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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. [ABSTRACT FROM AUTHOR]

Modeling high-spatial dimensional (high-D) distributed parameter systems (DPSs) is very difficult because of the spatially distributed characteristic and complex spatiotemporal coupling. In this article, a new framework based on high-order singular vector decomposition (HOSVD) is proposed to model a high-D DPS. A modified HOSVD is designed for separation of time and multiple spatial variables. It can well preserve the spatially distributed nature of the high-D DPS. It also considers the interaction across different spatial modes, which is an important part of spatiotemporal coupling in the high-D DPS. Experiments of a two-spatial dimensional thermal curing process are used to verify the effectiveness of the proposed method. An average prediction error near 1% of the curing temperature can be achieved. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

This paper considers the estimator-based $H_{\infty }$ 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 $H_{\infty }$ performance is developed via a Lyapunov functional. The outcome of the estimator-based $H_{\infty }$ 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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, a novel method is developed to detect fault and identify its spatial location for a class of parabolic distributed parameter systems (DPSs) with limited sensors. The normal situation of the DPSs is first modeled under limited sensors. Then, the spatio–temporal dynamics of DPSs is decoupled under time/space separation. After the temporal coefficients are further decomposed using the independent component analysis method, the dominant temporal components are taken and then the spatial residual errors are used to form two monitoring statistics. Using the kernel density function, the confidence bounds of these two statistics (fault free) can be established as the reference signals. Unlike model-based fault detection methods that require explicit mathematical models of the processes, the proposed method is data driven and only utilizes the separable characteristic of parabolic DPSs. Experiments on a typical parabolic process and a snap curing oven are used to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The temperature distribution of a lithium-ion battery (LIB) belongs to a nonlinearly distributed parameter system (DPS), which is infinite dimensional in the space direction. Modeling of such systems often leads to the following challenges: time/space-coupled dynamics; time-varying dynamics; and spatial nonlinearity. For the first two challenges, Karhunen–Loève (KL) decomposition based data-driven spatiotemporal models have been widely researched and successfully applied to industrial thermal processes. However, this method is a global linear model reduction method that ignores the nonlinear properties of measurements. This will prohibit the model performance of a strong nonlinear DPS, which has strong spatial nonlinearity refers to the aforementioned third challenge. To address this problem, a local-properties-embedding-based modeling method is developed for the nonlinear DPS. First, the finite-dimensional nonlinear spatial basis functions that can be the representative of the nonlinear feature of the original space are learned by the local-properties-embedding-based method. Then, the low-dimensional representative can be derived using the time/space separation and the unknown temporal coefficients can be identified through the traditional neural learning algorithm. Finally, the spatiotemporal temperature distribution can be reconstructed by the time/space synthesis. Since the nonlinear structure feature of the spatiotemporal datasets has been considered, the proposed modeling method can be more effective than the traditional KL-based method for modeling the nonlinear DPS. Numerical simulations on the LIB showed that the proposed methods are more robust than the KL-based method in both the time direction and the space direction. [ABSTRACT FROM AUTHOR]

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 $L^\infty$ norm $\Vert \cdot \Vert _\infty$ 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 $\Vert \cdot \Vert _\infty$ , 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. [ABSTRACT FROM AUTHOR]

Jet dispensing has been widely considered as the next generation of dispensing technology. Since there is no online measurement of the droplet volume in the jetting process, the dispensing usually operates in open loop without any online control. The droplet consistency has been a long-standing challenge. As the jetting process is driven by the needle motion, the dispensed volume will be greatly affected by the needle motion. To monitor the jetting process, a novel measurement mechanism is designed for sensing the needle motion of the jet dispenser. Using the space/time separation method, the complex distributed fluid flow model is approximated by a simple analytical model. With the added motion measurement, this hybrid sensing/model approach can serve for online estimation of the dispensing performance. The model parameters can be identified using the experimental data. The experimental study verifies that the proposed method can satisfactorily estimate the dispensed volume in real-time operation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

Silicone jet dispensing has grown increasingly common in light-emitting diode (LED) packaging owing to its high speed and low cost. However, differences in breakup behavior result in different silicone jetting volumes that create challenges in maintaining dispensing volume consistency during silicone jet dispensing process; this severely affects the performance of LED packaging. To reveal the breakup behavior during the jet dispensing process, the experimental and modeling studies were conducted. First, the ultrafast breakup process was experimentally observed using a high-speed camera, which shows that this process only requires approximately 50 ms. Then, an analytical model was developed and verified through an experiment. Using this analytical model, the effects of initial disturbance amplitude, initial disturbance wavelength, and thread length on the thread breakup were studied. The simulation demonstrated that it is necessary to control the disturbance amplitude under 0.005 for volume consistency in jet dispensing; thus, a moving work piece rather than a moving nozzle is recommended in jet dispensing. A disturbance wavelength between 0.3 and 0.6 mm is beneficial for both thread breakup and high-volume consistency. Thread length has little effect on the breakup position but significant effects on the volume consistency and breakup time. A low substrate increases the volume and the consistency of thread breakup. This paper will provide a useful guide for dispenser designs of modern LED packages. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

In this paper, a saturation-based tuning method for fuzzy proportional–integral–derivative (PID) controller is proposed. The key feature is that this tuning method adopts an inherent saturation property resulting from finite rules in practical application. Based on the saturation, fuzzy PID controller can be expressed as a sliding-mode controller that has two nonlinear terms: One plays as an equivalent control, and the other acts as a switching control. A nominal tuning is first presented to design a stable equivalent control using gain margin and phase margin. Then, a robust tuning is presented to design the switching control by using maximum sensitivity function or compensation sensitivity function. The maximum bound of uncertainty is given by the robust analysis. Finally, this proposed tuning method is used to control a clamp rotation of a forging manipulator. The simulations and real-time experiments demonstrate the effectiveness of the proposed tuning method. [ABSTRACT FROM PUBLISHER]

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 L2 performance bound is provided under a prescribed 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 L2 performance bound. Finally, the proposed method is applied to the control of the temperature profile of a catalytic rod. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]