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.

This paper presents an innovative event-triggered control approach for a class of nonlinear parabolic distributed parameter systems with time-varying delays. The novel event triggering mechanism enables control or measurement signals to be updated only when a predefined trigger condition exceeds a specified threshold. Multiple actuators and sensors, strategically distributed at specific points or partial regions of the spatial domain, are employed to perform pointwise/piecewise control and measurement. Two variations of event-triggered feedback (ETF) controllers are designed to address the collocated and non-collocated observation cases based on the distributions of actuators and sensors in space, respectively. The well-posedness of the open-loop and closed-loop systems is analyzed via the$C_{0}$-semigroup theory, respectively. Furthermore, the non-existence of zeno behavior is guaranteed by demonstrating that the inter-event time intervals are nontrivial. Finally, the proposed method is applied to address the temperature control problem in the catalytic reaction process. Numerical simulation results validate the effectiveness of the proposed ETF control method in practical applications. Note to Practitioners—This work is motivated by the temperature control challenges in catalytic reaction process, with an extended application to the production of hot-rolled steel strips. This paper proposes an innovative event-triggered control method to reduce the demands on communication and computational resources. Extensive comparative experimental results have thoroughly validated the effectiveness of the proposed method in practical applications.

In comparison to common quadrotors, the structure deformation of morphing quadrotors endows them with better flight performance but also results in more complex flight dynamics. Generally, it is extremely difficult or impossible for these morphing quadrotors to develop an accurate mathematical model that describes their complex flight dynamics. This fact leads to a particularly challenging situation, as the existing mature model-based flight control theory fails to address the flight control design issue of morphing quadrotors. By resorting to a combination of model-free control techniques [e.g., deep reinforcement learning (DRL)] and convex combination (CC) technique, a convex-combined-DRL (cc-DRL) flight control algorithm is proposed for flight trajectory tracking and attitude stabilization of a class of morphing quadrotors with arm-length deformation. In the proposed cc-DRL flight control algorithm, a proximal policy optimization algorithm is utilized to offline train the corresponding optimal flight control laws for some selected representative arm length modes. Hereby, a cc-DRL flight control scheme is constructed by the CC technique. Finally, simulation results are presented to show the effectiveness and merit of the proposed DRL flight control algorithm.

The current work concerns on cooperative control of exponential stabilization and control performance improvement in the spatial domain for a linear spatiotemporal dynamic system associated with multiple control actuators and multiple collaborative measurement sensors. By assuming that the system dynamics is modeled by a MIMO parabolic partial differential equation (PPDE) and each sensor can share measurement information with its topological neighbors in directed and switching topological networks, a cooperative control protocol is proposed to achieve the control aim of this article. With the help of a combination of multiagent consensus theory, Lyapunov’s method, and integral inequality technique, sufficient conditions are presented for the closed-loop exponential stability of the PPDE in the norm$|\cdot|_{2}$. Moreover, some performance indexes are defined to evaluate the closed-loop control performance improvement in the spatial domain. Extensive simulation results are finally presented for a simple numerical example and a practical heat treatment process to verify the effectiveness and performance improvement capability of the proposed cooperative control protocol.

Assisted by the Takagi-Sugeno (T-S) fuzzy modelbased nonlinear control technique, nonlinear spatiotemporal feedback compensators are proposed in this article for exponential stabilization of parabolic partial differential dynamic systems with measurement outputs transmitted over a communication network. More specifically, an approximate T-S fuzzy partial differential equation (PDE) model with C ∞-smooth membership functions is constructed to describe the complex spatiotemporal dynamics of the nonlinear partial differential systems, and its approximation capability is analyzed via the uniform approximation theorem on a real separable Hilbert space. A spatiotemporally asynchronous sampled-data measurement output equation is proposed to model the transmission process of networked measurement outputs. By the approximate T-S fuzzy PDE model, fuzzy-observer-based nonlinear continuous-time and sampleddata feedback compensators are constructed via the spatiotemporally asynchronous sampled-data measurement outputs. Given that sufficient conditions presented in terms of linear matrix inequalities are satisfied, the suggested fuzzy compensators can exponentially stabilize the nonlinear system in the Lyapunov sense. Simulation results are presented to show the effectiveness and merit of the suggested spatiotemporal fuzzy compensators.

The issue of spatiotemporal adaptive fuzzy state profile tracking (SAFSPT) control is addressed in this study for parabolic partial differential systems (PPDSs) on a hypercube exposed to unknown nonlinear dynamics. Specifically, a spatiotemporal fuzzy set on a hypercube is first constructed from the three-dimensional fuzzy set on a simple 1-D space domain to completely take into account the spatiotemporal coupling property of the PPDS state. Then a spatiotemporal fuzzy system is developed via the spatiotemporal fuzzy set to approximate any real continuous functions on an open subset of a separable Hilbert space. It is shown that any continuous functions can be approximated by the proposed spatiotemporal fuzzy system in arbitrary precision. Both indirect and direct SAFSPT control strategies are put forth with the use of the spatiotemporal fuzzy system. The closed-loop tracking error system's stability is thoroughly examined in terms of Lyapunov stability. Finally, the effectiveness and benefit of theoretical results are illustrated by extensive simulation experiments.

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.

This article presents a robust${H_{\infty }}$feedback compensator design approach for semilinear parabolic distributed parameter systems (DPSs) with external disturbances via mobile actuators and sensors. An${H_{\infty }}$performance constraint is introduced to deal with the external disturbances from the model and measurement noise. Two types of feedback compensators are designed in terms of the collocated and noncollocated mobile actuators and sensors. By the Lyapunov direct technique, some sufficient conditions based on LMI constraints are proposed for the exponential stability under${H_{\infty }}$performance constraints in the$\mathcal {L}^{2}$-norm. Moreover, the open-loop and closed-loop well-posedness of the semilinear DPSs with external disturbances are analyzed via the${C_{0}}$-semigroup theory approach. Finally, extensive numerical simulation results for semilinear DPSs with external disturbances via collocated and noncollocated mobile actuators and sensors are shown to verify the effectiveness of the proposed method.

In this article, we utilize a combination of integral control, fuzzy control, and observer-based output feedback control to deal with the issue of nonlinear output tracking control (OTC) design for nonlinear infinite-dimensional dynamic systems. The system dynamics model is represented by a semilinear parabolic partial differential equation (PDE) with boundary control and noncollocated boundary measurement. Initially, a Takagi–Sugeno (T–S) fuzzy parabolic PDE model is constructed to surmount the OTC design difficulty from the infinite-dimensional nonlinear system dynamics. Subsequently, a fuzzy-observer-based OTC law is proposed via the T–S fuzzy PDE model and the integral control approach. Here, the integral control ensures asymptotic output regulation, and the observer-based output feedback control is employed to conquer the stabilizing control design difficulty caused by the noncollocation between control actuation and measurement. It is shown via the Lyapunov technique with variants of vector-valued Poincaré–Wirtinger's inequality that the suggested fuzzy OTC law drives the measurement output to asymptotically track the desired reference signal and ensures the boundedness of the resulting closed-loop system, provided that a sufficient condition given in the form of linear matrix inequalities is fulfilled. Moreover, the proposed fuzzy-model-based OTC design is also revised for the exponential stabilization case. Finally, extensive simulation results for a numerical example and a cooling process in hot strip mills are provided to examine the effectiveness and merit of the proposed fuzzy OTC scheme.

This article proposes an adaptive fuzzy control approach with an event-triggered mechanism and spatial motion constraint for a hybrid spacecraft system. The spacecraft system is composed of a rigid body and a slender flexible panel, with coupled dynamics captured by three ordinary differential equations and two partial differential equations. The overall control objective lies in utilizing an event-triggered control input to regulate the angular velocities of the rigid body and stabilize the vibrations of the flexible panel under unknown input disturbances and prescribed spatial motion performance. We collectively address the posture regulation and disturbance rejection purposes by introducing a barrier Lyapunov function and a fuzzy logic system. The event-triggered solution only updates the control signals at some discrete-time instants, and hence the communication burden is reduced significantly. The potential effectiveness and thrifty efficiency of the developed control strategy are theoretically demonstrated and numerically verified.

This article addresses the H∞stabilization problems for a class of nonlinear distributed parameter systems which is described by the first-order hyperbolic partial differential equations (PDEs). First, the first-order hyperbolic PDE systems are identified as a polynomial fuzzy PDE system and the polynomial fuzzy controller for the polynomial fuzzy PDE system is proposed. By utilizing the proposed homogeneous polynomial Lyapunov functional, Euler's homogeneous function theorem, and the proposed theorems, a spatial derivative sum-of-squares (SDSOS) exponential stabilization condition is proposed. In addition, a recursive algorithm for the SDSOS exponential stabilization condition is developed to find the feasible solution. Furthermore, in order to reduce the conservatism of the proposed results, a relaxed H∞stabilization condition for the polynomial fuzzy PDE system is provided. Finally, the nonisothermal plug-flow reactor (PFR) is used to demonstrate the effectiveness and feasibility of the proposed method.

This paper discusses the problem of suboptimal local piecewise H∞fuzzy control of quasi-linear spatiotemporal dynamic systems with control magnitude constraints. A Takagi-Sugeno fuzzy partial differential equation (PDE) model with space-varying coefficient matrices is first assumed to be derived for exactly describing nonlinear system dynamics. In the light of the fuzzy model, a local piecewise fuzzy feedback controller is then constructed to guarantee the exponential stability with a prescribed H∞disturbance attenuation level for the resulting closed-loop system, while the control constraints are also ensured. A sufficient condition on the existence of such fuzzy controller is developed by the Lyapunov direct method and an integral inequality and presented in terms of space algebraic linear matrix inequalities (LMIs) coupled with LMIs. By virtue of extreme value theorem, a suboptimal-constrained local piecewise H∞fuzzy control design in the sense of minimizing the disturbance attenuation level is formulated as a minimization optimization problem with LMI constraints. Finally, the proposed method is applied to solve the feedback control of a quasi-linear FitzHugh-Nagumo equation with space-varying coefficients, and simulation results show its effectiveness and merit.

This article addresses the issue of fuzzy control design subject to a mixed H2/H∞performance constraint and guidance law design for semilinear parabolic distributed parameter systems (DPSs) with mobile collocated actuator/sensor pairs. Initially, via the local sector nonlinearity method, a Takagi-Sugeno (T-S) fuzzy model is constructed to accurately describe the spatiotemporal dynamics of the DPSs. Then, based on the obtained T-S fuzzy model and Lyapunov technique, a membership-function-dependent mixed H2/H∞fuzzy control design is developed and the mobile actuator/sensor guidance laws are also determined simultaneously, such that the resulting closed-loop system is exponentially stable while providing an H2performance bound under the given H∞performance of disturbance attenuation, and the transient response of closed-loop state is improved. Moreover, a suboptimal mixed H2/H∞fuzzy control design is derived in the sense of minimizing the upper bound of the given H2performance function by applying the existing linear matrix inequality optimization techniques. At last, some simulation results for a numerical example are presented to verify the proposed method.

This article addresses dynamic exponential stabilization problem of a linear scalar parabolic partial differential equation (PDE) with multiple spatially piecewise control inputs and multiple sampled-data measurement outputs in time represented as state averages over spatially noncollocated local piecewise subdomains. A sampled-data-observer-based feedback controller is constructed to guarantee the exponential convergence of the resulting closed-loop PDE. By Lyapunov's direct method with Poincaré-Wirtinger inequality's variants, a sufficient condition of the form linear matrix inequalities is derived for such observer-based feedback controller's existence. This sufficient condition is extended for the case of spatially pointwise control. With the aid of semigroup theory, the closed-loop well-posedness analysis is carried out. The simulation results for a numerical example are provided to demonstrate the effectiveness of the proposed design method and its extension.

The problem of dynamic boundary fuzzy control design is investigated in this paper for nonlinear parabolic partial differential equation (PDE) systems with spatially noncollocated discrete observation. Two cases of noncollocated discrete observation in space (i.e., pointwise observation in space and local piecewise uniform observation in space) are considered, respectively. The spatially noncollocated discrete observation makes the control design very difficult. Such design difficulty can be surmounted by an observer-based feedback control technique. It is assumed that the semilinear PDEs are accurately represented by a Takagi-Sugeno fuzzy PDE model. On the basis of the obtained fuzzy PDE model, a fuzzy Luenberger-type PDE state observer with above two cases of noncollocated discrete observation in space is first proposed for exponential estimation of the PDE system state. An observer-based dynamic fuzzy controller is then constructed such that the resulting closed-loop system is exponentially stable. Sufficient conditions on existence of such fuzzy controller are developed by Lyapunov technique with variations of vector-valued Poincaré-Wirtinger inequality, and presented in terms of linear matrix inequalities. Finally, extensive numerical simulation results of two examples are provided to support the proposed design 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.

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.

This paper deals with the problem of exponential stabilization for nonlinear parabolic distributed parameter systems using the Takagi-Sugeno (T-S) fuzzy partial differential equation (PDE) model, where a finite number of actuators are active only at some specified points of the spatial domain (these actuators are referred to as pointwise actuators). Three cases of state feedback are respectively considered in this study as follows: full state feedback, piecewise state feedback, and collocated pointwise state feedback. It is initially assumed that a T-S fuzzy PDE model obtained via the sector nonlinearity approach is employed to accurately represent the semilinear parabolic PDE system. Based on the obtained T-S fuzzy PDE model, Lyapunov-based design methodologies of fuzzy feedback control laws are subsequently derived for the above three state feedback cases by using the vector-valued Wirtinger's inequality to guarantee locally exponential pointwise stabilization of the semilinear PDE system, and presented in terms of standard linear matrix inequalities (LMIs). Moreover, the favorable property offered by sharing all the same premises in the T-S fuzzy PDE models and fuzzy controllers is not applicable for the case of collocated pointwise state feedback. A parameterized LMI is introduced for this case to enhance the stabilization ability of the fuzzy controller. Finally, the merit and effectiveness of the proposed design methods are demonstrated by numerical simulation results of two examples.

This paper investigates the guaranteed cost fuzzy control (GCFC) problem for a class of nonlinear systems modeled by an n-dimension ordinary differential equation (ODE) coupled with a semilinear scalar parabolic partial differential equation (PDE). A Takagi-Sugeno (T-S) fuzzy coupled parabolic PDE-ODE model is initially proposed to accurately represent the nonlinear coupled system. Then, on the basis of the T-S fuzzy coupled model, a GCFC design is developed in terms of linear matrix inequalities to exponentially stabilize the coupled system while providing an upper bound for a prescribed quadratic cost function. The proposed fuzzy control scheme consists of the ODE state feedback and the PDE static output feedback employing locally collocated piecewise uniform actuators and sensors. Moreover, a suboptimal GCFC problem is also addressed to minimize the cost bound. Finally, the developed method is applied to the cruise control and surface temperature cooling of a hypersonic rocket car.

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.

An H∞fuzzy control design is presented for the disturbance attenuation of a class of coupled systems described by a set of nonlinear ordinary differential equations (ODEs) and a semi-linear parabolic partial differential equation (PDE). The fuzzy control scheme consists of an ODE state feedback fuzzy subcontroller for the ODE subsystem and a PDE static output feedback fuzzy subcontroller for the PDE subsystem by using piecewise uniform actuators and pointwise sensors. Initially, the original nonlinear system is accurately represented by employing a Takagi-Sugeno fuzzy coupled parabolic PDE-ODE model. Then, an H∞fuzzy controller is developed to exponentially stabilize the fuzzy coupled system while satisfying a prescribed H∞performance of disturbance attenuation, whose existence condition is given by linear matrix inequalities. Finally, simulation results on a hypersonic rocket car are given to show the effectiveness of the proposed design method.

This paper deals with the problem of H∞fuzzy control design with an input constraint for a class of coupled systems, which consist of an n-dimensional nonlinear subsystem of ordinary differential equations (ODEs) and a scalar linear parabolic subsystem of partial differential equation (PDE) connected in feedback. Initially, the nonlinear coupled system is represented by a Takagi-Sugeno (T-S) fuzzy-coupled ODE-PDE model. Then, based on the fuzzy model and parallel distributed compensation scheme, a fuzzy state feedback control design is developed via Lyapunov's direct method, such that the resulting closed-loop fuzzy-coupled system is exponentially stable, and a prescribed H∞performance of disturbance attenuation is satisfied. The existing condition of the proposed H∞ fuzzy controllers is given in terms of linear matrix inequalities (LMIs). Moreover, in order to make the attenuation level as small as possible while the input constraint is respected to avoid the high magnitude, a suboptimal H∞-constrained fuzzy control problem is also addressed, which is formulated as an LMI optimization problem. Finally, the proposed method is applied to the control of a hypersonic rocket car to illustrate its effectiveness.

The fuzzy feedback control design problem is addressed in this paper by using the distributed proportional-spatial integral (P-sI) control approach for a class of nonlinear distributed parameter systems represented by semi-linear parabolic partial differential-integral equations (PDIEs). The objective of this paper is to develop a fuzzy distributed P-sI controller for the semi-linear parabolic PDIE system such that the resulting closed-loop system is exponentially stable. To do this, the semi-linear parabolic PDIE system is first assumed to be exactly represented by a Takagi-Sugeno (T-S) fuzzy parabolic PDIE model. A new vector-valued integral inequality is established via the vector-valued Wirtinger's inequality. Then, based on the T-S fuzzy PDIE model and this new integral inequality, a distributed fuzzy P-sI state feedback controller is proposed such that the closed-loop PDIE system is exponentially stable. The sufficient condition on the existence of this fuzzy controller is given in terms of a set of standard linear matrix inequalities (LMIs), which can be effectively solved by using the existing convex optimization techniques. Finally, the developed design methodology is successfully applied to solve the feedback control design of a semi-linear reaction-diffusion system with a spatial integral term.

This paper addresses the problem of exponential synchronization via boundary control for a class of networked linear spatiotemporal dynamical networks consisting of N identical nodes, in which the spatiotemporal behavior of the each node is described by parabolic partial differential equations (PDEs). The purpose of this paper is to design boundary controllers ensuring the exponential synchronization of the networked parabolic PDE system. To do this, Lyapunov's direct method, the vector-valued Wirtinger's inequality, and the technique of integration by parts are employed. A sufficient condition on the existence of the boundary controllers is developed in term of standard of linear matrix inequality (LMI). Finally, numerical simulation results on a numerical example are presented to illustrate the effectiveness of the proposed design method.

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.

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.

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.

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.