Detection and Defense-Based Fixed-Time Output Synchronization of Fuzzy Stochastic Multilayered Networks Under Deception Attacks

Abstract

The coexistence of stochastic disturbances and cyber-attacks presents fundamental challenges to traditional deterministic fixed-time stability theory, hindering rigorous solutions to fixed-time synchronization of stochastic complex networks in adversarial environments. To address this problem, this article investigates fixed-time output synchronization in probability for fuzzy stochastic multilayered networks under deception attacks. First, a relaxed fixed-time convergence condition is established for stochastic systems, providing refined parameter constraints and accurate convergence time estimates. Based on these stability results, a concise power-law-based controller is designed for attack-free networks to achieve stochastic fixed-time synchronization. For networks subject to deception attacks, a discontinuous controller is proposed along with an $L_{2}$-norm Lyapunov function. Furthermore, a novel detection mechanism based on likelihood-ratio and its corresponding active defense control algorithm are developed to accurately identify anomalous system dynamics under attack interference. Finally, the theoretical results are validated through numerical simulations based on a traffic network model.