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 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.

This article is concerned with the human behavior identification problem for linear human-in-the-loop (HiTL) systems in adversarial environments. By modeling the human as an optimal controller that minimizes his/her individual cost function and the adversarial environment as an opponent to maximize the cost function, the HiTL system is formulated as a linear-quadratic zero-sum differential game that consists of two players that are the human and adversarial environment. Then, the human behavior identification is transformed to an inverse reinforcement learning (IRL) problem. Accordingly, the main works carried out in this article can be summarized as follows: 1) an integral concurrent learning (ICL) law is proposed to estimate the feedback matrix of the human and 2) based on the estimated feedback matrix, the weighting matrices in human cost function are retrieved by minimizing a residual. The main focus of the developed human behavior identification method is to remove the persisting excitation constraint and the demand for measuring the control input of humans that are universally required in existing online learning approaches. Finally, the results of simulation and experiment on the lane keeping scenario of a vehicle verify the validity of the proposed adaptive-IRL-based human behavior identification strategy.

This article proposes a dynamic neural network (DNN)-based control method to realize the optimal control of nonlinear parameter-varying (NPV) systems. Specifically, a DNN-based control policy (DNN-CP) composed of static shared layers and a parameter-related dynamic layer is constructed to improve the generalization and adaptability. An extreme learning machine (ELM)-based weight prediction model is established to fit the relationship between the dynamic weights and the system parameters. The shared layers are updated by solving the constrained multiobjective problem to reduce performance conflicts among different systems, and the weight prediction model is tuned by maximizing parameter-related objectives to achieve optimal control of each system. To improve data efficiency and adaptability, a supervised learning-based pretraining and reinforcement learning (RL)-based fine-tuning algorithm is developed. Finally, the control performance of the DNN-CP is verified on morphing aircraft. We demonstrate that the designed DNN-CP and training algorithm can achieve generalization capabilities, and DNN-CP can be immediately generalized to any system within the parameter space without sample collection or fine-tuning. Compared with other methods, DNN-CP has better control performance on the system with continuously varying parameters.

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.

To improve machines’ intelligence, it is necessary for the machines to learn human’s behavior. In this paper, we make a reasonable hypothesis that a human behaves like a linear quadratic regulator whose cost function is unknown to the machine when performing a task. In addition, the system dynamics in many real applications is completely unknown. Therefore, our purpose is to search for an equivalent cost function to the human only from control input and system state data for continuous-time linear human-in-the-loop (HiTL) systems with completely unknown dynamics. An adaptive inverse optimal control (IOC) method is proposed for this purpose, which can help the machine conduct a better understanding for the human behavior and makes it possible to reproduce a similar optimal controller in other environments. Noticing the difficulty of directly obtaining the weighting matrix, an adaptive integral concurrent learning (ICL) algorithm is developed to identify the system matrices and human feedback gain matrix online, which removes the persistent excitation (PE) conditions. Then, the weighting matrix is determined via solving a convex programming problem. Finally, simulation results on the lane-keeping assist system of an intelligent vehicle are presented to demonstrate the validity of the proposed adaptive IOC algorithm. Note to Practitioners—In practice, it is hoped that the machine can work like a human such that it can replace the human to complete certain tasks. However, it is not easy to design corresponding algorithms for the machine because many tests need to be carried out for selecting appropriate parameters. Instead, an effective method is to teach the machine learn the human’s demonstrated behavior. It is noteworthy that the environment (system dynamics) may be not prior knowledge and only system state and control input are measurable. To this end, an adaptive IOC method is developed for imitation learning the human’s behavior, which is implemented online but requires only limited data. The proposed approach can be used in autonomous driving vehicle, service robot, and medical rehabilitation, etc. In future research, we will extent the proposed method to more complex environment.

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).

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.

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.

In this paper, a novel synchronization learning scheme is proposed for secure communication, where the signal transmission architecture with a chaotic encryption process is considered. Firstly, to realize the information security in communication, the original signals are encrypted by fractional order dynamics from the sender, and decrypted by receiver to achieve synchronization. For the process, a hybrid order dynamic optimization is constructed, where the fractional order and the integer order systems are modeled as constraints. Secondly, a transformation formula is developed to convert these constraints into new integer order dynamics, and the equivalence between two dynamic optimizations is obtained. Thirdly, to obtain the synchronization solution, a new iterative learning algorithm is designed, and the adaptive dynamic programming is successfully embedded into the solving process. Finally, we apply the proposed synchronization scheme into the secure image transmission, and the simulation results demonstrate the effectiveness and practicality successfully.

To improve the hybrid augmented intelligence of a human-in-the-loop (HiTL) control system, it is desirable to investigate the issue of human behavior learning (HBL), i.e., empower the machine to understand how a human expert performs a manipulation task. The human expert is commonly modeled as an optimal controller with unknown weighting matrices that depict the tradeoff between different control objectives. Therefore, the goal of this article is to determine the weighting matrices of the human objective function with fast convergence rate, which is usually pursued to achieve better efficiency and performance in practice. Accordingly, for a class of HiTL system, we propose a novel adaptive inverse optimal control (IOC) approach for online learning human behavior with a fixed-time guarantee. Our proposed method consists of two parts. In the first step, a dynamic regressor extension and mixing (DREM)-based estimation method is used for online learning of the human feedback gain with fixed-time convergence using the demonstrated system state measurement only. Then, with the estimated human feedback gain, a semidefinite programming (SDP) problem is solved to determine the weighting matrices of the human objective function. The simulation and the experiment on a steering control have validated the effectiveness and applicability of the developed approach.

Owing to the immaturity of current artificial intelligence techniques, practical multiagent systems (MASs) often require supervision and intervention from humans. However, it is unrealistic for a human to monitor the entire MAS and provide appropriate input in some circumstances. A viable approach is to allow a human to control an agent as the leader which in turn influences the other autonomous followers. To this end, a critical issue is how to learn human behavior to improve the autonomy of followers for collaborating with human effectively, since the autonomous followers do not have prior knowledge of human behavior. In this article, the human leading behavior learning problem is studied for a class of human-in-the-loop (HiTL) MASs that are not fully connected. A linear quadratic differential game framework is applied to formulate the collaborative control problem in the HiTL MAS where the human behavior is represented as a cost function whose weighting matrix is unknown to the followers. In the HiTL MAS, we select a follower that has strong computing power called follower 1 to learn the human behavior via an online adaptive inverse differential game (IDG) approach. Based on concurrent learning (CL) technique, an adaptive law is developed for follower 1 to determine the human feedback matrix online, and at the same time the interaction strategies for the autonomous followers are also calculated by follower 1 in case of the constrained communication topology. Subsequently, the weighting matrix in the human cost function is recovered by addressing a linear matrix inequality (LMI) optimization problem. Finally, a numerical example is presented to demonstrate the effectiveness of the proposed method.

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 investigates the problem of inverse optimal control (IOC) for a class of nonlinear affine systems. An adaptive IOC approach is proposed to recover the cost functional using only the system state data, which integrates the finite-time concurrent learning (FTCL) technique and the semidefinite programming (SDP) technique. First, an identifier neural network (NN) is employed to approximate the unknown nonlinear control policy, and an FTCL-based update law is proposed to estimate the weights of the identifier NN online, which removes the traditional persistent excitation (PE) condition. Moreover, the finite-time convergence as well as the uniformly ultimately boundness (UUB) of estimation error of the identifier NN weights are analysed according to whether or not there exists the identifier NN approximation error. Then, with the help of a value NN for approximating the value function, an SDP problem with a quadratic objective function can be set up for determining the weighting matrices of the cost functional. Finally, simulation results are presented to validate the proposed method.

To enhance the collaborative intelligence of a machine, it is important for the machine to understand what behavior a human may adopt to interact with the machine when performing a task in shared control. In this study, an online behavior learning method is proposed for continuous-time linear human-in-the-loop shared control systems by using the system state data only. A two-player nonzero-sum linear quadratic dynamic game paradigm is used for modeling the control interaction between a human operator and an automation that actively compensates for human control action. In this game model, the cost function representing the human behavior is assumed to have an unknown weighting matrix. Here, we want to learn the human behavior or retrieve the weighting matrix by using the system state data only. Accordingly, a new adaptive inverse differential game (IDG) method, which integrates concurrent learning (CL) and linear matrix inequality (LMI) optimization, is proposed. First, a CL-based adaptive law and an interactive controller of the automation are developed to estimate the feedback gain matrix of the human online, and second, an LMI optimization problem is solved to determine the weighting matrix of the human cost function. Finally, simulation results on a cooperative shared control driver assistance system are provided to elucidate the feasibility of the developed method.

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.

In this paper, the issue of human behavior learning (HBL) is addressed for a class of nonlinear human-in-the-loop (HiTL) systems where the human operator is viewed as a nonlinear optimal controller. Owing to its outstanding interpretability and strong nonlinear representation capability, the Takagi-Sugeno (T-S) fuzzy model is employed to represent the nonlinear HiTL control system and approximate the unknown human control law based on the parallel distributed compensation (PDC) scheme. A quadratic-like cost function with fuzzy weighting matrices is built to depict the human behavior, which conforms to human thinking and is unknown to the machine. The aim of the HBL is to retrieve the fuzzy weighting matrices such that the human control law will be optimal in the sense of minimizing the retrieved cost function. In the proposed HBL scheme, the state-dependent Riccati equation (SDRE) based nonlinear optimal control technique plays an important role, which has a similar structure to the linear quadratic regulator (LQR) theory and thus is of low computational complexity. With the help of the PDC based fuzzy approximator for the unknown human control law, a two-step procedure is proposed for the HBL. First, a filter-based adaptive law is developed to learn the gain matrices of the fuzzy approximator using the system state data only. The convergence analysis of the adaptive estimator is also given. Then, a semidefinite programming (SDP) problem with the quadratic objective function can be set up for determining the fuzzy weighting matrices of the cost function. The simulation study on a steering control system of the intelligent vehicle is given to show the effectiveness and applicability of the developed approach.

In this article, the distributed formation control problem for a class of human-in-the-loop (HiTL) multiagent systems (MASs) is studied. A hidden Markov jump MAS is employed to model the HiTL MAS, which integrates the human models, the MAS model, and their interactions. The HiTL MAS investigated in this article is composed of two parts: a leader without human in the control loop and a group of followers in which each follower is simultaneously controlled by a human operator and an automation. For each follower, a hidden Markov model is used for modeling the human behaviors in consideration of the random nature of human internal state (HIS) reasoning and the uncertainty from HIS observation. By means of a stochastic Lyapunov function, a necessary and sufficient condition is first developed in terms of the linear matrix inequalities (LMIs) to ensure the formation of the HiTL MAS in the mean-square sense. Then, an LMI approach to the human-assistance control design is proposed for the automations in the followers to guarantee the mean-square formation of the HiTL MAS. Finally, simulation results are presented to verify the effectiveness of the proposed methods.

In light of optimization theory and swarm evolutionary schemes, under multiple single-integrator mobile agents equipped with sensors and prompters, this article addresses a discrete-time multiagent source exploration problem with information prompts. Regarding information prompts as constraints on the unknown target, by virtue of penalty function skills (PFSs) and sequential unconstrained minimization techniques (SUMTs), the agents are driven toward the source under the guidance of the control strategy. In two cases of available and unavailable gradient information, a quantum potential well, an average optimal position estimator (AOPE), and a global optimal position estimator (GOPE) are introduced into swarm evolutionary schemes with a periodically oscillating weight, such that distributed cooperative quantum learning (DCQL) policy is proposed as a control strategy under communication restrictions, where AOPE and GOPE are developed relying on distributed consensus theory. In particular, when the gradient is unavailable, we put forth an adaptive generalized Bernstein neural network (AGBNN) to replace it based on excellent properties of Bernstein polynomials and adaptive approaches. Further, a performance analysis for the proposed policy is executed on the convergence and computational complexity, which ensures the accuracy and efficiency of the source exploration in theory. Ultimately, a simulation test is carried out, and the results validate the practicability and effectiveness of the offered method.

This article focuses on finite-time passivity (FTP) and finite-time synchronization (FTS) for complex dynamical networks with multiple state/derivative couplings based on the proportional-derivative (PD) control method. Several criteria of FTP for complex dynamical networks with multiple state couplings (CDNMSCs) are formulated by utilizing the PD controller and constructing an appropriate Lyapunov function. Furthermore, FTP is further used to investigate the FTS in CDNMSCs under the PD controller. In addition, the FTP and FTS for complex dynamical networks with multiple derivative couplings (CDNMDCs) are also studied by exploiting the PD control method and some inequality techniques. Finally, two numerical examples are worked out to demonstrate the validity of the presented PD controllers.

One goal of artificial intelligence (AI) research is to teach machines how to learn from humans, such that they can perform a certain task in a natural human-like way. In this article, an online adaptive inverse reinforcement learning (IRL) approach to human behavior modeling is proposed to enhance machine intelligence for a class of linear human-in-the-loop (HiTL) systems using the state data only, where the human behavior is described by a linear quadratic optimal control model with an unknown weighting matrix for the quadratic cost function. First, an integral concurrent adaptive law is developed to learn the human feedback gain matrix online using the demonstrated state data only, which removes the persistent excitation (PE) conditions required by traditional adaptive estimation approaches and thus is more in line with real applications. Then, with the learned feedback gain matrix, the IRL problem is formulated as a linear matrix inequality (LMI) optimization problem, which can be efficiently solved to retrieve the weighting matrix of the human cost function. Finally, a simulation example is provided to illustrate the effectiveness of the proposed approach.

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.

The key to enhancing machine intelligence is to make the machine learn how human beings perform tasks. In this article, the issue of finite-horizon inverse linear quadratic (LQ) optimal control is investigated for human behavior learning in a class of human-in-the-loop (HiTL) systems. A novel finite-horizon inverse optimal control (FHIOC) approach is developed by integrating time-varying parameter identification and linear matrix inequality (LMI) optimization techniques. The proposed approach covers three steps: by only using the system state measurement, 1) an offline identification method is developed to provide a batch least-squares estimation for the human time-varying feedback gain matrix; 2) a recursive least-squares adaptive law is proposed to online learn the human time-varying feedback gain in real time; and 3) the weighting matrices of the human cost function are recovered via the time-convexity and LMI optimization techniques with the learned time-varying feedback gain. Finally, the validity of the proposed methods is supported by a supplementary steering system of an intelligent vehicle.

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.

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.

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.

This article studies the boundary fuzzy control problem for nonlinear parabolic partial differential equation (PDE) systems under spatially noncollocated mobile sensors. In a real setup, sensors and actuators can never be placed at the same location, and the noncollocated setting may be beneficial in some application scenarios. The control design is very difficult due to the noncollocated mobile observation, which can be solved by an observer-based technique. At first, a Takagi–Sugeno fuzzy PDE model is devoted to accurately representing the nonlinear parabolic PDE system. Next, we present a state estimation scheme including fuzzy Luenberger-type PDE state observer plus mobile sensor guidance. Then, an observer-based boundary fuzzy controller is posed to render the resulting closed-loop system exponentially stable, and the exponential decay rate is increased by the designed mobile sensor guidance laws. At last, two examples verify the proposed method.

In combination with optimization theory and swarm evolutionary mechanisms, based on multiple mobile robots equipped with sensors, this paper deals with a plume source localization issue with environmental obstacles and communication restrictions for robots. First of all, we offer the plume modeling process and analyze some internal characteristics about its source, such that the source localization issue can be addressed by solving a path planning one with constraints for cooperative swarm robots. Secondly, a quantum potential well, an average estimator and a minimum estimator are introduced into swarm evolutionary mechanisms with an oscillation weight, such that quantum-behaved cooperative navigation (QBCN) scheme is proposed as a guidance strategy, where the average estimator and the minimum estimator are designed depending on distributed consensus theory. Subsequently, we put forth a formation behavior consisting of leader-follower tactics, obstacle avoidance tactics and motion optimization tactics, which not only provides a practical collision/obstacle measure, but also increases the coverage area for the objective. Afterwards, a performance analysis for the proposed policy is executed on the convergence and computational complexity, which ensures the accuracy and timeliness of source localization in theory. Finally, simulation tests are performed in different scenarios, and the results validate the practicability and effectiveness of the developed method.

This article mainly delves into the finite-time passivity (FTP) for coupled fractional-order neural networks with multistate couplings (CFNNMSCs) or coupled fractional-order neural networks with multiderivative couplings (CFNNMDCs). Distinguishing from the traditional FTP definitions, several concepts of FTP for fractional-order systems are given. On one hand, we present several sufficient conditions to ensure the FTP for CFNNMSCs by artfully designing a state-feedback controller and an adaptive state-feedback controller. On the other hand, by utilizing some inequality techniques, two sets of FTP criteria for CFNNMDCs are also established on the basis of the state-feedback and adaptive state-feedback controllers. Finally, numerical examples are used to demonstrate the validity of the derived FTP criteria.

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 presents several new α -passivity and α -finite-time passivity ( α -FTP) concepts for the fractional-order systems with different input and output dimensions, which are distinct from the concepts for integer-order systems and extend the existing passivity and FTP definitions to some extent. On one hand, we not only develop some sufficient conditions for ensuring the α -passivity of the multi-weighted fractional-order complex dynamical networks (MWFOCDNs) with fixed and adaptive couplings, but also discuss the synchronization for the MWFOCDNs based on the α -output-strict passivity ( α -OSP). On the other hand, the α -FTP for the MWFOCDNs with fixed and adaptive couplings are also studied on the basis of the designed state feedback controller, and the relationship between finite-time synchronization (FTS) and α -FTP for the MWFOCDNs is also illustrated. Finally, two numerical examples with simulation results are used to demonstrate the validity of the obtained criteria.

In this article, we, respectively, take the synchronization into consideration for directed and undirected complex networks (CNs) with multiple state or delayed state couplings subject to recoverable attacks. By selecting appropriate Lyapunov functional, employing inequality techniques, and adopting the designed state-feedback controller, two criteria of the synchronization are established for the directed CN with multiple state couplings (CNMSCs). Moreover, the synchronization of CNMSCs is also discussed for the case that the network topology is undirected. In addition, two types of CNs with multiple delayed state couplings are also proposed, and several criteria of synchronization are formulated for these networks. Finally, two examples are given to verify the correctness of the derived synchronization criteria.

This article investigates the issue of the fuzzy observer design for the semilinear parabolic partial differential equation (PDE) systems with mobile sensing measurements. Initially, we employ a Takagi-Sugeno (T-S) fuzzy PDE model to represent the semilinear parabolic PDE system accurately in a local region. Afterward, via the T-S fuzzy model and under the hypothesis that the spatial domain is divided by several subdomains in the light of the number of sensors, a state observation scheme which contains a fuzzy observer and the mobile sensor guidance is proposed. Then, by means of the Lyapunov direct method and integral inequalities, a design method of the fuzzy observer and mobile sensor guidance is provided to render the resulting state estimation error system exponentially stable, while the designed mobile sensor guidance can increase the exponential decay rate. Finally, numerical simulations are presented to show that the proposed fuzzy observer design approach is effective and the employment of mobile sensors contributes to improving the response speed of the state estimation error in comparison with the static ones.

This article studies the problem of synthesis with guaranteed cost and less human intervention for linear human-in-the-loop (HiTL) control systems. Initially, the human behaviors are modeled via a hidden controlled Markov process, which not only considers the inference's stochasticity and observation's uncertainty of the human internal state but also takes the control input to human into account. Then, to integrate both models of human and machine as well as their interaction, a hidden controlled Markov jump system (HCMJS) is constructed. With the aid of the stochastic Lyapunov functional together with the bilinear matrix inequality technique, a sufficient condition for the existence of human-assistance controllers is derived on the basis of the HCMJS model, which not only guarantees the stochastic stability of the closed-loop HiTL system but also provides a prescribed upper bound for the quadratic cost function. Moreover, to achieve less human intervention while meeting the desired cost level, an algorithm that mixes the particle swarm optimization and linear matrix inequality technique is proposed to seek a suitable feedback control law to the human and a human-assistance control law to the machine. Finally, the proposed method is applied to a driver-assistance system to verify its effectiveness.

Via mobile sensing measurements, this study applies the Takagi-Sugeno (T-S) fuzzy model to deal with the mobile fuzzy control design problem for nonlinear time-delay parabolic partial differential equation (PDE) systems. Initially, we use a T-S fuzzy model to accurately represent the nonlinear time-delay parabolic PDE system. Subsequently, under the assumption that the actuators and sensors are collocated while the spatial domain is divided by several subdomains, a control scheme containing the fuzzy controllers and the guidance of mobile actuator/sensor pairs is proposed based on the obtained T-S fuzzy model, where the projection modification guidance to be designed can guarantee that each mobile actuator/sensor pair moves within the prescribed area. Then, using the Lyapunov direct method and integral inequalities, a membership-function-dependent design of fuzzy controllers plus mobile actuator/sensor guidance laws is developed to render the resulting closed-loop time-delay system exponentially stable. Moreover, the exponential decay rate can also be increased by the proposed mobile guidance laws. Finally, numerical simulations are presented to illustrate the effectiveness of the proposed design method and the application of mobile actuator/sensor pairs contributes to accelerating the convergence speed of the closed-loop state.

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.

To enhance the machines’ intelligence, it is important for them to learn how humans perform tasks. In this article, the issue of online adaptive learning human behavior is addressed for a class of human-in-the-loop (HiTL) systems using the state measurement only. The hypothesis underlying our study is that human behavior can be described by a linear quadratic optimal control model with an unknown weighting matrix for the quadratic cost function. In this model, the weighting matrix depicts the human tradeoff of various objectives. Our aim is thus to only use the system state measurement for learning the weighting matrix under the condition that human feedback gain matrix is unknown. A novel adaptive inverse optimal control approach to online learning human behavior is proposed for the HiTL system, which integrates adaptive estimation and linear matrix inequality (LMI) optimization techniques. Our approach consists of two steps: First, an adaptive law is developed to learn the human feedback gain matrix online using the system state measurement only, and second, the weighting matrix of human cost function is retrieved by solving an LMI optimization problem with the learned feedback gain matrix. Finally, simulation and experiment results on a steering assist system of intelligent vehicles are presented to illustrate the effectiveness of the proposed method.

This article studies the problem of multiobjective control design for a class of human–machine systems (HMSs) with safety performance constraints containing state constraints and input constraints. The HMSs under consideration not only monitor the human but also need to take proper actions to both the human and machine. A model of controlled hidden Markov jump system (CHMJS) is applied to represent the HMSs. Based on the CHMJS model, a sufficient condition for the practical mean square stability of the unconstrained HMSs is first derived using a stochastic Lyapunov functional. A sufficient condition for ensuring the safety performance constraints of the HMSs is also deduced by employing reachability analysis and set invariance theory. Subsequently, a bilinear matrix inequality-based control design is presented to guarantee both the practical mean square stability and safety performance constraints of the HMSs. A multiobjective optimization problem (MOP) is then formulated to determine a feedback controller for the human and a human-assistance controller for the machine such that both the practical mean square stability and safety performance constraints as well as the less human intervention can be satisfied. An algorithm that mixes the multiobjective particle swarm optimization and linear matrix inequality technique is developed to solve this MOP. Finally, a lane departure example is given to illustrate its effectiveness.

This paper focuses on source location for scalar fields through multiple mobile robots with sensors. Combined with field strength measurements and swarm evolution mechanisms, the robots are guided to move toward the source of the field. Upon introducing an adaptive weight strategy, a swarm timely update mechanism and a leading-following behavior into quantum particle swarm optimization (QPSO) algorithm, quantum-leading-following-based optimization (QLFBO) algorithm is proposed to direct the movement of robots for a more efficient search. Meanwhile, a collision/obstacle avoidance strategy is designed for the robot to avert accidents. Considering the minimum problem as an optimization objective, the global convergence is proved for QLFBO algorithm. Besides, we study the computational complexity on QLFBO algorithm and the collision/obstacle avoidance strategy. Thus the performance analysis on the global convergence and computational complexity provides theoretical guarantee and feasibility support for multi-robot source location. Finally, simulation tests show the practicality and effectiveness of the developed scheme.

There have been a wide variety of practical control applications having human in the loop in today’s society, such as automobile systems, health care, and energy management. In this article, a Markov jump system with controlled and hidden modes (MJSCHM) is employed to model a class of human-in-the-loop (HiTL) control systems which passively monitor human internal state (HIS) and take appropriate control actions to the human and the machine. By means of the MJSCHM, the human model, the machine model, and their interaction can be integrated in a probabilistic framework. In the MJSCHM, a controlled hidden Markov model (CHMM) is used for the human behavior modeling, which takes into account the random nature of HIS reasoning and the uncertainty from HIS observation, as well as the effect of control input for the human on the HIS. The stability analysis and human-assistance control design for linear discrete-time HiTL systems are addressed using the stochastic Lyapunov functional and linear matrix inequality (LMI) technique. Necessary and sufficient condition for stochastic stability of the HiTL system is first developed on the basis of the MJSCHM model. An LMI approach to the human-assistance control design is then proposed such that the HiTL system is stochastically stable. Finally, simulation results on a driver-assistance system are presented to illustrate the effectiveness of the proposed methods.

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 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.

In this paper, the output synchronization problem for complex dynamical networks (CDNs) with multiple output or output derivative couplings is discussed in detail. Under the help of Lyapunov functional and inequality techniques, an output synchronization criterion is presented for CDNs with multiple output couplings (CDNMOCs). To ensure the output synchronization of CDNMOCs, an adaptive control scheme is also devised. Similarly, we also take into account the adaptive output synchronization and output synchronization of CDNs with multiple output derivative couplings. At last, several numerical examples are designed to testify the effectiveness of the proposed results.

In this article, two kinds of complex dynamical networks (CDNs) with state and derivative coupling are investigated, respectively. First, some important concepts about finite-time passivity (FTP), finite-time output strict passivity, and finite-time input strict passivity are introduced. By making use of state-feedback controllers and adaptive state-feedback controllers, several sufficient conditions are given to guarantee the FTP of these two network models. On the other hand, based on the obtained FTP results, some finite-time synchronization criteria for the CDNs with state and derivative coupling are gained. Finally, two simulation examples are proposed to verify the availability of the derived results.

This article investigates the finite-time output synchronization and$H_{\infty }$output synchronization problems for coupled neural networks with multiple output couplings (CNNMOC), respectively. By choosing appropriate state feedback controllers, several finite-time output synchronization and$H_{\infty }$output synchronization criteria are proposed for the CNNMOC. Moreover, a coupling-weight adjustment scheme is also developed to guarantee the finite-time output synchronization and$H_{\infty }$output synchronization of CNNMOC. Finally, two numerical examples are given to verify the effectiveness of the presented criteria.

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 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.

In this paper, two kinds of multiweighted and adaptive state coupled complex networks (CNs) with or without coupling delays are presented. First, we develop the appropriate state feedback controller and adaptive law for the sake of guaranteeing that the proposed network models without coupling delays can be finite-timely synchronized and H∞synchronized. Furthermore, for the multiweighted CNs with coupling delays and adaptive state couplings, some finite-time synchronization and H∞synchronization criteria are presented by choosing the appropriate adaptive law and controllers. Eventually, we give two numerical simulations to verify the validity of the theoretical results.

In this paper, the finite-time passivity (FTP) problem for two classes of coupled neural networks (CNNs) with adaptive coupling weights is discussed. By selecting appropriate adaptive laws and controllers, several FTP conditions are given for CNNs with undirected and directed topologies. Furthermore, some finite-time synchronization conditions are also established by employing the FTP of the CNNs. At last, two numeral examples are used to check the correctness of the obtained criteria.

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 article investigates a fuzzy boundary control problem of a class of stochastic nonlinear systems modeled by the Itô-type parabolic stochastic partial differential equation (SPDE). Initially, a Takagi-Sugeno fuzzy SPDE model is proposed to accurately represent the nonlinear SPDE system. Then, on the basis of the infinite-dimensional infinitesimal operator, a fuzzy boundary static output feedback controller is developed in terms of a set of linear matrix inequalities to locally exponentially stabilize the resulting system in the mean square sense. By using an approximation argument and constructing a Lyapunov function for the mild solution, the local mean square exponential stability of the closed-loop system is proved. Meanwhile, the closed-loop well-posedness analysis is also given by virtue of the semigroup theory. Finally, a simulation study on a Belousov-Zhabotinsky reaction-diffusion system with random parameter variation is presented to illustrate the effectiveness of the proposed method.

This paper deals with a fuzzy stabilization design problem for a class of semilinear parabolic partial differential equation (PDE) systems using mobile actuators and sensors. Initially, a Takagi-Sugeno (T-S) fuzzy PDE model is employed to accurately represent the semilinear parabolic PDE system. Subsequently, based on the T-S fuzzy model, a stabilization scheme containing the fuzzy controllers and the guidance of mobile actuator/sensor pairs is proposed, where the spatial domain is decomposed into multiple subdomains according to the number of actuator/sensor pairs and each actuator/sensor pair is capable of moving within the respective subdomain. Then, by a Lyapunov direct technique, an integrated design of fuzzy controllers plus mobile actuator/sensor guidance laws is developed in the form of bilinear matrix inequalities (BMIs), such that the resulting closed-loop system is exponentially stable and the mobile actuator/sensor guidance can enhance the transient performance of the closed-loop system. Furthermore, an iterative algorithm based on linear matrix inequalities is proposed to solve the BMIs. Finally, two examples are given to illustrate the effectiveness of the proposed method.

This paper studies the problem of event-triggered optimal control (ETOC) for continuous-time nonlinear systems and proposes a novel event-triggering condition that enables designing ETOC methods directly based on the solution of the Hamilton-Jacobi-Bellman (HJB) equation. We provide formal performance guarantees by proving a predetermined upper bound. Moreover, we also prove the existence of a lower bound for interexecution time. For implementation purposes, an adaptive dynamic programming (ADP) method is developed to realize the ETOC using a critic neural network (NN) to approximate the value function of the HJB equation. Subsequently, we prove that semiglobal uniform ultimate boundedness can be guaranteed for states and NN weight errors with the ADP-based ETOC. Simulation results demonstrate the effectiveness of the developed ADP-based ETOC method.

Recently, the dynamical behaviors of coupled neural networks (CNNs) with and without reaction-diffusion terms have been widely researched due to their successful applications in different fields. This article introduces some important and interesting results on this topic. First, synchronization, passivity, and stability analysis results for various CNNs with and without reaction-diffusion terms are summarized, including the results for impulsive, time-varying, time-invariant, uncertain, fuzzy, and stochastic network models. In addition, some control methods, such as sampled-data control, pinning control, impulsive control, state feedback control, and adaptive control, have been used to realize the desired dynamical behaviors in CNNs with and without reaction-diffusion terms. In this article, these methods are summarized. Finally, some challenging and interesting problems deserving of further investigation are discussed.

The optimal control problem of discrete-time nonlinear systems depends on the solution of the Bellman equation. In this paper, an adaptive reinforcement learning (RL) method is developed to solve the complex Bellman equation, which balances value iteration (VI) and policy iteration (PI). By adding a balance parameter, an adaptive RL integrates VI and PI together, which accelerates VI and avoids the need of an initial admissible control. The convergence of the adaptive RL is proved by showing that it converges to the Bellman equation. Subsequently, the adaptive RL is realized by using the neural network (NN) approximation for value function and a least-squares scheme is developed for updating NN weights. Then, the convergence of NN-based adaptive RL is proved with considering NN approximation error. To further improve its performance, an adaptive rule is developed for tuning balance parameter in adaptive RL iteration by iteration. Finally, the effectiveness of the adaptive RL is validated with simulation studies.

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.

Controllers learned from data are more practical and promising than the existing model-based ones and their capability can be enhanced if a priori information about the controlled plant is available. Under this viewpoint, a data-driven guaranteed cost control (GCC) design is investigated for linear systems with time-varying parameter uncertainties. Initially, the GCC design is shown to be equivalent to an H∞state feedback control problem subject to a specific disturbance attenuation performance requirement. Then such an H∞control problem is regarded as a zero-sum game and reduces to seek the stabilizing solution of a parameterized algebraic Riccati equation (ARE). Furthermore, to solve the ARE approximately, a modified simultaneous policy update algorithm (SPUA) and the corresponding data-driven variant based on off-policy reinforcement learning (RL) and experience replay technique is proposed. Finally, a numerical simulation for aircrafts with harsh uncertainties is illustrated to validate the merits of the proposed methods.

The output synchronization and H∞output synchronization problems for multiweighted complex network are discussed in this paper. First, we analyze the output synchronization of multiweighted complex network by exploiting Lyapunov functional and Barbalat's lemma. In addition, some nodes- and edges-based pinning control strategies are developed to ensure the output synchronization of multiweighted complex network. Similarly, the H∞output synchronization problem of multiweighted complex network is also discussed. Finally, two numerical examples are presented to verify the correctness of the obtained results.

In this paper, two multiple weighted coupled reaction-diffusion neural networks (CRDNNs) with and without coupling delays are introduced. On the one hand, some finite-time passivity (FTP) concepts are proposed for the spatially and temporally system with different dimensions of output and input. By choosing appropriate Lyapunov functionals and controllers, several sufficient conditions are presented to ensure the FTP of these CRDNNs. On the other hand, the finite-time synchronization (FTS) problem is also discussed for the multiple weighted CRDNNs with and without coupling delays, respectively. Finally, two numeral examples with simulation results are provided to verify the effectiveness of the obtained FTP and FTS criteria.

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 complex network model consisting of N uncertain reaction-diffusion neural networks with multiple time delays. We analyze the passivity and synchronization of the proposed network model and derive several passivity and synchronization criteria based on some inequality techniques. In addition, by considering the difficulty in achieving passivity (synchronization) in such a network, an adaptive control scheme is also developed to ensure that the proposed network achieves passivity (synchronization). Finally, we design two numerical examples to verify the effectiveness of the derived passivity and synchronization criteria.

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, we introduce two complex dynamical networks with multiweights, which have several different sorts of weights between two nodes. By means of Lyapunov functional method and pinning control technique, some sufficient conditions are derived to ensure the synchronization for proposed network models. Moreover, some adaptive strategies are given to acquire suitable coupling strengths and feedback gains. By exploiting these designed adaptive laws, several general criteria for network synchronization are established. Finally, two numerical examples are also provided to show the validity of the theoretical results.

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 addresses a mixed fuzzy/boundary control problem of a class of nonlinear coupled systems described by ordinary differential equation (ODE) and boundary-disturbed uncertain beam equation. The control scheme consists of an ODE-state feedback fuzzy controller for the ODE system and an antidisturbance robust boundary controller for the boundary-disturbed uncertain beam. The boundary controller includes a linear feedback controller for the beam stabilization via boundary measurements, a nonlinear compensator with adaptive bounding, and a disturbance observer based compensator for canceling the effects of the uncertain nonlinearity and the boundary disturbance of the beam. The mixed control design is developed in terms of space dependent bilinear matrix inequalities (SDBMIs) to guarantee the closed-loop input-to-state practical stability. Meanwhile, the closed-loop well-posedness analysis is also given. Furthermore, a two-step procedure is introduced to solve the SDBMI feasibility problem by the existing linear matrix inequality optimization techniques. Finally, a simulation study on a flexible spacecraft is 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.

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.

Reinforcement learning has proved to be a powerful tool to solve optimal control problems over the past few years. However, the data-based constrained optimal control problem of nonaffine nonlinear discrete-time systems has rarely been studied yet. To solve this problem, an adaptive optimal control approach is developed by using the value iteration-based Q-learning (VIQL) with the critic-only structure. Most of the existing constrained control methods require the use of a certain performance index and only suit for linear or affine nonlinear systems, which is unreasonable in practice. To overcome this problem, the system transformation is first introduced with the general performance index. Then, the constrained optimal control problem is converted to an unconstrained optimal control problem. By introducing the action-state value function, i.e., Q-function, the VIQL algorithm is proposed to learn the optimal Q-function of the data-based unconstrained optimal control problem. The convergence results of the VIQL algorithm are established with an easy-to-realize initial condition . To implement the VIQL algorithm, the critic-only structure is developed, where only one neural network is required to approximate the Q-function. The converged Q-function obtained from the critic-only VIQL method is employed to design the adaptive constrained optimal controller based on the gradient descent scheme. Finally, the effectiveness of the developed adaptive control method is tested on three examples with computer simulation.

This paper considers a complex dynamical network model, in which the input and output vectors have different dimensions. We, respectively, investigate the passivity and the relationship between output strict passivity and output synchronization of the complex dynamical network with fixed and adaptive coupling strength. First, two new passivity definitions are proposed, which generalize some existing concepts of passivity. By constructing appropriate Lyapunov functional, some sufficient conditions ensuring the passivity, input strict passivity and output strict passivity are derived for the complex dynamical network with fixed coupling strength. In addition, we also reveal the relationship between output strict passivity and output synchronization of the complex dynamical network with fixed coupling strength. By employing the relationship between output strict passivity and output synchronization, a sufficient condition for output synchronization of the complex dynamical network with fixed coupling strength is established. Then, we extend these results to the case when the coupling strength is adaptively adjusted. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the proposed criteria.

This research focuses on the problem of output synchronization in undirected and directed complex dynamical networks, respectively, by applying Barbalat's lemma. First, to ensure the output synchronization, several sufficient criteria are established for these network models based on some mathematical techniques, such as the Lyapunov functional method and matrix theory. Furthermore, some adaptive schemes to adjust the coupling weights among network nodes are developed to achieve the output synchronization. By applying the designed adaptive laws, several criteria for output synchronization are deduced for the network models. In addition, a design procedure of the adaptive law is shown. Finally, two simulation examples are used to show the effectiveness of the previous results.

The model-free optimal control problem of general discrete-time nonlinear systems is considered in this paper, and a data-based policy gradient adaptive dynamic programming (PGADP) algorithm is developed to design an adaptive optimal controller method. By using offline and online data rather than the mathematical system model, the PGADP algorithm improves control policy with a gradient descent scheme. The convergence of the PGADP algorithm is proved by demonstrating that the constructed Q -function sequence converges to the optimal Q -function. Based on the PGADP algorithm, the adaptive control method is developed with an actor-critic structure and the method of weighted residuals. Its convergence properties are analyzed, where the approximate Q -function converges to its optimum. Computer simulation results demonstrate the effectiveness of the PGADP-based adaptive control method.

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

This paper introduces a hybrid robust boundary and fuzzy control design for disturbance attenuation of a class of coupled systems described by nonlinear ordinary differential equations (ODEs) and two nonlinear beam equations. Initially, a Takagi–Sugeno (T–S) model is employed to exactly represent the nonlinear ODE subsystem. Then, a fuzzy controller is designed for the ODE subsystem based on the T–S fuzzy model, and a robust boundary controller via beam boundary measurements is proposed for the nonlinear beam subsystem. Such a hybrid robust boundary and fuzzy controller is developed in terms of a set of space-dependent bilinear matrix inequalities (BMIs) by Lyapunov's direct method, which can exponentially stabilize the coupled system in the absence of disturbances and achieve an prescribed$H_{\infty }$performance of disturbance attenuation in the presence of disturbances. Furthermore, in order to make the level of disturbance attenuation as small as possible, a suboptimal$H_{\infty }$control problem is formulated as a BMI optimization problem. A two-step procedure is subsequently presented to solve this BMI optimization problem by the existing linear matrix inequality optimization techniques. Finally, the proposed control method is applied to the control of a flexible spacecraft to illustrate its effectiveness.

A complex dynamical network consisting of N identical neural networks with reaction-diffusion terms is considered in this paper. First, several passivity definitions for the systems with different dimensions of input and output are given. By utilizing some inequality techniques, several criteria are presented, ensuring the passivity of the complex dynamical network under the designed adaptive law. Then, we discuss the relationship between the synchronization and output strict passivity of the proposed network model. Furthermore, these results are extended to the case when the topological structure of the network is undirected. Finally, two examples with numerical simulations are provided to illustrate the correctness and effectiveness of the proposed results.

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.

Two coupled reaction-diffusion neural networks (CRDNNs) with different dimensions of input and output are considered in this paper. The only difference between them is whether time-varying delay is incorporated in the mathematical model of network. We respectively analyze dissipativity and passivity of these CRDNNs. First, for the systems with different dimensions of input and output vectors, two new passivity definitions are proposed. Then, by exploiting some inequality techniques, several dissipativity and passivity criteria for these CRDNNs are established. Furthermore, we analyze stability of passive CRDNNs. Finally, two examples with simulation results are presented to verify the effectiveness of the proposed criteria.

This paper investigates the guaranteed-cost finite-time fuzzy control problem subject to a temperature constraint for a class of coupled systems represented by nonlinear ordinary differential equations (ODEs) and a scalar nonlinear heat equation. Initially, a finite-dimensional nonlinear coupled system is derived by combining the slow system of heat equation with the original ODE system, which can be exactly represented by the Takagi–Sugeno fuzzy model. Meanwhile, the temperature constraint is transformed into the state constraint performed on the finite-dimensional coupled system. Then, a guaranteed-cost finite-time constrained fuzzy control design is developed in terms of a set of time-dependent differential linear matrix inequalities (LMIs) to make the closed-loop of the original ODE system finite-time quasi-contractively stable with an upper bound of quadratic cost function, while the temperature constraint is respected. Furthermore, by utilizing the time-convexity and LMI optimization techniques, a suboptimal controller is obtained by means of minimizing the guaranteed-cost bound. Finally, the proposed design method is applied to the control of a temperature constrained hypersonic rocket car.

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.

A design method of low-dimensional disturbance rejection fuzzy control (DRFC) via multiple observers is proposed for a class of nonlinear parabolic partial differential equation (PDE) systems, where the disturbance is modeled by an exosystem of ordinary differential equations (ODEs) and enters into the PDE system through the control channel. In the proposed scheme, the modal decomposition technique is initially applied to the PDE system to derive a slow subsystem of low-dimensional nonlinear ODEs, which accurately captures the dominant dynamics of the PDE system. The resulting nonlinear slow subsystem is subsequently represented by a Takagi-Sugeno (T-S) fuzzy model. From the T-S fuzzy model and the exosystem, a fuzzy slow mode observer and a fuzzy disturbance observer are constructed to estimate the slow mode and the disturbance, respectively. Furthermore, a nonlinear observation spillover observer is proposed to compensate the effect of observation spillover. Then, based on these observers, a low-dimensional DRFC design is developed in terms of linear matrix inequalities to guarantee the exponential stability of the closed-loop PDE system in the presence of the disturbance. Finally, the effectiveness of the proposed design method is demonstrated on the control of one-dimensional Burgers-KPP-Fisher diffusion-reaction system and the temperature profile of a catalytic rod.

Two types of coupled neural networks with reaction-diffusion terms are considered in this paper. In the first one, the nodes are coupled through their states. In the second one, the nodes are coupled through the spatial diffusion terms. For the former, utilizing Lyapunov functional method and pinning control technique, we obtain some sufficient conditions to guarantee that network can realize synchronization. In addition, considering that the theoretical coupling strength required for synchronization may be much larger than the needed value, we propose an adaptive strategy to adjust the coupling strength for achieving a suitable value. For the latter, we establish a criterion for synchronization using the designed pinning controllers. It is found that the coupled reaction-diffusion neural networks with state coupling under the given linear feedback pinning controllers can realize synchronization when the coupling strength is very large, which is contrary to the coupled reaction-diffusion neural networks with spatial diffusion coupling. Moreover, a general criterion for ensuring network synchronization is derived by pinning a small fraction of nodes with adaptive feedback controllers. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

This paper proposes a directed complex dynamical network consisting of N linearly and diffusively coupled identical reaction-diffusion neural networks. Based on the Lyapunov functional method and the pinning control technique, some sufficient conditions are obtained to guarantee the synchronization of the proposed network model. In addition, an adaptive strategy is proposed to obtain appropriate coupling strength for achieving network synchronization. Furthermore, the pinning adaptive synchronization problem is also investigated in this paper, and a general criterion for ensuring network synchronization is established. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria.

The H∞ control design problem is considered for nonlinear systems with unknown internal system model. It is known that the nonlinear H∞ control problem can be transformed into solving the so-called Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that is generally impossible to be solved analytically. Even worse, model-based approaches cannot be used for approximately solving HJI equation, when the accurate system model is unavailable or costly to obtain in practice. To overcome these difficulties, an off-policy reinforcement leaning (RL) method is introduced to learn the solution of HJI equation from real system data instead of mathematical system model, and its convergence is proved. In the off-policy RL method, the system data can be generated with arbitrary policies rather than the evaluating policy, which is extremely important and promising for practical systems. For implementation purpose, a neural network (NN)-based actor-critic structure is employed and a least-square NN weight update algorithm is derived based on the method of weighted residuals. Finally, the developed NN-based off-policy RL method is tested on a linear F16 aircraft plant, and further applied to a rotational/translational actuator system.

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.

In this paper, we study a general array model of coupled reaction-diffusion neural networks (NNs) with adaptive coupling. In order to ensure the passivity of the coupled reaction-diffusion neural networks, some adaptive strategies to tune the coupling strengths among network nodes are designed. By utilizing some inequality techniques and the designed adaptive laws, several sufficient conditions ensuring passivity are obtained. In addition, we reveal the relationship between passivity and synchronization of the coupled reaction-diffusion NNs. Based on the obtained passivity results and the relationship between passivity and synchronization, a global synchronization criterion is established. Finally, numerical simulations are presented to illustrate the correctness and effectiveness of the proposed results.

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 data-driven H∞ control problem of nonlinear distributed parameter systems is considered in this paper. An off-policy learning method is developed to learn the H∞ control policy from real system data rather than the mathematical model. First, Karhunen-Loève decomposition is used to compute the empirical eigenfunctions, which are then employed to derive a reduced-order model (ROM) of slow subsystem based on the singular perturbation theory. The H∞ control problem is reformulated based on the ROM, which can be transformed to solve the Hamilton-Jacobi-Isaacs (HJI) equation, theoretically. To learn the solution of the HJI equation from real system data, a data-driven off-policy learning approach is proposed based on the simultaneous policy update algorithm and its convergence is proved. For implementation purpose, a neural network (NN)- based action-critic structure is developed, where a critic NN and two action NNs are employed to approximate the value function, control, and disturbance policies, respectively. Subsequently, a least-square NN weight-tuning rule is derived with the method of weighted residuals. Finally, the developed data-driven off-policy learning approach is applied to a nonlinear diffusion-reaction process, and the obtained results demonstrate its effectiveness.

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

This paper studies the finite-horizon optimal guaranteed cost control (GCC) problem for a class of time-varying uncertain nonlinear systems. The aim of this problem is to find a robust state feedback controller such that the closed-loop system has not only a bounded response in a finite duration of time for all admissible uncertainties but also a minimal guaranteed cost. A neural network (NN) based approximate optimal GCC design is developed. Initially, by modifying the cost function to account for the nonlinear perturbation of system, the optimal GCC problem is transformed into a finite-horizon optimal control problem of the nominal system. Subsequently, with the help of the modified cost function together with a parametrized bounding function for all admissible uncertainties, the solution to the optimal GCC problem is given in terms of a parametrized Hamilton-Jacobi-Bellman (PHJB) equation. Then, a NN method is developed to solve offline the PHJB equation approximately and thus obtain the nearly optimal GCC policy. Furthermore, the convergence of approximate PHJB equation and the robust admissibility of nearly optimal GCC policy are also analyzed. Finally, by applying the proposed design method to the entry guidance problem of the Mars lander, the achieved simulation results show the effectiveness of the proposed controller.

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.

In this paper, we propose a general array model of coupled reaction-diffusion neural networks with hybrid coupling, which is composed of spatial diffusion coupling and state coupling. By utilizing the Lyapunov functional method combined with the inequality techniques, a sufficient condition is given to ensure that the proposed network model is synchronized. In addition, when the external disturbances appear in the network, a criterion is obtained to guarantee the H∞ synchronization of the network. Moreover, some adaptive strategies to tune the coupling strengths among network nodes are designed for reaching synchronization and H∞ synchronization. Some criteria for synchronization and H∞ synchronization are derived by using the designed adaptive laws. Numerical simulations are presented finally to demonstrate the effectiveness of the obtained theoretical results.

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.

A novel robust fuzzy disturbance observer-based control (DOBC) design methodology with adaptive bounding is proposed for the longitudinal dynamics of a generic hypersonic vehicle (HV) with modeled and unmodeled disturbances. A Takagi-Sugeno (T-S) fuzzy model is first employed to approximate the nonlinear dynamics of an HV. Subsequently, a new fuzzy disturbance observer is constructed to estimate the modeled disturbance. An augmented system with multiple disturbances is thus obtained by combining the dynamics of HV and the state estimation error of the modeled-disturbance generator. Then, a robust L∞ -gain fuzzy DOBC design with adaptive bounding is developed to guarantee that the closed-loop augmented system is semiglobally input-to-state practically stable (ISpS) with an L∞-gain performance. In the proposed control scheme, the compound disturbance, including the unmodeled disturbance and the approximation error in fuzzy modeling procedure, is divided into the matched part and the mismatched one, which are attenuated by adaptive bounding control and L∞ -gain control, respectively. The outcome of the robust L∞-gain fuzzy DOBC problem is formulated as a linear matrix inequality (LMI) problem. Moreover, by means of the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of L∞-gain, meanwhile a control constraint is respected. Finally, simulation results demonstrate the effectiveness of the proposed controller.

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.

In this paper, two types of linearly coupled neural networks with reaction-diffusion terms are proposed. We respectively investigate the adaptive synchronization of these two types of complex network models. With local information of node dynamics, some novel adaptive strategies to tune the coupling strengths among network nodes are designed. By constructing appropriate Lyapunov functionals and using inequality techniques, several sufficient conditions are given for reaching synchronization by using the designed adaptive laws. Finally, two examples with numerical simulations are provided to demonstrate the effectiveness of the theoretical results.

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.

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

It is well known that the nonlinear H∞ state feedback control problem relies on the solution of the Hamilton-Jacobi-Isaacs (HJI) equation, which is a nonlinear partial differential equation that has proven to be impossible to solve analytically. In this paper, a neural network (NN)-based online simultaneous policy update algorithm (SPUA) is developed to solve the HJI equation, in which knowledge of internal system dynamics is not required. First, we propose an online SPUA which can be viewed as a reinforcement learning technique for two players to learn their optimal actions in an unknown environment. The proposed online SPUA updates control and disturbance policies simultaneously; thus, only one iterative loop is needed. Second, the convergence of the online SPUA is established by proving that it is mathematically equivalent to Newton's method for finding a fixed point in a Banach space. Third, we develop an actor-critic structure for the implementation of the online SPUA, in which only one critic NN is needed for approximating the cost function, and a least-square method is given for estimating the NN weight parameters. Finally, simulation studies are provided to demonstrate the effectiveness of the proposed algorithm.

This paper addresses the approximate optimal control problem for a class of parabolic partial differential equation (PDE) systems with nonlinear spatial differential operators. An approximate optimal control design method is proposed on the basis of the empirical eigenfunctions (EEFs) and neural network (NN). First, based on the data collected from the PDE system, the Karhunen-Loève decomposition is used to compute the EEFs. With those EEFs, the PDE system is formulated as a high-order ordinary differential equation (ODE) system. To further reduce its dimension, the singular perturbation (SP) technique is employed to derive a reduced-order model (ROM), which can accurately describe the dominant dynamics of the PDE system. Second, the Hamilton-Jacobi-Bellman (HJB) method is applied to synthesize an optimal controller based on the ROM, where the closed-loop asymptotic stability of the high-order ODE system can be guaranteed by the SP theory. By dividing the optimal control law into two parts, the linear part is obtained by solving an algebraic Riccati equation, and a new type of HJB-like equation is derived for designing the nonlinear part. Third, a control update strategy based on successive approximation is proposed to solve the HJB-like equation, and its convergence is proved. Furthermore, an NN approach is used to approximate the cost function. Finally, we apply the developed approximate optimal control method to a diffusion-reaction process with a nonlinear spatial operator, and the simulation results illustrate its effectiveness.

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.

This paper is concerned with the passivity and stability problems of reaction-diffusion neural networks (RDNNs) in which the input and output variables are varied with the time and space variables. By utilizing the Lyapunov functional method combined with the inequality techniques, some sufficient conditions ensuring the passivity and global exponential stability are derived. Furthermore, when the parameter uncertainties appear in RDNNs, several criteria for robust passivity and robust global exponential stability are also presented. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria.

In this paper, an adaptive fuzzy fault accommodation (FA) control design with a guaranteed L(∞)-gain performance is developed for a class of nonlinear time-delay systems with persistent bounded disturbances. Using the Lyapunov technique and the Razumikhin-type lemma, the existence condition of the L(∞) -gain adaptive fuzzy FA controllers is provided in terms of linear matrix inequalities (LMIs). In the proposed FA scheme, a fuzzy logic system is employed to approximate the unknown term in the derivative of the Lyapunov function due to the unknown fault function; a continuous-state feedback control strategy is adopted for the control design to avoid the undesirable chattering phenomenon. The resulting FA controllers can ensure that every response of the closed-loop system is uniformly ultimately bounded with a guaranteed L(∞)-gain performance in the presence of a fault. Moreover, by the existing LMI optimization technique, a suboptimal controller is obtained in the sense of minimizing an upper bound of the L(∞)-gain. Finally, the achieved simulation results on the FA control of a continuous stirred tank reactor (CSTR) show the effectiveness of the proposed design procedure.

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

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

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

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

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

This paper is concerned with the design of reliable$ H_infty $fuzzy controllers for continuous-time nonlinear systems with actuator failures. The Takagi and Sugeno fuzzy model is employed to represent a nonlinear system. The objective is to find a stabilizing state-feedback fuzzy controller such that the nominal$ H_infty $performance is optimized while satisfying a prescribed$ H_infty $performance constraint in the actuator failure cases. Based on the linear matrix inequality (LMI) techniques, two efficient methods for the design of a suboptimal reliable$ H_infty$fuzzy controller are proposed. Different Lyapunov functions are used during the design for the nominal and actuator failure cases, which lead to a less conservative controller design. In the first method, a single Lyapunov function is used for the actuator failure cases. The second method adopts a parameter-dependent Lyapunov function for the actuator failure cases, which further reduces the conservatism of the design. Finally, numerical simulations on the chaotic Rossler system are given to illustrate the effectiveness of the proposed design methods.

This correspondence studies stability analysis and stabilization for discrete-time Takagi and Sugeno fuzzy systems with state delay. First, a new fuzzy Lyapunov-Krasovskii functional (LKF) is constructed to derive a delay-dependent stability condition for open-loop fuzzy systems. Then, a delay-dependent stabilization approach based on a nonparallel distributed compensation scheme is provided for closed-loop fuzzy systems. Both state feedback and observer-based control cases are considered. The proposed stability and stabilization conditions are represented in terms of linear matrix inequalities (LMIs), which can be solved efficiently by using existing LMI optimization techniques. Finally, two numerical examples are given to illustrate the effectiveness of the proposed method.

This paper is concerned with the robust-stabilization problem of uncertain Markovian jump nonlinear systems (MJNSs) without mode observations via a fuzzy-control approach. The Takagi and Sugeno (T-S) fuzzy model is employed to represent a nonlinear system with norm-bounded parameter uncertainties and Markovian jump parameters. The aim is to design a mode-independent fuzzy controller such that the closed-loop Markovian jump fuzzy system (MJFS) is robustly stochastically stable. Based on a stochastic Lyapunov function, a robust-stabilization condition using a mode-independent fuzzy controller is derived for the uncertain MJFS in terms of linear matrix inequalities (LMIs). A new improved LMI formulation is used to alleviate the interrelation between the stochastic Lyapunov matrix and the system matrices containing controller variables in the derivation process. Finally, a simulation example is presented to illustrate the effectiveness of the proposed design method.

This paper deals with the reliable linear quadratic (LQ) fuzzy control problem for continuous-time nonlinear systems with actuator faults. The Takagi-Sugeno (T-S) fuzzy model is employed to represent a nonlinear system. By using multiple Lyapunov functions, an improved linear matrix inequality (LMI) method for the design of reliable LQ fuzzy controllers is investigated, which reduces the conservatism of using a single Lyapunov function. The different upper bounds on the LQ performance cost function for the normal and different actuator fault cases are provided. A suboptimal reliable LQ fuzzy controller is given by means of an LMI optimization procedure, which can not only guarantee the stability of the closed-loop overall fuzzy system for all cases, but also provide an optimized upper bound on a weighted average LQ performance cost function. Finally, numerical simulations on the chaotic Lorenz system are given to illustrate the application of the proposed design method.

This paper studies reliable linear quadratic (LQ) fuzzy regulator problem for nonlinear discrete-time systems with actuator faults. The Takagi and Sugeno fuzzy model is employed to represent a nonlinear system. A sufficient condition expressed in linear matrix inequality (LMI) terms for the existence of reliable guaranteed cost (GC) fuzzy controllers is obtained. The fuzzy controller directly obtained from the LMI solutions can guarantee the stability of the closed-loop overall fuzzy system, while provide a guaranteed cost on the quadratic cost function of the system in the normal and actuator fault cases. Furthermore, an optimal reliable GC fuzzy controller in the sense of minimizing a bound on the worst or nominal case guaranteed cost is also given by means of an LMI optimization procedure. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.