This work studies the decentralized sliding mode control problem for interconnected systems based on a dynamic event-triggered transmission mechanism. To model unreliable communication networks that are susceptible to both energy-limited denial-of-service (DoS) attacks and transmission failures, a Markov model is adopted. A decentralized dynamic event-triggered mechanism is introduced to efficiently utilize limited channel resources by regulating data transmission based on system measurement outputs. Moreover, a hidden Markov model is used to estimate the working operation of the network transmission channel such that a hidden Markov model-based sliding mode controller can be designed by using the output feedback control method. By constructing a Lyapunov function, sufficient conditions are deduced to ensure the stochastic stability of the system and the reachability of the specified sliding mode surface, and a solvable criterion for obtaining the hidden Markov model-based sliding mode controller gains is presented. Finally, simulation results of a four-area interconnected power system are presented to demonstrate the effectiveness of the proposed method.

This paper investigates the control problem of two-dimensional nonlinear semi-Markov jump systems with saturation constraints in the Roesser model. To address the nonlinearity of the system, the Takagi–Sugeno fuzzy model is employed, and a less conservative approach in handling the mismatched double fuzzy summation inequality is adopted, which removes the introduction of additional decision variables. Moreover, a novel mode generation method is employed, ensuring that the system mode index depends only on the sum of variables in two directions. In this case, the mode ambiguity problem in traditional methods is solved effectively. Furthermore, considering that the control input of a real two-dimensional process is limited by the physical capabilities of the actuator, actuator saturation is incorporated into the controller design within the proposed fuzzy framework. Then, by introducing concepts from the switching system and based on fuzzy model methods and Lyapunov theory, an almost inevitable exponential stability condition for the two-dimensional semi-Markov jump fuzzy nonlinear systems is established. By solving the optimization problem under the established stability condition, the attraction region is estimated. Finally, the effectiveness of the designed controller is verified through a numerical example and an example of heat exchange between a heated fluid inside a pipe.

This work considers the$H\_{\infty }$fuzzy control issue of 2-D fuzzy systems susceptible to hybrid cyberattacks due to the unreliable communication networks modeled by the Markov chain, in which the hybrid cyberattacks include deception attacks and denial-of-service attacks. Meanwhile, considering the concealment characteristics of cyberattacks, it may be impossible to know which type of attack the system is suffered. Therefore, a unified hidden Markov model is used in this work, in which the hidden mode represents the real attack mode, the observed mode is the estimated value of the attack mode and it can be directly utilized by the designed security controller. By utilizing the attack mode-dependent Lyapunov function, the asymptotically mean square stability of the 2-D resultant system can be ensured and a set of sufficient conditions can be obtained. Finally, two illustrative examples are provided to demonstrate the applicability of the obtained results.

This article concerns the problem of an event-triggered predefined-time neural tracking control for high-order nonlinear systems (HONSs) through a switching event-triggered strategy (ETS). In contrast to the previous research on HONSs, one prominent virtue of this work is that the upper bound of settling time can be determined a priori by a separate controller parameter. First, by employing the addition of a power integrator technique and a switching event-triggered rule, an adaptive event-triggered controller is developed under the backstepping framework. Therein, the unknown nonlinearities can be approximated effectively through neural networks (NNs). Unlike many existing approaches, the proposed control strategy is not only proficient in coping with the coupling term caused by the event-triggered rule and the nonlinear function, but also has excellent effects in saving communication resources. In terms of the predefined time stability theory, the boundedness of all variables and the fast convergence characteristics of the tracking error within the predetermined time in the system are guaranteed. Finally, the simulations are provided to validate the effectiveness of the suggested control scheme.

This paper studies the event-triggered sliding mode control problem for interval type-2 fuzzy interconnected systems under hybrid cyberattacks modeled by Markov processes. Under the framework of an interval type-2 fuzzy model, the nonlinear relationship in the interconnected system is modeled and analyzed, and a fuzzy sliding mode controller is designed which can effectively resist hybrid cyberattacks. To rationally utilize limited channel resources, a decentralized event-triggered mechanism is used to reduce unnecessary information transmission. By constructing a Lyapunov function, some criteria are deduced to ensure that the closed-loop system is stochastically passive and the reachability of the designed sliding area is guaranteed. Finally, a four-area networked interconnected system is used to verify the effectiveness of the decentralized fuzzy sliding mode control strategy.

2-D systems which can model many practical engineering systems, have attractive research in the control topic in both practice and theoretical aspects. Due to the complex engineering environment, systems may encounter sudden structural changes and be unable to work properly. Fortunately, the Markov jump process can model this situation. Meanwhile, the information of systems may not be accessed timely or only partial information can be accessed. This work focuses on the hidden Markov model-based sliding mode control for 2-D Markov jump systems with partially unknown information and its application in the metal rolling process. By utilizing the Lyapunov function approach, some criteria are obtained to guarantee that the dynamics state reaches the designed sliding surface within a finite time, and the system is passive. Finally, the practicability of asynchronous sliding mode control law is verified by providing a metal rolling process. Note to Practitioners—In some practical systems, their state depends on two independent variables, and the internal structure or parameters of the system are changed due to sudden environmental interference and device failure, which can be described as 2-D Markov jump systems. Meanwhile, in practical engineering applications, obtaining all statistical probability information of systems requires a great cost or is impossible to accomplish. This paper proposes the sliding mode control method for 2-D Markov jump Roesser systems with partial information, in which the partial information problems include the partially known system operation mode information and the partially known probabilities information. A hidden Markov model is used to address the above two partial information problems. The design approach of a hidden Markov model-based sliding mode controller with partially unknown statistical probability information is proposed. The engineering applicability of the method is verified by the metal rolling technology. This study provides a new sliding mode control method to address the control problem for 2-D systems where the system information is partially obtained or accessed.

This article proposes a new result on mismatched double fuzzy summation inequality. The mismatched double fuzzy summation inequality usually originates from the control system design with using the Takagi–Sugeno (TS) fuzzy model, in which the controller and the system are with mismatched membership functions. Compared with the existing method to deal with the mismatched double fuzzy summation inequality, the proposed one is less conservative and does not introduce additional decision variables. Three examples including the mismatched membership functions of the TS fuzzy control system in the discrete-time case, the continuous-time case and the interval type-2 fuzzy system under state feedback control mechanism are used to show that the new result is less conservative than the existing one.

In this paper, the asynchronous state estimation problem of two-time-scale Markov jump complex networks under analog fading channels is investigated, in which the mode of the designed state estimator is asynchronous to the system mode and the asynchronous probabilities are partially known. The two-time-scale phenomenon of complex networks is modeled by a singular perturbation parameter and the changes in connection mode between the complex networks are subject to a Markov chain. The output measurements are transmitted via analog fading channels and fading gains are used to represent the magnitude of the decline of the transmitted information. The purpose of this study is to design an asynchronous state estimator related to the asynchronous mode of the network topology such that the stochastic stability with an$H_{\infty}$performance index of the resultant error dynamics can be guaranteed. By designing the Lyapunov function which is associated with the singular perturbation parameter and the system mode, the stochastic stability condition of the estimation error system is derived. A new decoupling method to obtain the state estimator gains is proposed, which removes the limitation on the relaxation matrix of previous research results. Finally, the effectiveness of the methods are verified by a numerical simulation example and a capacitor-resistance circuit model.

This article investigates the passivity-based fuzzy control problem for discrete-time nonlinear semi-Markov jump singularly perturbed systems (SPSs) by the semi-Markov kernel (SMK) approach. Due to the fact that the statistical information of SMK is difficult to acquire completely, the generally partially available case, covering the completely available and completely unavailable cases, is considered to remove the ideal assumption that the system information is invariably available to controllers. Additionally, the mode-dependent fuzzy rules describing nonlinear behavior are constructed, that is, the membership functions are dependent on the system modes, thus promoting the previous results efficacious in a more accurate form. Subsequently, by fully utilizing available SMK information, some sufficient conditions based on the slow state feedback technique are derived to ensure that the semi-Markov jump fuzzy SPSs are stabilized and satisfy the given passive performance. Finally, the superiority and practicability of the presented theoretical results are explained by a numerical example and an inverted pendulum model.

In this article, the hidden Markov model (HMM)-based fuzzy control problem is addressed for slow sampling model nonlinear Markov jump singularly perturbed systems (SPSs), in which the general transition and mode detection information issue is considered. The general information issue is formulated as the one with not only the transition probabilities (TPs) and the mode detection probabilities (MDPs) being partly known but also with the certain estimation errors existing in the known elements of them. This formulation covers the cases with both the TPs and the MDPs being fully known, or one of them being fully known but another being partly known, or both them being partly known but without the certain estimation errors, which were considered in some previous literature. By utilizing the HMM with general information, some strictly stochastic dissipativity analysis criteria are derived for the slow sampling model nonlinear Markov jump SPSs. In addition, a unified HMM-based fuzzy controller design methodology is established for slow sampling model nonlinear Markov jump SPSs such that a fuzzy controller can be designed depending on whether the fast dynamics of the systems are available or not. A numerical example and a tunnel diode circuit are finally used to illustrate the validity of the obtained results.

Singularly perturbed systems have found widespread applications in practice. The existing results on singularly perturbed systems mainly focused on the Lyapunov asymptotic stability, which are unable to deal with the cases that the system states cannot exceed a given threshold during a fixed time interval. This article addresses the finite-time fuzzy control issue for discrete-time nonlinear singularly perturbed systems with input constraints. The aim is to guarantee the boundedness of the states of singularly perturbed systems during a finite-time interval. Based on the matrix inequality technique, some conditions are established to guarantee the finite-time boundedness of the fuzzy singularly perturbed systems, where the singularly perturbed parameter is independent so as to avoid the ill-conditioned problem caused by the small singularly perturbed parameter. The gains of the finite-time fuzzy controller can be obtained by solving some singularly perturbed parameter independent linear matrix inequalities. Finally, the proposed finite-time fuzzy controller design approach for nonlinear singularly perturbed systems is illustrated via the Van der Pol circuit.

This article deals with the extended dissipativity-based control issue for singularly perturbed systems (SPSs) with Markov jump parameters, in which the partial information issues of the Markov chain are fully considered. A comprehensive hidden Markov model (HMM) is established for the partial information issues on Markov chain, in which the transition probabilities of the hidden Markov state and the observation probabilities of the observed state are general, that is, the uncertainty and the unknown peculiarity of them may be encountered simultaneously. By using the HMM with general probabilities, a comprehensive criterion is derived to analyze the extended stochastic dissipativity of the hidden Markov jump SPSs with the different partial information issues on the Markov chain. Based on the derived criterion, an explicit expression to acquire the desired HMM-based controller is presented. An illustrative example and a vehicle active suspension system are, finally, show the validity of the established theoretical results.

This article investigates the reliable output feedback control problem for networked nonlinear semi-Markov jump systems, in which a control strategy with redundant channels is established to reduce the adverse effect caused by packet dropouts. The actuator faults are fully considered in the setup. On the basis of stochastic analysis theory and fuzzy-model-based method, some criteria are established to guarantee the σ -error mean-square stability for the considered systems. As a consequence, the reliable output feedback controller design method is proposed, which can be utilized to deal with the actuator failures problem effectively. Finally, two illustrative examples are employed to explain the availability of the presented design approach, where the single-link robot arm system model is contained.

This paper studies the resilient asynchronous H∞control problem for slow sampling discrete-time uncertain Markov jump singularly perturbed systems (SPSs). Compared with slow state variables feedback controller, a new controller is proposed for slow sampling discrete-time SPSs, which has less conservatism. A more realistic situation, i.e., the system modes cannot be directly acquired for controller design, is considered with the help of hidden Markov model (HMM). The goal is to design a resilient asynchronous controller based on HMM such that the closed-loop system is stochastically stable while meeting an expected H∞performance in the presence of random controller gain fluctuation and the system modes hiding for controller. By utilizing matrix inequality techniques and Lyapunov function method, some criteria are established for the existence of the resilient asynchronous controller. The superiority and practicability of the obtained theoretical results are demonstrated by a numerical example and an inverted pendulum system.

This paper concentrates on the fuzzy-model-based H∞ control for Markov jump nonlinear slow sampling singularly perturbed systems with partial information. The partial information problems including partial information on the transition probabilities of the Markov chain, on the Markov state, and on detection probabilities are taken into account simultaneously. A new hidden Markov model (HMM), in which some elements need not be known, is introduced to formulate the partial information problems. Some criteria on H∞ performance analysis and the existence of the desired HMM-based asynchronous fuzzy controller are derived. An optimized relaxation matrix is introduced to improve the decoupling method such that the obtained HMM-based asynchronous fuzzy controller is less conservative. Finally, two examples show the availability of the HMM-based asynchronous controller design procedures.

This paper is concerned with the fuzzy-model-based nonfragile control problem for discrete-time nonlinear singularly perturbed systems with stochastic jumping parameters. The stochastic parameters are generated from the semi-Markov process. The memory property of the transition probabilities among subsystems is fully considered in the investigated systems. Consequently, the restriction that the transition probabilities are memoryless in widely used discrete-time Markov jump model can be removed. Based on the T-S fuzzy model approach and semi-Markov kernel concept, several criteria ensuring δ-error mean square stability of the underlying closed-loop system are established. With the help of those criteria, the designed procedures which could well deal with the fragility problem in the implementation of the proposed fuzzy-model-based controller are presented. A technique is developed to estimate the permissible maximum value of singularly perturbed parameter for discrete-time nonlinear semi-Markov jump singularly perturbed systems. Finally, the validity of the established theoretical results is illustrated by a numerical example and a modified tunnel diode circuit model.

This paper investigates the finite-time event-triggered 'I-1 control problem for Takagi-Sugeno Markov jump fuzzy systems. Because of the sampling behaviors and the effect of network environment, the premise variables considered in this paper are subject to asynchronous constraints. The aim of this paper is to synthesize a controller via an event-triggered communication scheme such that not only the resulting closed-loop system is finite-time bounded and satisfies a prescribed 'I-1 performance level, but also the communication burden is reduced. First, a sufficient condition is established for the finite-time bounded 'I-1 performance analysis of the closed-loop fuzzy system with fully considering the asynchronous premises. Then, based on the derived condition, the method of the desired controller design is presented. Two illustrative examples are finally presented to demonstrate the practicability and efficacy of the proposed method.