This paper develops a novel event-triggered (ET) leader-follower fault-tolerant fuzzy consensus framework for nonlinear parabolic distributed parameter system (DPS)-based multi-agent systems (MASs) under multiple cyber attacks. First, a dual-scale modeling framework is proposed, synergizing Galerkin spectral decomposition with Takagi-Sugeno fuzzy techniques to derive a finite-dimensional MASs that accurately captures the dominant dynamics of the original DPS. Second, a resilient hybrid dynamic ET mechanism is devised to intelligently schedule transmissions, significantly alleviating network bandwidth burden while enhancing dynamic performance beyond conventional ET schemes. Subsequently, an event-based fault-tolerant consensus protocol incorporating three data compression mechanisms is designed to counteract multiple cyber attacks. Sufficient conditions for achieving attack-resilient cooperative consensus are then established using a tailored Lyapunov functional approach, with controller gains derived via linear matrix inequality formulations. Finally, simulations on a thermal management system for hypersonic vehicle cooling fins validate the theoretical advances and demonstrate significant engineering applicability.

This paper investigates the boundary control for a general kind of nonlinear reaction diffusion (RD) systems. A novel observer-based control strategy is proposed, which is only need state information of two boundary positions. Furthermore, the intermittent control technique is applied to reduce the control cost. Firstly, the stability problem of the RD system is studied under the proposed observer-based two-point intermittent boundary controllers. Secondly, exponential stability results of the RD system with periodical intermittent controllers are obtained. Thirdly, the synchronization problem between two RD systems is analyzed by applying the above results directly. Numerical examples are given to show the effective of the proposed control method, among which, the proposed control method also applies to the cooling process of hot strip mills.

This study constructs an innovative event-triggered (ET) fuzzy consensus framework for nonlinear delayed parabolic PDE-based multi-agent systems (MASs) to resist multiple attacks. Firstly, a novel dual-scale modeling approach is introduced that synergizes Galerkin-based order reduction with Takagi-Sugeno fuzzy technique to construct a relatively precise ODE-based MASs capturing the dominant dynamics. Secondly, a resilient dynamic ET strategy is formulated to orchestrate communication scheduling, which not only curtails the demand on network bandwidth but also delivers superior dynamic performance over established ET schemes. Building upon this mechanism, a distributed consensus protocol is devised with inherent robustness to counteract cyber attacks. Subsequently, by employing a constructed Lyapunov functional, sufficient criteria guaranteeing resilient cooperative control are deduced, and the corresponding controller parameters are computed by solving linear matrix inequalities. The practical effectiveness and theoretical contributions of the proposed approach are ultimately corroborated through simulations conducted on thermal management systems for cooling fins of a hypersonic vehicle.

This article focuses on the attack-tolerant and fault-tolerant cooperative fuzzy security control problem for nonlinear delayed Markov jump distributed parameter systems (DPSs) under the stochastic sampling that randomly switches between two sampling periods. First, a Takagi-Sugeno (T-S) fuzzy partial differential equation (PDE) model is presented to accurately describe the nonlinear delayed Markov jump DPSs. Subsequently, in consideration of possible random deception attacks and actuator faults, an attack-tolerant and fault-tolerant cooperative fuzzy security control approach with stochastic sampling is proposed under spatially point measurements (SPMs). Then, linear matrix inequality (LMI)-based sufficient conditions that guarantee the stochastically mean-square exponential stability of closed-loop nonlinear delayed Markov jump DPSs are obtained by employing a mode-dependent Lyapunov functional (LF). Lastly, two examples are given to illustrate the effectiveness of the presented control scheme.

This article addresses the issue of output synchronization via intermittent dynamic event-triggered sampled-data (IDETSD) security control of reaction-diffusion neural networks (RDNNs) under spatially local averaged measurements (SLAMs) subject to both delays and random deception attacks, where a Bernoulli distribution is utilized to describe whether channels suffer from the cyberattacks. An IDETSD security control method under SLAMs and random deception attacks is presented to achieve the output synchronization of delayed RDNNs. Compared with time-triggered intermittent sampled-data (SD) control strategies, a dynamic event-triggered (ET) mechanism to more effectively mitigate the impact induced by random deception attacks that intentionally tamper with the state transmission signals from sensors to controllers is introduced in this article. Moreover, new output synchronization criteria are established by applying an ET-dependent switched Lyapunov functional (LF) and inequality techniques. Then, the desired IDETSD controller is obtained by solving linear matrix inequalities (LMIs). To validate the efficacy of the proposed approach, simulation outcomes from two numerical studies are presented.

Accurate bed temperature prediction is crucial in the circulating fluidized bed (CFB) combustion process, as it provides early warning of abnormal conditions, allowing timely intervention to prevent potential safety risks. However, the inherently complex multiphase flows and nonlinear chemical reactions in CFB systems make time series prediction of bed temperature a highly challenging task. Starting from the intrinsic spatial correlations and the temporal dependencies, this article proposes an adaptive learning-based bed temperature prediction method. The proposed model integrates dynamic correlation-guided Graph Convolutional Networks (GCN) and Long Short-Term Memory (LSTM) networks. Specifically, the GCN guided by prior knowledge adaptively learns complex topological structures to capture spatial dependencies. LSTM receives both raw input features and the spatial features extracted by GCN as parallel inputs, effectively capturing the temporal evolution of bed temperature. The proposed method is then applied to the task of bed temperature prediction in CFB. The experimental findings indicate that the proposed method consistently outperforms other comparative methods across different forecasting horizons, achieving a leading level of performance.

Aiming to address the stealthy cyber attacks faced by multiarea interconnected power systems, this article proposes a new decentralized resilient predictive load frequency control (LFC) scheme, which has several prominent features, such as privacy preservation, active attack detection, network blocking defense, and attack tolerance. Compared with the relevant studies in the literature, the novelty of these features is specifically demonstrated by: 1) a dynamic scaling and masking method is constructed to achieve the real-time dynamic protection of network transmission data, which not only enables a closed-loop cyber privacy preservation against eavesdropping attacks, but also guarantees the effectiveness of active detection of attack appearance and disappearance; 2) a scaled one-step-ahead predictive interpolation control strategy is further proposed to achieve dynamic privacy preservation of control algorithm, and to apply a check-before-use mechanism to avoid the false data injected by the stealthy attacks to be loaded into the actuator; and 3) an active attack defense method with fail-safe feature is constructed to block the attacks from penetrating the actuator from the input transmission channels, while providing some finite-time open-loop control capability to suboptimally regulate the LFC before the attacks disappear. A case study of a three-area power system is given to validate the effectiveness of the proposed LFC method.

This article addresses adaptive event-triggered sampled-data (SD) fuzzy security control under spatially local averaged measurements (LAMs) for nonlinear delayed distributed parameter systems (DPSs) with denial of service (DoS) attacks and stochastic actuator failures. Firstly, a Takagi–Sugeno (T–S) fuzzy model of delayed partial differential equations (PDEs) is introduced to precisely characterize the dynamic behavior of nonlinear delayed DPS. Secondly, an adaptive event-triggered SD fuzzy security control strategy is designed under DoS attacks and stochastic actuator failures, which can be flexibly modified in accordance with the present sampling and the most recently transmitted signals, and is implemented utilizing a restricted number of sensors and actuators. Subsequently, by establishing a Lyapunov functional, sufficient conditions that guarantee the mean square exponential stability of closed-loop nonlinear delayed DPSs are obtained based on linear matrix inequalities (LMIs). Finally, two examples are provided and the presented controller are compared to demonstrate the applications and advantages of the proposed approach.

This paper studies the state observer design of a spatial two-dimensional (2-D) linear diffusion process described by a linear parabolic partial differential equation (PDE) under mobile sensors. Firstly, we analyze the well-posedness of the PDE system and give the structure form of the state observer with mobile sensors. Subsequently, according to the number of mobile sensors, the 2-D space domain is divided into multiple sub-domains, and the mobile sensors are guided by the projection operator method, which can guarantee that the mobile sensors can only move in their respective 2-D sub-domains. Then, in the light of Lyapunov theory, Poincaré-Wirtinger inequality and Barbalat lemma, we propose an observation-plus-guidance design method to ensure the asymptotic stability of the state estimation error system. In the designed mobile strategy, the actual guidance of mobile sensors is essentially a physical synthesis of two direction guidance laws, where two dimensional guidance laws are designed separately. Moreover, the existence condition of the observer is given by linear matrix inequalities. At last, a numerical example is provided to demonstrate the efficacy of the proposed design scheme. Note to Practitioners—For the actual physical temporal-space process, the spatial 2-D case makes more sense. With the increase of space dimension, the difficulty of system design increases sharply. The observer design methodology and mobile sensor guidance approach developed for spatial 1-D systems are not directly extendable to 2-D systems. However, there have also been few reports on the observer design of 2-D physical temporal-space process using mobile sensors, and it is still a challenging problem. In this article, this study addresses the problem of designing state observer for 2-D linear parabolic PDE systems utilizing mobile sensors. To prevent collisions among mobile sensors, the 2-D spatial domain is partitioned into several subregions, and the projection operator approach is employed to develop the motion strategy. Then, a Lyapunov-based observation-plus-guidance design method is provided to achieve the desired design goals. At last, the finite difference method is used to verify the design method.

We study the synchronization of delayed reaction-diffusion neural networks (RDNNs) with Neumann boundary conditions, considering both distributed and discrete delays. Particularly, boundary sampled-data (SD) control is proposed to synchronize delayed RDNNs. In the proposed synchronization strategy, boundary SD control is based on boundary and distributed SD measurements. Based on the Lyapunov stability theory and inequality techniques, some synchronization criteria via the boundary SD control are proposed for delayed RDNNs. The boundary SD control gains are obtained by solving the conditions with linear matrix inequalities. Finally, a numerical example is presented to demonstrate the feasibility and effectiveness of the proposed method.

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).

Under the influence of nonlinearity, time-varying delay, and uncertainty, the consensus problem is concerned in this study for multiagent systems modeled by partial differential equations, which means that both the time and space variables are included in the dynamic behavior of each agent. First, with a directed graph, an adaptive boundary controller is developed under boundary measurements, which can effectively reduce the control cost with dynamic control gains and a few actuators and sensors installed at the boundary of the spatial domain. Then, through the designed adaptive boundary controller, the linear matrix inequality (LMI)-based consensus conditions are obtained to ensure the exponential stability of the consensus error systems derived by utilizing the inequality techniques and Lyapunov direct approach. Lastly, two numerical examples demonstrate the effectiveness of the presented adaptive boundary control protocols.

For nonlinear coupled ODE-PDE systems with stochastic actuator failures, this article introduces an intermittent sampled-data fuzzy (ISDF) control under spatially local averaged measurements (LAMs). To precisely characterize the nonlinear coupled ODE-PDE system, a Takagi-Sugeno fuzzy model is firstly introduced. Second, considering the stochastic actuator failures caused by Markov jump, an ISDF control strategy is developed for the nonlinear coupled ODE-PDE system under spatially LAMs, which only demands a minimal number of sensors and actuators. Then, through constructing a time-dependent switched Lyapunov functional, the stochastically exponential stability conditions are given in terms of linear matrix inequalities (LMIs) and ISDF control gains are obtained by solving these LMIs. Finally, the effectiveness of the developed approach is validated through its application to hypersonic rocket car (HRC) control.

Controlling boiler–turbine systems (BTS) is challenging due to their complex nonlinearity and dynamic nature. To address these issues, we propose a novel dual event-triggered fuzzy model predictive control (DEFMPC) method. First, an event-triggered online update strategy is established for the fuzzy prediction model. To save computing resources and communication costs, a dual-channel event-triggered mechanism with a control efficiency evaluation index is then developed. This mechanism updates the prediction model and control input based on the control effect, ensuring efficient control interventions. The stability of the method is analyzed, and its superior performance is demonstrated through numerical simulations on the BTS, showcasing significant improvements in control accuracy and energy efficiency. The results highlight the potential of DEFMPC to enhance the performance and sustainability of thermal power generation systems.

Options, the temporally extended courses of actions that can be taken at varying time scale, have provided a concrete, key framework for learning levels of temporal abstraction in hierarchical tasks. While methods of learning options end-to-end is well researched, how to explore good options and actions simultaneously is still challenging. We address this issue by maximizing reward augmented with entropies of both option and action selection policy in options learning. To this end, we reveal our novel optimization objective by reformulating options learning from perspective of probabilistic inference and propose a soft options iteration method to guarantee convergence to the optimum. In implementation, we propose an off-policy algorithm called the maximum-entropy options critic (MEOC) and evaluate it on series of continuous control benchmarks. Comparative results demonstrate that our method outperforms baselines in efficiency and final result on most benchmarks, and the performance exhibits superiority and robustness especially on complex tasks. Ablated studies further explain that entropy maximization on hierarchical exploration promotes learning performance through efficient options specialization and multimodality in action level.

This article addresses the synchronization problem of reaction-diffusion neural networks (RDNNs) with random time-varying delay (RTVD) via boundary control (BC) (including adaptive BC and BC with constant-valued gain) under distributed measurements or boundary measurements. First, a novel BC strategy with constant-valued gain is designed, which considers three cases of the measurements, that is, distributed measurements, boundary measurements, and both coexist. Subsequently, an adaptive BC scheme under boundary measurements is proposed, where the control gain is regulated effectively. Next, based on the inequality techniques and Lyapunov direct approach, the delay-dependent synchronization conditions are gained and some linear matrix inequalities (LMIs) based theorems are given. Then, the BC design for the delayed RDNNs is transformed into an LMI feasibility problem. Finally, the developed BC approaches are validated by the simulation results.

Under spatially point measurements (SPMs), this paper introduces a fault-tolerant event-triggered sampled-data (FETSD) control for the output synchronization of reaction-diffusion neural networks (RDNNs). Considering the possible actuator failure and to reduce the communication burden, a FETSD control method presented by linear matrix inequalities (LMIs) conditions is designed according to an appropriate Lyapunov functional (LF) and inequality techniques, which can guarantee the exponential stability of the synchronization error system. Lastly, one numerical example is presented to illustrate the effectiveness of the designed strategy,

For a nonlinear parabolic distributed parameter system (DPS), a fuzzy boundary sampled-data (SD) control method is introduced in this article, where distributed SD measurement and boundary SD measurement are respected. Initially, this nonlinear parabolic DPS is represented precisely by a Takagi-Sugeno (T-S) fuzzy parabolic partial differential equation (PDE) model. Subsequently, under distributed SD measurement and boundary SD measurement, a fuzzy boundary SD control design is obtained via linear matrix inequalities (LMIs) on the basis of the T-S fuzzy parabolic PDE model to guarantee exponential stability for closed-loop parabolic DPS by using inequality techniques and a acrlong LF. Furthermore, respecting the property of membership functions, we present some LMI-based fuzzy boundary SD control design conditions. Finally, the effectiveness of the designed fuzzy boundary SD controller is demonstrated via two simulation examples.

This article addresses fault-tolerant event-triggered sampled-data (SD) fuzzy control for nonlinear delayed parabolic partial differential equation (PDE) systems under spatially point measurements (SPMs). First, a Takagi–Sugeno fuzzy delayed PDE model is presented to accurately describe the nonlinear delayed parabolic PDE systems. Second, a fault-tolerant event-triggered SD fuzzy control strategy under SPMs is designed to cope with Markov jump faults occurring in actuators, which can effectively reduce the unnecessary data transmission and be achieved by finite sensors and actuators. The membership functions of the proposed controller are determined by the measurement output and independent of the fuzzy delayed PDE plant model. Then, by constructing a Lyapunov functional, sufficient conditions that guarantee the stochastically exponential stability of closed-loop nonlinear delayed parabolic PDE systems are obtained based on linear matrix inequalities. Finally, two examples are given to illustrate the designed approach.

This article introduces a fuzzy boundary sampled-data (SD) control approach for a nonlinear distributed parameter system (DPS) with random time-varying delay, which belongs to two intervals and is considered by a probabilistic way to take the influence of uncertain factors, and boundary and distributed SD measurements are respected. Initially, this nonlinear DPS is represented precisely by a Takagi–Sugeno (T–S) fuzzy delayed partial differential equation (PDE) model. Subsequently, a fuzzy boundary SD control design is achieved under boundary and distributed SD measurements, employing linear matrix inequalities based on the T–S fuzzy delayed PDE model. This design ensures mean square exponential stability for the closed-loop delayed DPS through the use of inequality techniques and a Lyapunov functional. The membership functions of the proposed fuzzy boundary SD control law are independent of the fuzzy delayed PDE plant model and determined by the measurement output. Finally, the effectiveness of the designed fuzzy boundary SD controller is demonstrated via two simulation examples.

A mixed fuzzy intermittent control method based on boundary control under boundary measurement and distributed control under spatial local averaged measurements (SLAMs) is introduced for nonlinear ordinary differential equations (ODE)-partial differential equations(PDE) coupled systems in this article. To accurately characterize the nonlinear ODE-PDE coupled systems, a Takagi–Sugeno fuzzy model is first employed. Then, based on the fuzzy model, the switched Lyapunov function is proposed to design the mixed fuzzy intermittent controller under boundary measurement and SLAMs. Sufficient conditions on stability for the closed-loop coupled system are obtained via a set of space dependent linear matrix inequalities. The simulation results ultimately confirm the effectiveness of the proposed design approach in controlling hypersonic rocket car.

For nonlinear distributed parameter systems (DPSs) with multiple delays, this study considers a fuzzy fault-tolerant boundary control (BC) with stochastic actuator failures under boundary measurement. First, we exactly represent the nonlinear DPS with multiple delays by the Takagi-Sugeno (T-S) fuzzy delayed partial differential equation (PDE). Next, on basis of T-S fuzzy delayed PDE model, a fuzzy fault-tolerant BC design with stochastic actuator failures under boundary measurement guaranteeing the stochastically exponential stability for closedloop DPS with multiple delays is subsequently presented by linear matrix inequalities (LMIs). Lastly, the effectiveness of the investigated fuzzy fault-tolerant BC strategy with stochastic actuator failures under boundary measurement is proposed via a simulation example.

Under intermittent noncollocated boundary measurement (BM), this article introduces a dynamic intermittent boundary output-feedback control for reaction–diffusion systems (RDSs). Since the system state is not fully available and intermittent noncollocated BM makes the intermittent BC design very difficult, an observer-based control technique is given to surmount this design difficulty. Initially, a PDE state observer under intermittent noncollocated BM is provided to estimate the RDS state. Then, the exponential stability of closed-loop RDSs is ensured by constructing an observer-based controller. Sufficient conditions of such dynamic controller are subsequently presented by linear matrix inequalities (LMIs) via employing a switching time-dependent LF and inequality techniques. Finally, two numerical examples are presented to demonstrate the effectiveness of the proposed design approach.

For nonlinear delayed distributed parameter systems (DDPSs), this article considers a fuzzy boundary control (FBC) under boundary measurements (BMs). Initially, we accurately describe the nonlinear DDPS through a Takagi-Sugeno (T-S) fuzzy partial differential-difference equation (PDDE). Then, in accordance with the T-S fuzzy PDDE model, an FBC design under BMs ensuring the exponential stability for closed-loop DDPS is subsequently presented by spatial linear matrix inequalities (SLMIs) via using Wirtinger's inequality, Halanay's inequality, and the Lyapunov direct method, which respects the fast-varying and slow-varying delays. Moreover, we formulate SLMIs as LMIs for solving the fuzzy boundary controller design of nonlinear DDPSs under BMs. Finally, the effectiveness of the proposed FBC strategy is presented via simulation examples.

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.

For nonlinear space-varying parabolic partial differential equation systems (PPDESs) with random time-varying delay, this article introduces a dynamic fuzzy boundary output feedback (DFBOF) control under noncollocated boundary measurement (NCBM). Initially, the nonlinear delayed PPDESs are represented by Takagi–Sugeno (T–S) fuzzy models and random time-varying delay is considered by taking the influence of uncertain factors, which belongs to two intervals in a probabilistic way. Since the system state is not fully available and NCBM makes the boundary control design very difficult, a fuzzy observer under NCBM is presented to surmount the design difficulty. Subsequently, an observer-based fuzzy boundary controller is proposed and spatial linear matrix inequality (SLMI)-based sufficient conditions to ensure mean-square exponential stability are obtained for closed-loop delayed PPDESs by utilizing the Lyapunov direct method and Wirtinger inequality. Then, to solve the SLMIs, the feasibility conditions of DFBOF controller design for nonlinear delayed PPDES are expressed in LMIs. Finally, two examples are offered to demonstrate the validity of the presented dynamic fuzzy boundary control approach.

In this article, we investigate the pinning spatiotemporal sampled-data (SD) synchronization of coupled reaction-diffusion neural networks (CRDNNs), which are directed networks with SD in time and space communications under random deception attacks. In order to handle with the random deception attacks, we establish a directed CRDNN model, which respects the impacts of variable sampling and random deception attacks within a unified framework. Through the designed pinning spatiotemporal SD controller, sufficient conditions are obtained by linear matrix inequalities (LMIs) that guarantee the mean square exponential stability of the synchronization error system (SES) derived by utilizing inequality techniques, the stochastic analysis technique, and Lyapunov-Krasovskii functional (LKF). Finally, a numerical example is utilized to support the presented pinning spatiotemporal SD synchronization method.

This article proposes a novel unknown input functional observer design approach toward discrete-time interval type-2 Takagi–Sugeno fuzzy system models subject to measurable and unmeasurable premise variables. By constructing a new state vector that contains both the unknown inputs and the system states, functional observers are proposed for the cases with measurable and unmeasurable premise variables to estimate this new state vector for unknown input and/or state estimation. The observer design problem is converted into the solvability issue of a linear matrix equation involving observer gain matrices, and the existence conditions of the observers are explicitly obtained based on matrix rank analysis. Meanwhile, instead of solving the intricate Sylvester equation directly, the solution of the simplified matrix equation is employed to derive the observer gains. Moreover, the effectiveness and the superiority of the presented method are demonstrated via two illustrative examples.

This article introduces a spatially local piecewise fuzzy control (SLPFC) for nonlinear delayed distributed parameter systems (DPSs) with random packet losses. Due to the limited bandwidth of the channels, the random packet losses could occur simultaneously in the communication channels from the sensor to the controller and from the controller to the actuator, which are assumed to obey the Bernoulli random binary distribution. An SLPFC design is given such that, for all possible random packet losses, the closed-loop delayed DPS is mean square exponentially stable. Delay-dependent conditions are obtained and then two procedures are given for designing the spatially local piecewise fuzzy controller: one casts the controller design into an iterative linear matrix inequality (LMI) algorithm and the other casts the controller design into a parameter-dependent LMI problem. Two examples are provided to illustrate the usefulness of the presented design approach.

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.

This article considers the H∞sampled-data fuzzy observer (SDFO) design problem for nonlinear parabolic partial differential equation (PDE) systems under spatially local averaged measurements (SLAMs). Initially, the nonlinear PDE system is accurately represented by the Takagi-Sugeno (T-S) fuzzy PDE model. Then, based on the T-S fuzzy PDE model, an SDFO under SLAMs is constructed for the state estimation. To attenuate the effect of the exogenous disturbance and the design disturbance, an H∞SDFO design under SLAMs is developed in terms of linear matrix inequalities by utilizing Lyapunov functional and inequality techniques, which can guarantee the exponential stability and satisfy an H∞performance for the estimation error fuzzy PDE system. Finally, simulation results on the state estimation of the FitzHugh-Nagumo equation are given to support the presented H∞SDFO design method.

Under spatially local averaged measurements (SLAMs), this article introduces a sampled-data fuzzy control (SDFC) for nonlinear delayed distributed parameter systems (DDPSs). First, we use a Takagi–Sugeno (T–S) fuzzy parabolic partial differential-difference equation (PDDE) to accurately describe the nonlinear DDPS. Then, on basis of the T–S fuzzy PDDE model, an SDFC design under SLAMs via space-dependent linear matrix inequalities (SDLMIs) is subsequently developed to ensure the exponential stability of the closed-loop nonlinear DDPSs by using inequality techniques and Lyapunov functional, where slow-varying and fast-varying delays are respected. Furthermore, to solve SDLMIs, the SDFC design problem for nonlinear DDPS under SLAMs is formulated as a linear matrix inequality feasibility problem. Finally, numerical simulations of two examples are presented to support the given SDFC strategy.

This article introduces a sampled-data (SD) static output feedback fuzzy control (FC) with guaranteed cost for nonlinear parabolic partial differential equation (PDE) systems. First, a Takagi-Sugeno (T-S) fuzzy parabolic PDE model is employed to represent the nonlinear PDE system. Second, with the aid of the T-S fuzzy PDE model, a SD FC design with guaranteed cost under spatially averaged measurements is developed in the formulation of linear matrix inequalities by utilizing a time-dependent Lyapunov functional and inequality techniques, which can stabilize exponentially the PDE system while providing an optimized upper bound on the cost function. The membership functions of the proposed controller are determined by the measurement output and independent of the fuzzy PDE plant model. Finally, simulation results are presented to control the diffusion equation and the FitzHugh-Nagumo equation for demonstrating the effectiveness of the proposed method.

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.

This paper introduces a fuzzy control (FC) under spatially point measurements for nonlinear time-delay distributed parameter systems (DPSs) described by parabolic partial differential-difference equations (PDdEs). First, a Takagi-Sugeno (T-S) fuzzy PDdE model is employed to represent the nonlinear time-delay DPSs. Second, with the aid of the T-S fuzzy PDdE model, an FC design under spatially point measurements is developed in the formulation of linear matrix inequalities by constructing an appropriate Lyapunov functional, which can stabilize exponentially the time-delay DPSs. This stabilization condition can be applied to either slowing-varying time delay or fast-varying one. Finally, simulation results of a numerical example are provided to illustrate the effectiveness of the proposed method.

This paper presents a robust guaranteed cost sampled-data fuzzy control (GCSDFC) design for Takagi-Sugeno fuzzy systems with parametric uncertainties and time-delay. Initially, a robust guaranteed cost sampled-data fuzzy controller is developed to stabilize exponentially the closed-loop fuzzy system while providing an upper bound for the quadratic cost function. In order to make full information of the actual sampling pattern, a novel time-dependent Lyapunov functional is subsequently constructed to derive the condition for the existence of the proposed controller which is given in terms of linear matrix inequalities (LMIs). Then, to minimize the upper bound of the cost function, a suboptimal robust GCSDFC problem can be formed as an LMI optimization problem. Finally, two examples are given to illustrate the effectiveness of the proposed method.

In this paper, an observer-based H∞sampled-data fuzzy control problem is addressed for a class of nonlinear parabolic partial differential equation (PDE) systems. With the aid of the modal decomposition technique, a nonlinear ordinary differential equation (ODE) model is initially derived to describe the dominant (slow) dynamics of the PDE system. Subsequently, the resulting nonlinear ODE model is accurately represented by the Takagi-Sugeno (T-S) fuzzy model. Then, based on the T- S fuzzy model, a finite-dimensional observer-based sampled-data fuzzy control design with H∞performance is developed for the PDE system via employing a novel time-dependent functional. The outcome of the observer-based H∞sampled-data fuzzy control problem can be formulated as a bilinear matrix inequality optimization problem. Moreover, an iterative optimization algorithm based on the linear matrix inequalities is given to obtain a suboptimal H∞sampled-data fuzzy controller. Finally, simulation results on the Fisher equation and a temperature cooling fin of high-speed aerospace vehicle illustrate that the proposed design method is effective.

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.

In this paper, a novel approach to fuzzy sampled-data control of chaotic systems is presented by using a time-dependent Lyapunov functional. The advantage of the new method is that the Lyapunov functional is continuous at sampling times but not necessarily positive definite inside the sampling intervals. Compared with the existing works, the constructed Lyapunov functional makes full use of the information on the piecewise constant input and the actual sampling pattern. In terms of a new parameterized linear matrix inequality (LMI) technique, a less conservative stabilization condition is derived to guarantee the exponential stability for the closed-loop fuzzy sampled-data system. By solving a set of LMIs, the fuzzy sampled-data controller can be easily obtained. Finally, the chaotic Lorenz system and Rössler's system are employed to illustrate the feasibility and effectiveness of the proposed method.