This article is concerned with the neural network (NN)-based event-triggered control problem for discrete-time networked Markov jump systems with hybrid cyberattacks and unmeasured states. The event-triggered mechanism (ETM) is used to reduce the communication load, and a Luenberger observer is introduced to estimate the unmeasured states. Two kinds of cyberattacks, denial-of-service (DoS) attacks and deception attacks, are investigated due to the vulnerability of cyberlayer. For the sake of mitigating the impact of these two types of cyberattacks on system performance, the ETM under DoS jamming attacks is discussed first, and a new estimation of such mechanism is given. Then, the NN technique is applied to approximate the injected false information. Some sufficient conditions are derived to guarantee the boundedness of the closed-loop system, and the observer and controller gains are presented by solving a set of matrix inequalities. The effectiveness of the presented control method is demonstrated by a numerical example.

This article is concerned with $H_\infty$ control problem for discrete-time Takagi–Sugeno fuzzy Markov jump systems with event-triggering scheme (ETS) and denial-of-service (DoS) attacks. Aperiodic DoS attacks characterized by duration and frequency are introduced. In the light of DoS attacks and event-triggered fuzzy controller, the switched fuzzy Markov jump closed-loop system is established. Particularly, in order to address the issue of mismatched behavior between membership functions of fuzzy system and fuzzy controller, a novel ETS consisting of membership functions is developed. Then, with the help of multiple Lyapunov function method and iterative technique, some sufficient conditions are provided to ensure the $H_\infty$ performance of the resulting closed-loop system. Subsequently, the explicit parameter design of controller and ETS is provided. Finally, an example is employed to verify the validity of the proposed theoretical method.

This article investigates event-triggered and self-triggered $\mathcal {L}_{\infty }$ control problems for the Markov jump stochastic nonlinear systems subject to denial-of-service (DoS) attacks. When attacks prevent system devices from obtaining valid information over networks, a new switched model with unstable subsystems is constructed to characterize the effect of DoS attacks. On the basis of the switched model, a multiple Lyapunov function method is utilized and a set of sufficient conditions incorporating the event-triggering scheme (ETS) and restriction of DoS attacks are provided to preserve $\mathcal {L}_{\infty }$ performance. In particular, considering that ETS based on mathematical expectation is difficult to be implemented on a practical platform, a self-triggering scheme (STS) without mathematical expectation is presented. Meanwhile, to avoid the Zeno behavior resulted from general exogenous disturbance, a positive lower bound is fixed in STS in advance. In addition, the exponent parameters are designed in STS to reduce triggering frequency. Based on the STS, the mean-square asymptotical stability and almost sure exponential stability are both discussed when the system is in the absence of exogenous disturbance. Finally, two examples are given to substantiate the effectiveness of the proposed method.

In this article, the event-triggered resilient $\mathcal {L}_{\infty }$ control problem is concerned for the Markov jump systems in the presence of denial-of-service (DoS) jamming attacks. First, a fixed lower bound-based event-triggering scheme (ETS) is presented in order to avoid the Zeno problem caused by exogenous disturbance. Second, when DoS jamming attacks are involved, the transmitted data are blocked and the old control input is kept by using the zero-order holder (ZOH). On the basis of this process, the effect of DoS attacks on ETS is further discussed. Next, by utilizing the state-feedback controller and multiple Lyapunov functions method, some criteria incorporating the restriction of DoS jamming attacks are proposed to guarantee the $\mathcal {L}_{\infty }$ control performance of the event-triggered Markov closed-loop jump system. In particular, the bounded transition rates rather than the exact ones are taken into account. That is appropriate for the practical environment in which transition rates of the Markov process are difficult to measure accurately. Correspondingly, some criteria are proposed to obtain state-feedback gains and event-triggering parameters simultaneously. Finally, we provide two examples to show the effectiveness of the proposed method.