Input-Retention Strategies for Secure Synchronization of Piecewise Markov Neural Networks Under Hybrid Cyber-Attacks

How to achieve synchronization control for Piecewise Homogeneous Markov Delayed Neural Networks (PHMDNNs) under hybrid cyber-attacks is the primary focus of this research. Firstly, a Piecewise Homogeneous Markov Process (PHMP) is employed to model the mode transitions of system parameters and controllers, accurately capturing the dynamic characteristics of practical systems and providing a solid foundation for subsequent controller design. In response to the challenges arising from hybrid cyber-attacks, a novel controller is developed based on an input retention strategy. This ensures system stability under hybrid cyber-attacks, effectively avoiding the instability issues caused by traditional zero-input strategies and enhancing control robustness. To further optimize system performance, an improved Resilient Adaptive Event-triggered Mechanism (RAETM) is proposed. By optimizing triggering conditions and thresholds, the mechanism reduces communication overhead while strengthening system security, making it well-suited for networked control systems. In addition, a generalized common Lyapunov functional is constructed by incorporating sampling instants, time delays, and Markov jump parameters. Sufficient conditions for system synchronization and stability are derived, providing a simplified analytical framework. Finally, the effectiveness and superiority of the proposed approach are confirmed through simulation results, showcasing its robust performance against hybrid cyber-attacks and its ability to achieve secure synchronization.