A Finite-Time Adaptive Synchronization Control Algorithm for Stochastic Dynamical Complex Network with Periodical Coupling Structure

This paper addresses the finite-time adaptive synchronization control problem for a class of stochastic dynamical complex networks subject to unknown periodic coupling structures and bounded time-varying delays, a combination rarely tackled in the existing literature. To fill this gap, we develop a novel adaptive feedback control framework that integrates finite-time stochastic stability theory, differential inequality techniques, and adaptive learning laws. The paper investigates the concurrent estimation of unknown periodic coupling parameters through a period-based update law principally while enforcing finite-time synchronization in probability without prior knowledge of the coupling structure. The theoretical contributions include sufficient conditions ensuring stochastic finite-time synchronization, accompanied by an explicit upper bound on the expected settling time. Numerical simulations conducted on a five-node Sprott-O chaotic system validate the effectiveness and superiority of the proposed method, demonstrating that synchronization is attained within a time shorter than the theoretical estimate. In this paper, adaptive finite-time synchronization control of dynamical complex network with unknown periodical coupling structure and stochastic disturbances is investigated in detail from the perspective of improving convergence speed and lowering control costs. Basing on finite-time stochastic stability theory, differential inequality technique, and the adaptive feedback strategies, rigorous theoretical analysis establishes sufficient conditions to guarantee finite-time synchronization of the network. Furthermore, the unknown periodical coupling topological elements are estimated by proper adaptive update law simultaneously. Finally, numerical simulations are conducted to demonstrate the validity and superiority of the proposed control methodology.