This article studies the issue of resilient event-triggered (RET)-based security controller design for nonlinear networked control systems (NCSs) described by interval type-2 (IT2) fuzzy models subject to nonperiodic denial of service (DoS) attacks. Under the nonperiodic DoS attacks, the state error caused by the packets loss phenomenon is transformed into an uncertain variable in the designed event-triggered condition. Then, an RET strategy based on the uncertain event-triggered variable is firstly proposed for the nonlinear NCSs. The existing results that utilized the hybrid triggered scheme have the defect of complex control structure, and most of the security compensation methods for handling the impacts caused by DoS attacks need to transmit some compensation data when the DoS attacks disappear, which may lead to large performance loss of the systems. Different from these existing results, the proposed RET strategy can transmit the necessary packets to the controller under nonperiodic DoS attacks to reduce the performance loss of the systems and a new security controller subject to the RET scheme and mismatched membership functions is designed to simplify the network control structure under DoS attacks. Finally, some simulation results are utilized to testify the advantages of the presented approach. 

Security-Based Fuzzy Control for Nonlinear Networked Control Systems With DoS Attacks via a Resilient Event-Triggered Scheme

This paper focuses on the sliding mode control (SMC) problem of interval type-2 (IT2) fuzzy systems subject to the unmeasurable state and cyberattacks. A key issue is how to design a state observer under the constraint that only the bounds of membership functions are known. To this end, this paper introduces two weighting factors to construct a new membership function. Besides, the concept of input-to-state stability (ISS) is utilized to deal with the residual term resulting from the cyberattacks and external disturbances. The sufficient condition is established such that the sliding mode dynamics and the estimated error dynamics are input-to-state stable. Furthermore, by online estimating the unknown parameters in upper bounds of cyberattacks and external disturbances, an adaptive sliding mode controller is synthesized such that the reachability of the prescribed sliding surface can be guaranteed and the effect of cyberattacks on the system performance can be effectively attenuated. Finally, the validity of the proposed method is illustrated by a mass–spring–damper system.

Input-to-State Stabilization of Interval Type-2 Fuzzy Systems Subject to Cyberattacks: An Observer-Based Adaptive Sliding Mode Approach

This paper investigates the problem of dissipativity-based asynchronous fuzzy integral sliding mode control (AFISMC) for nonlinear Markov jump systems represented by Takagi–Sugeno (T–S) models, which are subject to external noise and matched uncertainties. Since modes of original systems cannot be directly obtained, the hidden Markov model is employed to detect mode information. With the detected mode and the parallel distributed compensation approach, a suitable fuzzy integral sliding surface is devised. Then using Lyapunov function, a sufficient condition for the existence of sliding mode controller gains is developed, which can also ensure the stochastic stability of the sliding mode dynamics with a satisfactory dissipative performance. An AFISMC law is proposed to drive system trajectories into the predetermined sliding mode boundary layer in finite time. For the case with unknown bound of uncertainties, an adaptive AFISMC law is developed as well. The studied T–S fuzzy Markov jump systems involve both continuous-time and discrete-time domains. Finally, some simulation results are presented to demonstrate the applicability and effectiveness of the proposed approaches.

Dissipativity-Based Asynchronous Fuzzy Sliding Mode Control for T–S Fuzzy Hidden Markov Jump Systems

This paper is concerned with the problem of interval type-2 (IT2) fuzzy sampled-data $H_{\infty }$ control for nonlinear networked control systems with parameter uncertainties, data dropout, and transmission delay. The IT2 fuzzy system used to describe the networked control systems and the IT2 networked sampled-data controller implemented by a zero-order holder is connected in the closed-loop system. By means of the input delay approach, the resulting closed-loop system is converted into a continuous-time delayed system. Subsequently, the continuous-time Lyapunov–Krasovskii functional theory is used to carry out the stability analysis. Some slack matrices and the bound information in membership functions are introduced to obtain the relaxed sufficient conditions formed by the linear matrix inequalities, which guarantee the anticipant $H_{\infty }$ performance. Finally, the efficiency and merits of the proposed design method are verified by four practical systems.

Interval Type-2 Fuzzy Sampled-Data $H_{\infty }$ Control for Nonlinear Unreliable Networked Control Systems

This paper deals with the problem of dissipativity-based asynchronous fault detection (FD) for Takagi–Sugeno fuzzy Markov jump systems with network data dropouts. It is assumed that data dropouts happen intermittently from the plant to the FD filter, which is described by Bernoulli process. The hidden Markov model is employed to describe the asynchronous phenomenon between the plant and filter. Based on Lyapunov theory, a sufficient condition is developed to guarantee that the FD system is stochastically stable with strictly dissipative performance. By choosing an appropriate Lyapunov function with the slack matrix technique and Finsler's Lemma, two approaches are proposed to compute filter gains by solving linear matrix inequalities. Finally, an example is provided to illustrate the usefulness and effectiveness of the proposed design methods.

Networked Fault Detection for Markov Jump Nonlinear Systems

This paper investigates the output feedback model predictive control (OFMPC) for Takagi–Sugeno fuzzy networked control systems with bounded disturbance, where data quantization and data loss occur simultaneously. The quantization error is treated as sector bound uncertainties by using the sector bound approach and the data loss process is modeled as a time-homogeneous Markov chain. Invoking ${S}$ -procedure and the notion of quadratic boundedness which can specify closed-loop stability for system with disturbance, the state observer is offline designed and the networked output feedback model predictive controller is provided which explicitly considers the satisfaction of input constraints. Two online synthesis algorithms of OFMPC are presented, one parameterizing the infinite horizon control moves into a single feedback law, the other into one free control move followed by the single feedback law based on the state observer. A new formula is introduced to refresh the ellipsoidal bound of estimation error which can guarantee the recursive feasibility of optimization problem. An example is given to demonstrate the effectiveness of the proposed new design techniques.

Observer-Based Output Feedback MPC for T–S Fuzzy System With Data Loss and Bounded Disturbance

This paper investigates the synthesis approach of output feedback model predictive control (OFMPC) for nonlinear systems over networks where the data quantization and packet loss may occur simultaneously. The nonlinear system, which is subjected to parameter uncertainties, is represented by the interval type-2 Takagi–Sugeno fuzzy model. The quantization error is treated as sector bound uncertainties by using the sector bound approach, and a binary Markov chain is introduced to characterize the phenomenon of packet loss of the networked control systems (NCSs). The synthesis approach of OFMPC provided in this paper involves an offline designed state observer using the linear matrix inequality technique and an online model predictive control optimization problem, which minimizes an upper bound of the expect value of the infinite horizon performance cost based on the obtained estimated state. A new technique of refreshing the estimation error bound, which plays the key role of guaranteeing the recursive feasibility of optimization problem, is provided. An example is given to demonstrate the effectiveness of the proposed new design techniques.

Output feedback predictive control of interval type-2 T-S fuzzy systems with Markovian packet loss

Event-triggered robust model predictive control with stochastic event verification

This paper considers model predictive control (MPC) for the linear discrete-time systems in the presence of packet loss, quantization and actuator saturation. Compared with the previous work ([45]), this paper presents an improved networked MPC approach for networked control systems (NCSs) by applying the quantization dependent Lyapunov function (QDLF) method which leads to less conservative results. The additional improvement is made by placing the heavier weighting on the system corresponding to the actual linear feedback law and choosing the relative weighting on the actual and auxiliary feedback laws which further improves the control performance over the existing method. It is shown that the closed-loop stability is guaranteed and a quantized state-feedback controller is derived by solving the infinite horizon optimization problem. Moreover, this method is further extended to multiple-input case. A numerical example is given to illustrate the effectiveness of the proposed approach.

Improved predictive control approach to networked control systems based on quantization dependent Lyapunov function.

This article is concerned with event-triggered robust model predictive control for linear discrete-time systems with bounded disturbances. A two-step scheme involving a tentative verification of a triggering condition and a delayed triggering with a waiting horizon is proposed to reduce the average triggering rate and fully utilize the nominal optimal control sequence minimizing a quadratic cost function. The triggering condition and the waiting horizon are synthesized based on a prediction model of the plant and a robust positively invariant set associated with it. Under mild conditions, recursive feasibility and closed-loop robust stability are guaranteed. Two examples are used to show the effectiveness and merits of the proposed approach.

Robust Model Predictive Control Using a Two-Step Triggering Scheme

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