Dynamic-Memory Event-Triggered Sliding-Mode Secure Control for Nonlinear Semi-Markov Jump Systems With Stochastic Cyber Attacks

This paper presents an investigation of the sliding-mode secure control for nonlinear semi-Markov jump systems in the presence of non-periodic denial-of-service attacks and false data injection attacks. First of all, we employ Takagi-Sugeno fuzzy model to describe the nonlinear semi-Markov jump control systems. In order to optimize transmission efficiency and control performance, a novel dynamic-memory event-triggered mechanism is developed by incorporating auxiliary dynamic variable and historical transmitted data. Then, a memory-based fuzzy sliding surface is put forward to attenuate the influences of stochastic cyber attacks with the aid of event-triggered state information. Moreover, by utilizing Lyapunov stability theory, sufficient conditions are derived to guarantee the exponentially mean-square stability of the system with an $H_{\infty}$ performance index, even in the cases of generally uncertain and unknown transition rates. Furthermore, a memory-based sliding mode secure controller is designed to ensure the reachability of the predefined switching surface and desirable sliding motion within finite time. Finally, the efficacy of the proposed control scheme is demonstrated through a tunnel diode circuit model. Note to Practitioners —This study focuses on the issue of secure control for nonlinear semi-Markov jump systems, which holds practical significance across various domains, including applications in robotic manipulators, circuit models, and DC motors. We broaden the scope by considering more general jump parameter matrices to align more closely with the real-world system environment. Moreover, networked environments pose two primary challenges: network bandwidth constraints and the external network attacks. To tackle these issues, this paper introduces an innovative dynamic memory event triggering mechanism to enhance network transmission efficiency and optimize communication resource utilization. Meanwhile, to address cyber attacks resulting from the inherent openness of networks, the current study adopts a defensive sliding mode control strategy to provide robust protection against network attacks and disturbances. The effectiveness of the suggested approach is confirmed through a circuit system model. It is worth mentioning that the proposed method has the potential for broader application within real-world engineering scenarios, particularly those involving network-based nonlinear systems with various practical constraints.