两类耦合超图网络状态估计研究

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中图分类号：TP273；O231.5文献标识码：A

Abstract：This paper investigates the node state estimation of hypergraphs. First， the network model of hypergraphs with pairwise and triplet interactions is built. Second， considering the presence and absence of diffusive coupling，the observer networks are established，and the error dynamical networks are constructed for the two types of hypergraph network models，respectively. Then，using the Lyapunov stability theory， the asymptotic stability of the two types of error dynamical networks is proved and suficient conditions for state estimation are derived. Finally， the accuracy and effectiveness of the proposed method are verified by numerical simulations. The results indicate the applicability of our method in accurately estimating states within the diffusively coupled and non-diffusively coupled hypergraphs，thereby advancing our capabilities in estimating and controlling higher-order complex networks.

Keywords： hypergraphs； state estimation; Lyapunov stability theory; error dynamical network; linear matrix inequalities

0 引言

在过去二十年里，复杂动态网络已经广泛用于描述相互关联的实际系统和网络，包括电网[1]、交通网络[2]、生态系统[3等。（剩余7502字）