PID-Based Secure Cluster Synchronization of Discrete-Time Nonlinear IoT Networks Under Stochastic Replay Attacks

Abstract

Large-scale Internet of Things (IoT) systems are characterized by massive numbers of interconnected devices, heterogeneous dynamics, and complex interaction structures, which can be effectively modeled using complex networks. In many IoT applications, secure cluster synchronization is essential for coordinated and reliable operation, yet it is highly vulnerable to cyber-attacks, particularly replay attacks that maliciously reuse previously transmitted but valid data. This paper investigates the secure cluster synchronization problem for discrete-time nonlinear complex networks representing IoT systems under stochastic replay attacks. A probabilistic replay attack model with bounded consecutive attack duration is introduced to capture the random and intermittent characteristics of realistic attack behaviors. To mitigate the adverse impact of replayed information, a PID-based cluster synchronization control strategy is developed, where proportional, integral, and derivative actions are jointly exploited to enhance robustness against outdated and compromised signals. By constructing an appropriate Lyapunov functional and employing stochastic analysis techniques, sufficient conditions are derived to guarantee asymptotic mean-square cluster synchronization. A systematic controller synthesis procedure is further provided. Numerical simulations demonstrate the effectiveness and improved resilience of the proposed approach compared with conventional proportional control schemes.