为研究超图网络的节点状态估计问题,建立具有成对和三体相互作用的超图网络模型。针对是否考虑扩散耦合形式的两种超图网络模型,建立相应的观测器网络,并构造误差动态网络。然后,利用李雅普诺夫稳定性理论证明两种误差动态网络的渐近稳定性,推导实现状态估计所需满足的充分条件。最后,通过数值模拟验证了面对两种超图网络模型状态估计方案的准确性和有效性。结果表明,设计的方法能够准确估计是否考虑扩散耦合形式的两种超图网络节点状态,有利于提高对高阶复杂网络的估计和控制能力。
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 sufficient 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.
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