolic partial differential equations (PDEs). Initially, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is proposed to accurately represent the nonlinear parabolic PDE system. Then, based on the T-S fuzzy PDE model, a novel distributed fuzzy P-sD state feedback controller is developed by combining the PDE theory and the Lyapunov technique, such that the closed-loop PDE system is exponentially stable with a given decay rate. The sufficient condition on the existence of an exponentially stabilizing fuzzy controller is given in terms of a set of spatial differential linear matrix inequalities (SDLMIs). A recursive algorithm based on the finite-difference approximation and the linear matrix inequality (LMI) techniques is also provided to solve these SDLMIs. Finally, the developed design methodology is successfully applied to the feedback control of the Fitz-Hugh-Nagumo equation.

In this paper, an unified three-dimensional inference framework is proposed for modeling and pattern classification under the complex environment where both stochastic and fuzzy uncertainties exist. Based on a three-dimensional probabilistic fuzzy set, this novel inference method integrates the probabilistic inference and fuzzy inference into one operation to improve the computational efficiency and achieve a better performance than that of the traditional fuzzy method or the probabilistic method. The experiments on the wind speed data and Pima Indians Diabetes data demonstrate the advantages and effectiveness of the unified inference framework under the complex stochastic environment.

This paper considers the problem of fuzzy control design for a class of nonlinear distributed parameter systems that is described by first-order hyperbolic partial differential equations (PDEs), where the control actuators are continuously distributed in space. The goal of this paper is to develop a fuzzy state-feedback control design methodology for these systems by employing a combination of PDE theory and concepts from Takagi-Sugeno (T-S) fuzzy control. First, the T-S fuzzy hyperbolic PDE model is proposed to accurately represent the nonlinear first-order hyperbolic PDE system. Subsequently, based on the T-S fuzzy-PDE model, a Lyapunov technique is used to analyze the closed-loop exponential stability with a given decay rate. Then, a fuzzy state-feedback control design procedure is developed in terms of a set of spatial differential linear matrix inequalities (SDLMIs) from the resulting stability conditions. Furthermore, utilizing the finite-difference approximation method (with a backward difference for the spatial derivative), a recursive algorithm is presented to solve the SDLMIs via the existing LMI optimization techniques. Finally, the developed design methodology is successfully applied to the control of a nonisothermal plug-flow reactor.

There always exist stochastic and fuzzy uncertainties in the real-world. In this paper, the probabilistic fuzzy theory is used to construct a probabilistic fuzzy classifier for the pattern classification under these two uncertainties. By properly designing the secondary probability density function and the probabilistic fuzzy inference, and with a probabilistic voting method introduced, the probabilistic fuzzy classifier can achieve a better performance than that of the traditional fuzzy method or the pure probabilistic method. Moreover, probabilistic fuzzy rules extracted from expert knowledge or the process data will make the decision more realistic and easy to understand. The probabilistic property embedded in the data can be considered as the confidence level of the decision, which is impossibly shown in the traditional fuzzy classification. Finally, the experiment results have demonstrated that the advantages of the proposed PFC under the complex stochastic environment.

Many industrial processes are spatiotemporal dynamic systems. A three-dimensional fuzzy-logic controller (3-D FLC) has been recently developed to process the inherent capability of spatiotemporal dynamic systems. Sensor placement, which is always crucial to the control of spatiotemporal dynamic systems, is also critical to the design of the 3-D FLC. In this paper, a new sensor-placement strategy is developed. Its main feature is to position the sensor by utilizing the main characteristics of spatial distribution. The key technique is to use a spatial-constrained fuzzy c-means algorithm to extract the characteristics of spatial distribution. For an easy implementation, a systematic sensor-placement design scheme in four steps (i.e., data collection, dimension reduction, data clustering, and sensor locating) is developed. Finally, control of a catalytic packed-bed reactor is taken as an application to demonstrate the effectiveness of the proposed sensor-placement scheme.

In this paper, a probabilistic fuzzy logic system (PFLS) is discussed for modeling the stochastic and imprecise information. The PFLS uses a 3-dimensional probabilistic fuzzy set to capture the imprecise stochastic information. A unique 3-dimensional probabilistic fuzzy logic is designed to perform rule inference under such imprecise and stochastic environment. When the PFLS and neural networks are integrated in a unified framework, it can further adapt to time varying dynamics so as to improve its modeling performance. The paper briefly reviews this unique development and potential power of probabilistic fuzzy logic system.

Three-dimensional fuzzy logic controller (3-D FLC) is a new fuzzy logic controller for spatially distributed dynamic systems. The goal of this tutorial is to wipe of the magic behind the FLC. This tutorial focuses on building an intuition for how and why 3-D FLC works. Additionally, recent development on 3-D FLC is presented. The hope is that by addressing both aspects, readers of all levels will be able to gain a better understanding of 3-D FLC as well as the when, the how and the why of applying the techniques.

A novel application of type-2 fuzzy system is presented by developing a spatio-temporal fuzzy logic controller (FLC) for the distributed parameter system (DPS). The novel difference to the type-2 fuzzy system is to apply the secondary MF for a different physical variable - space domain. Using a number of sensors located on the spatial domain, the 3D fuzzy membership function can be obtained that contains spatio-temporal information. The 3D inference will include spatial T-norm operation and the traditional rule inference. The type-reduction will become the spatial reduction before the traditional defuzzification. This spaitio-temporal FLC is successfully applied to a catalytic reaction rod to demonstrate its effectiveness and potential to a wide range of engineering applications.

A completely new type of fuzzy logic system will be developed from the existing fuzzy structure and applied to modeling and control of complex processes under incomplete dynamics in the manufacturing industry. Using a unique three-dimensional membership function (fuzz grade, time and probability), the probabilistic processing features can be added into the existing fuzzy configuration to construct a probabilistic fuzzy inference engine. Thus, this developed probabilistic fuzzy logic system (PFLS) is able to learn uncertain information in both fuzzy and stochastic nature. The proposed PFLS will be very suitable to modeling of the complex stochastic process with incomplete dynamics. All the existing learning theories and methods can be directly applied to the proposed PFLS to enhance its learning performance. Integrated into the fuzzy-PID structure, it will turn into a probabilistic fuzzy logic controller for the stochastic control. Successful application of the proposed PLFS to the selected industrial process will have a great impact on both academia and industry.

In this paper, an adaptive neural network (NN) control with a guaranteed L(infinity)-gain performance is proposed for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities and persistent bounded disturbances. Initially, Galerkin method is applied to the PDE system to derive a low-order ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, based on the low-order slow model and the Lyapunov technique, an adaptive modal feedback controller is developed such that the closed-loop slow system is semiglobally input-to-state practically stable (ISpS) with an L(infinity)-gain performance. In the proposed control scheme, a radial basis function (RBF) NN is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown system nonlinearities. The outcome of the adaptive L(infinity)-gain control problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L(infinity)-gain, while control constraints are respected. Furthermore, it is shown that the proposed controller can ensure the semiglobal input-to-state practical stability and L(infinity)-gain performance of the closed-loop PDE system. Finally, by applying the developed design method to the temperature profile control of a catalytic rod, the achieved simulation results show the effectiveness of the proposed controller.

A new tuning method is proposed for fuzzy PID controller based on internal model control theory. First, the analytical model of the fuzzy PID controller is expressed as a linear PID controller plus a nonlinear compensation item. Then, the internal model control method can be used to approximately design the parameters of fuzzy PID controller analytically. Finally, stability of the fuzzy PID control system is analyzed, and the validity of the tuning methodology is demonstrated by simulation.

The paper investigates the flocking behaviors of multi-agent formation in 3-dimensional space which are based on leader following. A class of decentralized control laws for a group of mobile agents are proposed under the conditions that the topology of the control interconnections is fixed and dynamically time-variant, respectively. These control laws are a combination of attractive/repulsive and alignments forces which can guarantee the collision avoidance and cohesion of the formation and an aggregate motion along the same heading direction of the leader. According to the algebraic graph theory, differential inclusions and non-smooth analysis, we model the interconnection relationship of multi-agent formation, and achieve the stability analysis of the system by Lyapunov theory.

In this paper, a new sub-domain intelligent modeling method based on neural networks is proposed for modeling the nonlinear multivariate process. The new modeling method decomposes the process into several levels sub-models and the low level models are the sub-model of the high level models. Since the modeling method is step by step to build the sub-models from low level models to high level models, it avoids the persistent excitation signal in multi-dimensions space, which is difficult to be produced due to the constraint of industry conditions. The accuracies and efficiencies of the modeling methodology are verified by simulation.

A novel three-dimensional fuzzy logic controller (3D FLC) is presented for controlling the spatio-temporal systems, with the help of three-dimensional (3D) fuzzy sets and inference logic. The analytical model of the 3D FLC is derived to disclose its working principle and guide the control design. The derived model show that the 3D FLC has a global sliding mode structure over the spatial domain, which explains why the 3D FLC is able to process spatial information more effectively with a few more sensors. Based on its sliding mode feature, the 3D fuzzy logic control system can be analyzed and designed in the sense of Lyapunov stability. Finally, a catalytic reactor is presented as an example to validate the effectiveness of 3D FLC.

A probabilistic fuzzy neural network (PFNN) with a hybrid learning mechanism is proposed to handle complex stochastic uncertainties. Fuzzy logic systems (FLSs) are well known for vagueness processing. Embedded with the probabilistic method, an FLS will possess the capability to capture stochastic uncertainties. Further enhanced with the neural learning, it will be able to work under time-varying stochastic environment. Integrated with a statistical process control (SPC) based monitoring method, the PFNN can maintain the robust modeling performance. Finally, the successful simulation demonstrates the modeling effectiveness of the proposed PFNN under the time-varying stochastic conditions.

An Hinfinfuzzy observer-based control design is proposed for a class of nonlinear parabolic partial differential equation (PDE) systems with control constraints, for which the eigenspectrum of the spatial differential operator can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. In the proposed control scheme, Galerkin's method is initially applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently represented by the Takagi-Sugeno (T-S) fuzzy model. Then, based on the T-S fuzzy model, a fuzzy observer-based controller is developed to stabilize the nonlinear PDE system and achieve an optimized Hinfindisturbance attenuation performance for the finite-dimensional slow system, while control constraints are respected. The outcome of the Hinfinfuzzy observer-based control problem is formulated as a bilinear matrix inequality (BMI) optimization problem. A local optimization algorithm that treats the BMI as a double linear matrix inequality is presented to solve this BMI optimization problem. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod to illustrate its effectiveness.

In this paper, stabilization of the distributed parameter system (DPS) with time delay is studied using Galerkin's method and fuzzy control. With the help of Galerkin's method, the dynamics of DPS with time delay can be first converted into a group of low-order functional ordinary differential equations, which will be used for design of the robust fuzzy controller. The fuzzy controller designed can guarantee exponential stability of the closed-loop DPS. Some sufficient conditions are derived for the stabilization together with the linear matrix inequality design approach. The effectiveness of the proposed control design methodology is demonstrated in numerical simulations.

A novel 3-D fuzzy logic controller (3-D FLC) was presented to control a class of spatially distributed dynamic systems by Li(IEEE Trans. Fuzzy Syst., vol. 15, no. 3, pp. 470–481, Jun. 2007) by utilizing a 3-D fuzzy set and an inference mechanism with 3-D nature for spatial information processing. In this paper, the analytical mathematical model of the 3-D FLC is derived, and the controller structure is explained with the help of the existing conventional control techniques. The graphic analytical method for the traditional two-term FLC can be used for the analytical model derivation. The derived result shows that the 3-D FLC has a global sliding-mode structure over the spatial domain and explains why the 3-D FLC is able to process spatial information more effectively than its traditional counterpart using a few more sensors. Because of its sliding-mode feature, the Lyapunov stability criterion can be developed easily to analyze and design the 3-D FLC. Finally, a catalytic reactor is presented as an example to demonstrate the effectiveness of the 3-D FLC as compared with other controllers.

A new feedback-linearization-based neural network (NN) adaptive control is proposed for unknown nonaffine nonlinear discrete-time systems. An equivalent model in affine-like form is first derived for the original nonaffine discrete-time systems as feedback linearization methods cannot be implemented for such systems. Then, feedback linearization adaptive control is implemented based on the affine-like equivalent model identified with neural networks. Pretraining is not required and the weights of the neural networks used in adaptive control are directly updated online based on the input-output measurement. The dead-zone technique is used to remove the requirement of persistence excitation during the adaptation. With the proposed neural network adaptive control, stability and performance of the closed-loop system are rigorously established. Illustrated examples are provided to validate the theoretical findings.

This paper presents a Galerkin/neural-network- based guaranteed cost control (GCC) design for a class of parabolic partial differential equation (PDE) systems with unknown nonlinearities. A parabolic PDE system typically involves a spatial differential operator with eigenspectrum that can be partitioned into a finite-dimensional slow one and an infinite-dimensional stable fast complement. Motivated by this, in the proposed control scheme, Galerkin method is initially applied to the PDE system to derive an ordinary differential equation (ODE) system with unknown nonlinearities, which accurately describes the dynamics of the dominant (slow) modes of the PDE system. The resulting nonlinear ODE system is subsequently parameterized by a multilayer neural network (MNN) with one-hidden layer and zero bias terms. Then, based on the neural model and a Lure-type Lyapunov function, a linear modal feedback controller is developed to stabilize the closed-loop PDE system and provide an upper bound for the quadratic cost function associated with the finite-dimensional slow system for all admissible approximation errors of the network. The outcome of the GCC problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by using the existing LMI optimization technique, a suboptimal guaranteed cost controller in the sense of minimizing the cost bound is obtained. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.

The key approaches for machine learning, particularly learning in unknown probabilistic environments, are new representations and computation mechanisms. In this paper, a novel quantum reinforcement learning (QRL) method is proposed by combining quantum theory and reinforcement learning (RL). Inspired by the state superposition principle and quantum parallelism, a framework of a value-updating algorithm is introduced. The state (action) in traditional RL is identified as the eigen state (eigen action) in QRL. The state (action) set can be represented with a quantum superposition state, and the eigen state (eigen action) can be obtained by randomly observing the simulated quantum state according to the collapse postulate of quantum measurement. The probability of the eigen action is determined by the probability amplitude, which is updated in parallel according to rewards. Some related characteristics of QRL such as convergence, optimality, and balancing between exploration and exploitation are also analyzed, which shows that this approach makes a good tradeoff between exploration and exploitation using the probability amplitude and can speedup learning through the quantum parallelism. To evaluate the performance and practicability of QRL, several simulated experiments are given, and the results demonstrate the effectiveness and superiority of the QRL algorithm for some complex problems. This paper is also an effective exploration on the application of quantum computation to artificial intelligence.

A probabilistic wavelet system (PWS) is proposed to model the unknown dynamic system with stochastic and incomplete data. When compared with the traditional wavelet system, the PWS uses a novel three-domain wavelet function to make a balance among the probability, time, and frequency domains, which achieves a robust modeling performance with poor data information. The definition, transformation, multiple-resolution analysis, and implementation of the PWS are presented to construct the whole theoretical framework. Simulation studies show that the performance of the proposed PWS is superior to the traditional one in a stochastic and incomplete data environment.

An interval-valued fuzzy logic controller (I-V FLC) is presented to control a class of nonlinear distributed parameter systems. The proposed FLC is inspired by human operators' knowledge or expert experience to control a distributed parameter process from the point of view of overall space domain. Based on spatial fuzzy set, the I-V FLC employs a centralized rule base over the space domain. Using spatial membership degree fusion operation, the I-V FLC can compress spatial input information into interval-valued fuzzy sets and then execute an interval-valued rule inference mechanism; thereby the I-V FLC has the capability to process spatial information over the space domain. Compared with traditional FLCs, the I-V FLC can improve its control performance due to its increased ability to express and process spatial information. The I-V FLC is successfully applied to a catalytic packed-bed reactor and compared with the traditional FLCs. The results demonstrate its effectiveness to control the unknown nonlinear distributed parameter process.

The traditional fuzzy set is two-dimensional (2-D) with one dimension for the universe of discourse of the variable and the other for its membership degree. This 2-D fuzzy set is not able to handle the spatial information. The traditional fuzzy logic controller (FLC) developed from this 2-D fuzzy set should not be able to control the distributed parameter system that has the tempo-spatial nature. A three-dimensional (3-D) fuzzy set is defined to be made of a traditional fuzzy set and an extra dimension for spatial information. Based on concept of the 3-D fuzzy set, a new fuzzy control methodology is proposed to control the distributed parameter system. Similar to the traditional FLC, it still consists of fuzzification, rule inference, and defuzzification operations. Different to the traditional FLC, it uses multiple sensors to provide 3-D fuzzy inputs and possesses the inference mechanism with 3-D nature that can fuse these inputs into a so called ldquospatial membership function.rdquo Thus, a simple 2-D rule base can still be used for two obvious advantages. One is that rules will not increase as sensors increase for the spatial measurement; the other is that computation of this 3-D fuzzy inference can be significantly reduced for real world applications. Using only a few more sensors, the proposed FLC is able to process the distributed parameter system with little complexity increased from the traditional FLC. The 3-D FLC is successfully applied to a catalytic packed-bed reactor and compared with the traditional FLC. The results demonstrate its effectiveness to the nonlinear unknown distributed parameter process and its potential to a wide range of engineering applications.

This paper is concerned with delay-dependent stability analysis and stabilization problems for continuous-time Takagi and Sugeno (T-S) fuzzy systems with a time-varying delay. A new method for the delay-dependent stability analysis and stabilization is suggested, which is less conservative than other existing ones. First, based on a fuzzy Lyapunov-Krasovskii functional (LKF), a delay-dependent stability criterion is derived for the open-loop fuzzy systems. In the derivation process, some free fuzzy weighting matrices are introduced to express the relationships among the terms of the system equation, and among the terms in the Leibniz-Newton formula. Then, a delay-dependent stabilization condition based on the so-called parallel distributed compensation (PDC) scheme is worked out for the closed-loop fuzzy systems. The proposed stability criterion and stabilization condition are represented in terms of linear matrix inequalities (LMIs) and compared with the existing ones via two examples. Finally, application to control of a truck-trailer is also given to illustrate the effectiveness of the proposed design method.

This correspondence studies the problem of finite-dimensional constrained fuzzy control for a class of systems described by nonlinear parabolic partial differential equations (PDEs). Initially, Galerkin's method is applied to the PDE system to derive a nonlinear ordinary differential equation (ODE) system that accurately describes the dynamics of the dominant (slow) modes of the PDE system. Subsequently, a systematic modeling procedure is given to construct exactly a Takagi-Sugeno (T-S) fuzzy model for the finite-dimensional ODE system under state constraints. Then, based on the T-S fuzzy model, a sufficient condition for the existence of a stabilizing fuzzy controller is derived, which guarantees that the state constraints are satisfied and provides an upper bound on the quadratic performance function for the finite-dimensional slow system. The resulting fuzzy controllers can also guarantee the exponential stability of the closed-loop PDE system. Moreover, a local optimization algorithm based on the linear matrix inequalities is proposed to compute the feedback gain matrices of a suboptimal fuzzy controller in the sense of minimizing the quadratic performance bound. Finally, the proposed design method is applied to the control of the temperature profile of a catalytic rod.

We have studied the comment about our original paper and we agree that a minor mistake was made in Eq. 37 of our original paper (see ibid., vol. 11, no. 3, p. 354-60 (2003)).

By employing the Lyapunov-Krasovskii functional and linear matrix inequality (LMI) approach, the problem of global asymptotical stability is studied for recurrent neural networks with both discrete time-varying delays and distributed time-varying delays. Some sufficient conditions are given for checking the global asymptotical stability of recurrent neural networks with mixed time-varying delay. The proposed LMI result is computationally efficient as it can be solved numerically using standard commercial software. Two examples are given to show the usefulness of the results.

This correspondence points out an incorrect statement in Adetona et al, 2000, and Adetona et al., 2004, about the application of the proposed control law to nonminimum phase systems. A counterexample shows the limitations of the control law and, furthermore, its control capability to nonminimum phase systems is explained.

An approximate internal model-based neural control (AIMNC) strategy is proposed for unknown nonaffine nonlinear discrete processes under disturbed environment. The proposed control strategy has some clear advantages in respect to existing neural internal model control methods. It can be used for open-loop unstable nonlinear processes or a class of systems with unstable zero dynamics. Based on a novel input-output approximation, the proposed neural control law can be derived directly and implemented straightforward for an unknown process. Only one neural network needs to be trained and control algorithm can be directly obtained from model identification without further training. The stability and robustness of a closed-loop system can be derived analytically. Extensive simulations demonstrate the superior performance of the proposed AIMNC strategy.

Rule-based production scheduling is analyzed from the perspective of closed-loop control. An integrated feedback control methodology is proposed to enhance the performance of rule-based scheduling. The integrated control system consists of a state feedback control module, a performance-based feedback module, and a supervisory control module. Performance criteria are analyzed and classified into job-related and resource-related criteria. The key factors of performance are identified and used as state variables in the feedback control. The performance-based feedback control compensates for the errors that are caused by the scheduling rules. The supervisory control is designed to enhance the overall performance by adjusting the feedforward gains according to scheduling objectives. Simulation results show that the integrated control scheme can significantly improve the overall performance of the scheduling system.

By combining Cohen-Grossberg neural networks with an arbitrary switching rule, the mathematical model of a class of switched Cohen-Grossberg neural networks with mixed time-varying delays is established. Moreover, robust stability for such switched Cohen-Grossberg neural networks is analyzed based on a Lyapunov approach and linear matrix inequality (LMI) technique. Simple sufficient conditions are given to guarantee the switched Cohen-Grossberg neural networks to be globally asymptotically stable for all admissible parametric uncertainties. The proposed LMI-based results are computationally efficient as they can be solved numerically using standard commercial software. An example is given to illustrate the usefulness of the results.

A probabilistic fuzzy logic system (PFLS) is proposed for the modeling and control problems. In addition to the traditional fuzzification, inference engine and defuzzification operation for processing fuzzy information, it uses the probabilistic modeling method to improve the stochastic modeling capability. With a proper three-dimensional membership function, the PFLS could be designed to handle the effect of random noise and stochastic uncertainties in the modeling process. The simulation result shows that the proposed PFLS can treat the uncertainty modeling problem well.

In this paper, a probabilistic fuzzy logic system (PFLS) is proposed for the modeling and control problems. Similar to the ordinary fuzzy logic system (FLS), the PFLS consists of the fuzzification, inference engine and defuzzification operation to process the fuzzy information. Different to the FLS, it uses the probabilistic modeling method to improve the stochastic modeling capability. By using a three-dimensional membership function (MF), the PFLS is able to handle the effect of random noise and stochastic uncertainties existing in the process. A unique defuzzification method is proposed to simplify the complex operation. Finally, the proposed PFLS is applied to a function approximation problem and a robotic system. It shows a better performance than an ordinary FLS in stochastic circumstance.

A novel neural approximate inverse control is proposed for general unknown single-input-single-output (SISO) and multi-input-multi-output (MIMO) nonlinear discrete dynamical systems. Based on an innovative input/output (I/O) approximation of neural network nonlinear models, the neural inverse control law can be derived directly and its implementation for an unknown process is straightforward. Only a general identification technique is involved in both model development and control design without extra training (online or offline) for the neural nonlinear inverse controller. With less approximation made on controller development, the control will be more robust to large variations in the operating region. The robustness of the stability and the performance of a closed-loop system can be rigorously established even if the nonlinear plant is of not well defined relative degree. Extensive simulations demonstrate the performance of the proposed neural inverse control.

Many fuzzy control schemes used in industrial practice today are based on some simplified fuzzy reasoning methods, which are simple but at the expense of losing robustness, missing fuzzy characteristics, and having inconsistent inference. The concept of optimal fuzzy reasoning is introduced in this paper to overcome these shortcomings. The main advantage is that an integration of the optimal fuzzy reasoning with a PID control structure will generate a new type of fuzzy-PID control schemes with inherent optimal-tuning features for both local optimal performance and global tracking robustness. This new fuzzy-PID controller is then analyzed quantitatively and compared with other existing fuzzy-PID control methods. Both analytical and numerical studies clearly show the improved robustness of the new fuzzy-PID controller.

It is very important to use a reliable and inexpensive sensor to obtain useful information about manufacturing processing, such as cutting force for monitoring automated machining. In this paper, the feed-cutting force is estimated using inexpensive current sensors installed on the ac servomotor of a computerized numerical control (CNC) turning center, with the results applied to the intelligent tool wear monitoring system. The mathematical model is used to disclose the implicit dependency of feed-cutting force on feed-motor current and feed speed. Afterwards, a neuro-fuzzy network is used to identify the cutting force with current measurement only. This hybrid math-fuzzy approach will reduce the modeling uncertainty and measurement cost. Finally, the estimated cutting force is applied in the tool-wear monitoring process. Successful experiments demonstrate robustness and effectiveness of the suggested method in the wide range of tool-wear monitoring applications.

In this paper, direct and indirect adaptive output-feedback fuzzy decentralized controllers for a class of uncertain large-scale nonlinear systems are developed. The proposed controllers do not need the availability of the state variables. By designing the state observer, the adaptive fuzzy systems, which are used to model the unknown functions, can be constructed using the state estimations, and a new hybrid adaptive fuzzy control methodology is proposed by combining the adaptive fuzzy systems with H infinity control and the sliding mode control techniques. Based on Lyapunov stability theorem, the stability of the closed-loop systems can be verified. Moreover, the proposed overall control schemes guarantee that all the signals involved are bounded and achieve the H infinity-tracking performance. To demonstrate the effectiveness of the proposed methods, simulation results are illustrated in this paper.

A spectral approximation based intelligent modelling method is proposed for the snap curing process, which belongs to nonlinear parabolic distributed parameter systems (DPSs). Unlike generic modelling approaches for DPSs, the proposed modelling method combines model reduction techniques of the snap curing process and intelligence based identification methods of nonlinear ODE (ordinary differential equation) systems. The exact model equations of the snap curing process do not need and only finite measurements are used in the modelling process. The built neural network model is of state space form that fits the general model-based controller formulations, thus the control techniques used for ODE models can be applied in the reduced-order model that represents the distributed parameter system. Moreover, the modelling process can be implemented offline or online. Experimental results show that the proposed modelling method is feasible and effective for a class of nonlinear DPSs.

A hybrid indirect and direct adaptive fuzzy output tracking control schemes are developed for a class of nonlinear multiple-input-multiple-output (MIMO) systems. This hybrid control system consists of observer and other different control components. Using the state observer, it does not require the system states to be available for measurement. Assisted by observer-based state feedback control component, the adaptive fuzzy system plays a dominant role to maintain the closed-loop stability. Being the auxiliary compensation, H/sup /spl infin// control and sliding mode control are designed to suppress the influence of external disturbance and remove fuzzy approximation error, respectively. Thus, the system performance can be greatly improved. The simulation results demonstrate that the proposed hybrid fuzzy control system can guarantee the system stability and also maintain a good tracking performance.

A stable adaptive fuzzy sliding-mode controller is developed for nonlinear multivariable systems with unavailable states. When the system states are not available, the estimated states from a semi-high gain observer are used to construct the output feedback fuzzy controller by incorporating the dynamic sliding mode. It is proved that uniformly asymptotic output feedback stabilization can be achieved with the tracking error approaching to zero. A nonlinear system simulation example is presented to verify the effectiveness of the proposed controller.

Some drawbacks of the aforementioned paper are pointed out, and a new direct adaptive fuzzy control algorithm is suggested for unknown nonlinear systems.

A new adaptive fuzzy control algorithm is developed in this paper, which has a regular fuzzy controller and a supervisory control term. This control algorithm does not require the system model, but has stability assurance for the closed-loop controlled system. The design is simple, in the sense that both the membership functions and the rule base are simple, yet generic. It can be applied to a large class of robotic and other mechanical systems.

Attempts to develop new structures for higher order fuzzy logic control (FLC) systems, which could handle the higher order process and the time-delay system as well. Two different approaches are proposed to construct the higher order FLC, namely, the hierarchical structure and the distributed structure. Both structures can be designed via the theory of variable structure control (VSC). The complexity of the structure depends on the order of the process. The necessary and sufficient stability condition provided by the VSC theory facilitates the design of the nominal scaling gains. The difficulty of the design is to estimate the upper bound of the undesirable dynamics. Practically, this upper bound can be approximated by the peak value of the undesirable dynamics in the steady-state period. The simulation shows that this approximation is feasible and nominal scaling gains designed can lead to a stable and reasonably good performance. The fine tuning can be more easily carried out to provide a better performance from these nominal values instead of from scratch. The proposed higher order structure can also be used to control the time-delayed process if the delay time is known. The structure configuration depends on the approximation of the delay compensation factor. A first-order approximation is usually accurate enough when the delay is not very long. A partially known delay will result in either overcompensation or undercompensation. The overcompensation seems better than the undercompensation due to the former contribution to the PID effects. The simulation shows the effectiveness of the proposed structure to both the higher order process and the time-delay system.

The difficult design of fuzzy logic control (FLC) can be processed in two separate stages: nominal design and optimal adjustment. The nominal design intends to figure out the nominal model of FLC including rule base, membership functions (MF's), and scaling gains. Different parameters require different design methods. A quantitative approach is presented in this paper to design the nominal scaling gain by using the idea of classical adaptive control. This adaptive mechanism requires only an approximate reference model of the plant, but it tolerates much more system uncertainties due to the inherent nonlinear feature of FLC. In reality, a first-order linear model is usually sufficient for achieving a reasonable performance. This approximate model reference based adaptive fuzzy control system is more robust than its classical counterpart in complex environment without deteriorating the original system stability. Therefore, it is an effective method to determine proper scaling gains for FLC.

A new methodology is introduced for designing and tuning the scaling gains of the conventional fuzzy logic controller (FLC) based on its well-tuned linear counterpart. The conventional FLC with a linear rule base is very similar to its linear counterpart. The linear three-term controller has proportional, integral and/or derivative gains. Similarly, the conventional fuzzy three-term controller also has fuzzy proportional, integral and/or derivative gains. The new concept "fuzzy transfer function" is invented to connect these fuzzy gains with the corresponding scaling gains. The comparative gain design is presented by using the gains of the well-tuned linear counterpart as the initial fuzzy gains of the conventional FLC. Furthermore, the relationship between the scaling gains and the performance can be deduced to produce the comparative tuning algorithm, which can tune the scaling gains to their optimum by less trial and error. The performance comparison in the simulation demonstrates the viability of the new methodology.

A new methodology is presented to improve the design and tuning of a fuzzy logic controller (FLC) using variable structure control (VSC) theory. A VSC-type rule base is constructed and the fundamentals of FLC explored quantitatively by VSC theory. A very concise mathematical expression for the FLC is presented, in which the Lyapunov stability criterion can be applied to guide the design and tuning. This results in a simpler and more systematic procedure. Application of the method to higher order systems is made straight forward by applying a hierarchical technique. The validity of the design methodology is demonstrated by simulation.

Conventional fuzzy control can be considered mainly composed of fuzzy two-term control and fuzzy three-term control. In this paper, more systematic analysis and design are given for the conventional fuzzy control. A general robust rule base is proposed for fuzzy two-term control, leaving the optimum tuning to the scaling gains, which greatly reduces the difficulties of design and tuning. The digital implementation of fuzzy control is also presented for avoiding the influence of the sampling time. Based on the results of previous fuzzy two-term controllers, a simplified fuzzy three-term controller is proposed to enhance performance. A two-level tuning strategy is also planned, which first tries to set up the relationship between fuzzy proportional/integral/derivative gain and scaling gains at the high level, and optionally tunes the control resolution at low level. Simulation of different order models show the characteristics of fuzzy control, effectiveness of the new design methodologies, and advantages of the enhanced fuzzy three-term control.

A new methodology is proposed for designing a fuzzy logic controller (FLC). A phase plane is used to bridge the gap between the time-response and rule base. The rule base can be easily built using the general dynamics of the process, and then readily updated to contain the delayed information for reducing the deadtime effects of the process. An adaptive gain method is also proposed to help the database design and the controller tuning. Much of the FLC design can be shifted to the design and tuning of gain. A good performance can be achieved both in transient state and steady state without use of multidecision tables. Application of FLC with these new methodologies is presented for a thermal process with a varying deadtime to show the robust performance of FLC and the effectiveness of these methodologies.>