In this article, theH∞fuzzy control problem is investigated for a class of nonlinear systems subject to replay attacks with frequency-duration constraints. Owing to the vulnerability of the open shared communication network, the information transmitted from the sensor to the controller may be exposed to replay attackers. A novel yet comprehensive replay attack model is constructed to characterize the repeated replay behavior of the adversary. On the basis of the constructed model, a fuzzy controller is designed to guarantee asymptotic stability and the desiredH∞performance. By employing Lyapunov stability theory and the orthogonal decomposition technique, sufficient conditions are derived to ensure the existence of the desired controller parameter. Finally, simulation results are presented to verify the effectiveness and correctness of the proposed fuzzy controller for T-S fuzzy systems under replay attacks.

This paper addresses the problem of distributed state estimation for smooth nonlinear systems over sensor networks by means of a generalized fuzzy proportional-integral observer (PIO). A sensor network is employed to collect system measurements, with a pull-type gossip protocol governing the intermittent data exchange among neighboring nodes. Under the gossip protocol, each sensor node randomly selects one neighbor to request data, facilitating distributed information updating. Furthermore, considering challenges such as long-distance communication and complex environmental conditions, signal transmission is subject to amplitude fading. To accommodate the characteristics of the gossip protocol, a generalized fuzzy PIO with a flexible structure is developed. Sufficient conditions are derived to guarantee the$H\_{\infty }$estimation performance of the proposed observer. Based on established conditions, the parameters of both the gossip protocol and the fuzzy PIO are co-designed via a particle-swarm-optimization-based iterative algorithm, with emphasis on enhancing observer robustness. Finally, an engineering-oriented simulation example is presented to illustrate the effectiveness of the proposed methodology.

This article investigates the proportional-integral-derivative (PID) containment control problem for a class of linear MAS with multirate measurements under the constraint of sensor resolution. The sensors of agents are classified into two distinct groups, characterized by their relatively fast and slow sampling periods. The concept of sensor resolution is introduced to quantify the ability of sensors to detect the smallest changes in information. A PID controller with an improved structure is proposed to achieve containment control, ensuring that follower agents remain within the convex hull formed by the leader agents. The closed-loop system is reformulated into a simplified representation, incorporating both sampling characteristics and communication topology. Sufficient conditions are then derived to guarantee the exponentially ultimate boundedness of the tracking error. Based on these conditions, an iterative algorithm is developed for computing the required controller gains. Finally, a simulation study, along with comparative analyses, is conducted to validate the effectiveness of the proposed approach.

This paper is concerned with the$H_{\infty }$proportional-integral-derivative (PID) control problem for Takagi-Sugeno fuzzy systems over lossy networks that are characterized by the Gilbert-Eillott model. The communication quality is reflected by the presence of two channel modes (i.e., “bad” mode and “good” mode), which switch randomly according to a Markov process. In the “bad” mode, packet dropouts are governed by a stochastic variable sequence. Considering the inaccessibility of channel modes, a mode detector is utilized to estimate the communication situation. The relationship between the actual channel mode and the estimated mode is depicted in terms of certain conditional probabilities. Moreover, a comprehensive model is constructed to represent the probability uncertainties arising from statistical errors in channel mode switching, packet dropouts, and mode detection processes. Subsequently, a robust asynchronous PID controller, based on the detected channel mode, is proposed. Sufficient conditions are then derived to ensure the mean-square stability of the closed-loop system while maintaining the desired$H_{\infty }$performance. Finally, the efficacy of the proposed design approach is demonstrated through a simulation example.

This article deals with the distributed proportional–integral state estimation problem for nonlinear systems over sensor networks (SNs), where a number of spatially distributed sensor nodes are utilized to collect the system information. The signal transmissions among different sensor nodes are realized via their individual channels subject to energy-constrained Denial-of-Service (EC-DoS) cyber-attacks launched by the adversaries whose aim is to block the nodewise communications. Such EC-DoS attacks are characterized by a sequence of attack starting time-instants and a sequence of attack durations. Based on the measurement outputs of each node, a novel distributed fuzzy proportional–integral estimator is proposed that reflects the topological information of the SNs. The estimation error dynamics is shown to be regulated by a switching system under certain assumptions on the frequency and the duration of the EC-DoS attacks. Then, by resorting to the average dwell-time method, a unified framework is established to analyze the dynamical behaviors of the resultant estimation error system, and sufficient conditions are obtained to guarantee the stability as well as the weighted$H_{\infty}$performance of the estimation error dynamics. Finally, a numerical example is given to verify the effectiveness of the proposed estimation scheme.

In this paper, we investigate the so-called$H_{\infty }$fuzzy proportional-integral observer (PIO) design problem for a class of nonlinear systems subject to relay effects, data missing, and multi-rate measurements. The considered multi-rate phenomenon is defined as the employment of sensors with diverse sampling periods due to specific engineering requirements. During the long transmission from multi-rate sensors to the remote fuzzy observer, the amplify-and-forward relay scheme is utilized to facilitate data communication, in which the measurement outputs are first directed to the relay nodes and then sent to the observer side. A unified model, incorporating both fast and slow sampling, is described using the switching system method. Subsequently, a fuzzy PIO is proposed by utilizing estimated premise variables along with current and historical system information. Through the application of stochastic analysis theory, the error dynamics of the state estimation is examined, and the observer gain matrices are determined by solving a specific convex optimization problem. Ultimately, two simulation experiments are conducted to validate the efficacy and utility of the formulated fuzzy PIO.

In this article, the problem of observer-based fuzzy proportional–integral–derivative (PID) tracking control is studied for networked nonlinear systems subject to protocol constraints and norm-bounded noises. The nonlinear plant under consideration is represented by an affine fuzzy model with immeasurable premise variables. The utilization of the try-once-discard protocol is proposed for information exchange between sensors and the controller, in order to mitigate the data transmission burden. An observer-based PID controller is put forward to achieve the desired tracking task and handle immeasurable premise variables, with sufficient consideration given to both available measurements and the reference trajectory. By analyzing the dynamics of the controlled tracking error system through the construction of a piecewise Lyapunov-like functional, the exponential ultimate boundedness of the tracking error dynamics is ensured. The controller parameters are designed using convex optimization technique and matrix theory, such that the tracking error dynamics is exponentially ultimately bounded. Finally, the validity and merits of the developed controller design method are verified through a simulation example.

This article addresses the problem of observer-based fuzzy proportional-integral-derivative (PID) control for a class of nonlinear systems subject to degraded measurements and randomly perturbed sampling periods (RPSPs). In the existing results, the degraded measurements and RPSPs are handled separately, where the sampling of different sensors is usually assumed to be synchronous. In our work, a comprehensive model is built to reflect the joint effects of degraded measurements and RPSPs by using a series of stochastic variable sequences and a set of Markov processes. In this model, the sampling periods of each sensor are allowed to be diverse, time-varying, and randomly perturbed, thereby fully capturing the environmental effects and device constraints. Different from the existing literature that uses proportional type controllers, an observer-based fuzzy PID controller with a modified structure is proposed, which fully utilizes the system information. To overcome the difficulties of the incomplete measurement information, some auxiliary variables related to the sampling periods are introduced under which the measurement output is transformed into a form delayed with stochastic delays. Subsequently, by using the special variable separation and inequality technique, sufficient conditions are derived to ensure the exponentially ultimate boundedness of the closed-loop system in the mean-square sense. The desired gains for the observer and PID controller are obtained through the solution of an optimization problem. Last, the effectiveness of the developed approach is demonstrated through simulation examples.

In this article, the state estimation problem is investigated for permanent magnet synchronous motors with sensor degradations under the encoding–decoding scheme. To reduce the network communication burden and enhance data transmission security, a uniform quantization-based encoding–decoding strategy is introduced in the sensor-to-estimator channel, which allows the transmitted power signals to be converted into digital format. Furthermore, the sensor degradation is represented by using a set of independent stochastic variables obeying uniform distributions. The primary objective of this article is to design a recursive state estimation algorithm such that, in the presence of sensor degradations and encoding–decoding strategy, a minimal upper bound on the estimation error covariance is derived by designing an appropriate estimator gain matrix. Simulation experiments for permanent magnet synchronous motors are conducted to validate the efficacy of the proposed recursive state estimation algorithm.

This article investigates the ultimately bounded proportional–integral–derivative (PID) control problem for a class of discrete-time Takagi–Sugeno fuzzy systems subject to unknown-but-bounded noises and protocol constraints. The signal transmissions from sensors to the remote controller are realized via a communication network, where the FlexRay protocol is employed to flexibly schedule the information exchange. The FlexRay protocol is characterized by both the time- and event-triggered mechanisms, which are conducted in a cyclic manner. By using a piecewise approach, the measurement outputs affected by the FlexRay protocol are established based on a switching model. Then, a fuzzy PID controller is proposed with a concise and realizable structure. To evaluate the performance of the controlled system, a special time sequence is introduced that accounts for the behavior of the FlexRay protocol. Subsequently, a general framework is obtained to verify the boundedness of the closed-loop system, and then, the controller gains are designed by minimizing the bound of the concerned variables. Finally, a simulation study is conducted to validate the effectiveness of the developed control scheme.

This article is concerned with the multiloop decentralized$H_{\infty }$fuzzy proportional–integral–derivative-like (PID-like) control problem for discrete-time Takagi–Sugeno fuzzy systems with time-varying delays under dynamical event-triggered mechanisms (ETMs). The sensors of the plant are grouped into several nodes according to their physical distribution. For resource-saving purposes, the signal transmission between each sensor node and the controller is implemented based on the dynamical ETM. Taking the node-based idea into account, a general multiloop decentralized fuzzy PID-like controller is designed with fixed integral windows to reduce the potential accumulation error. The overall decentralized fuzzy PID-like control scheme involves multiple single-loop controllers, each of which is designed to generate the local control law based on the measurements of the corresponding sensor node. These kinds of local controllers are convenient to apply in practice. Sufficient conditions are obtained under which the controlled system is exponentially stable with the prescribed$H_{\infty }$performance index. The desired controller gains are then characterized by solving an iterative optimization problem. Finally, a simulation example is presented to demonstrate the correctness and effectiveness of the proposed design procedure.

In this article, we consider the$H_{\infty }$proportional-integral (PI) state estimation (SE) problem for discrete-time T–S fuzzy systems subject to transmission delays, external disturbances, and redundant channels. Multiple redundant communication channels are utilized between the sensors and the remote estimator to enhance the reliability of data transmissions. In order to characterize the transmission delays in network-based communication, a family of random variables with partly known probabilities, which are independent and identically distributed, is adopted to describe the random behavior of the transmission delays with the redundant channels. The objective of this work is to put forward a PI state estimator such that the dynamics of the estimation error is exponentially mean-square stable and satisfies the prescribed$H_{\infty }$performance index of the disturbance attenuation/rejection. By employing the stochastic analysis approach, the error dynamics of the SE under the proposed state estimator is analyzed and sufficient conditions are obtained to ensure the existence of the required PI state estimator. Furthermore, the desired estimator parameters are derived by solving a nonlinear optimization problem. Finally, two simulation examples are exploited to demonstrate the validity of the proposed SE scheme.

This article is concerned with the$H_{\infty }$proportional–integral–derivative (PID) control problem for class of discrete-time Takagi–Sugeno fuzzy systems subject to infinite-distributed time delays and round-robin (RR) protocol scheduling effects. The information exchange between the sensors and the controller is conducted through a shared communication network. For the purpose of alleviating possible data collision, the well-known RR communication protocol is deployed to schedule the data transmissions. To stabilize the target system with guaranteed$H_{\infty }$performance index, a novel yet easy-to-implement fuzzy PID controller is developed whose integral term is calculated based on the past measurements defined in a limited time window with hope to improve computational efficiency and reduce accumulation error. Based on the Lyapunov stability theory and the convex optimization technique, sufficient conditions are derived to ensure the exponential stability as well as the$H_{\infty }$disturbance attenuation/rejection capacity of the underlying system. Furthermore, by utilizing the cone complementarity linearization algorithm, the nonconvex controller design problem is transformed into an iterative optimization one that facilitates the controller implementation. Finally, simulation examples are given to show the effectiveness and correctness of the developed control method.

This article is concerned with the extended dissipative fuzzy proportional–integral–derivative (PID) control problem for nonlinear systems subject to controller parameter perturbations over a class of mixed fading channels. The sensors of plant are divided into two groups according to engineering practice, where the individual sensor group transmits the measurements to the controller via a respective communication channel undergoing specific fading effects. Considering the complicated nature of the signal fading with the transmission channels, two stochastic models (i.e., the independent and identically distributed fading model and the Markov fading model) are simultaneously employed to describe the mixed fading effects of the two communication channels corresponding to the two sensor groups. The objective of this article is to design a nonfragile PID controller such that the closed-loop system is exponentially stable in mean square and extended stochastically dissipative. With the assistance of the Lyapunov stability theory and stochastic analysis method, sufficient conditions are obtained to analyze the system performance. Then, within the established theoretical framework, an iterative optimization algorithm is proposed to design the desired controller parameters by using the convex optimization technique. Finally, two simulation examples are given to verify the effectiveness of the proposed control schemes.