Mode-Holding Control for Markov Jump Systems: When Event-Triggering Effect Meets DoS Attack Threat

In this paper, a security problem is addressed for a kind of Markov jump system susceptible to stochastic DoS attacks via the sliding mode control method, in which an attack-tolerant adaptive event-triggered (ET) mechanism is designed to reduce the data transmission frequency. Although the ET control issues under DoS attacks have been investigated in abundance, the corresponding results are acquired by taking no account of the inter-effects between ET protocol and DoS attack random occurrence. Distinguished from the existing research, a new ET scheme is proposed whose triggering coefficient adaptively changes according to the state evolution trends. The adaptation law for the triggering coefficient is intrinsically tied to the probability of an attack's occurrence. The triggering strategy is regulated on the basis of observed attack patterns, thereby enhancing the resilience and adaptability of the ET mechanism against stochastic DoS attacks. To account for the influences on mode observation of both ET mechanism and DoS attacks, a mode-holding sliding mode controller is constructed whose mode is updated only when the controller receives new signals. Moreover, a model transformation method is used to analyze the mean-square exponential ultimate boundedness of closed-loop systems and the reachability of the sliding surface, simultaneously. An optimization problem is formulated to improve the performance of the sliding mode control, which is solved using the LMI-based sparrow search algorithm. Finally, an example is provided to illustrate the effectiveness of the proposed ET security control scheme.