Fixed-time synchronization in p-th moment for stochastic multi-layer neural networks: An adaptive graph-theoretic Lyapunov functional approach
Guan‐Nan Yu, Xiao‐Kang Liu, Yan Lei, Yan‐Wu Wang · Neurocomputing · 2025
In this paper, the p-th moment synchronization problem for a class of stochastic multi-layer neural networks with intra-layer and inter-layer connections is investigated. Due to the multiple connections with delays and stochastic noise, the typical methodologies that build a canonical linear or expanded matrix model to analyze its stability by constraining eigenvalues in the left-half plane, such as the Kronecker product method, linear matrix inequality and M -matrix approach are tough to tackle the problem. Consequently, a graph-theory-based Lyapunov functional is constructed by combining multiplicative principles and a graph-theoretic approach to help examine the effect of inter- and intra-layer connectivity on a unified framework. With the proposed adaptive fixed-time controller, sufficient conditions for the p-th moment synchronization in a fixed time are derived in terms of algebraic inequality. A corollary, together with a constant-gain fixed-time controller, is presented in case there is no delay. Finally, a confirmatory and two comparative simulations show the effectiveness and convenient implementation of the proposed control strategy.