A Dual-Layer Fuzzy Consensus Optimization Algorithm for Exponential Convergence in Distributed Networks

Distributed epidemic network scenarios have been widely employed as the foundational basis for robust and adaptive consensus estimation, leveraging data-driven methods to manage uncertainties in both epidemic parameters and network conditions. Traditional fixed-step gossip consensus protocols exhibit suboptimal performance due to their inability to dynamically adapt to fluctuations in local uncertainty and network quality. In this paper, we propose the Dual-Layer Fuzzy Consensus Optimization Algorithm (DLFCOA) scheme to address these challenges and achieve exponential convergence of the consensus error. Our approach integrates dual-layer Type'2 fuzzy inference with an adaptive step-size mechanism and rigorous Lyapunov stability analysis to dynamically adjust the gossip update rate based on real-time feedback. Experimental results demonstrate that DLFCOA reduces the global consensus error to the order of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$10^{-4}$</tex-math></inline-formula>, achieves a convergence rate of approximately 0.12, and requires significantly fewer iterations—around 150 compared to up to 800 in conventional methods—thus offering enhanced scalability, robustness, and efficiency.