On State Estimation for Hypergraphs with Two Types of Coupling
ZHOU Xuanxin, WU Yayong, JIANG Guoping
1. College of Automation and College of Artificial Intelligence, Nanjing University of Posts and Telecommunications; 2. Jiangsu Engineering Center for IOT Intelligent Robots (IOTRobot), Nanjing 210023, China
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 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.
周宣欣, 吴亚勇, 蒋国平. 两类耦合超图网络状态估计研究[J]. 复杂系统与复杂性科学, 2025, 22(2): 90-96.
ZHOU Xuanxin, WU Yayong, JIANG Guoping. On State Estimation for Hypergraphs with Two Types of Coupling[J]. Complex Systems and Complexity Science, 2025, 22(2): 90-96.
[1] HU Z, DENG F, SU Y, et al. Security control of networked systems with deception attacks and packet dropouts: a discrete-time approach[J]. Journal of the Franklin Institute, 2021, 358(16): 81938206. [2] FAN Y, DING J, LIU H, et al. Large-scale multimodal transportation network models and algorithms-Part I: the combined mode split and traffic assignment problem[J]. Transportation Research Part E: Logistics and Transportation Review, 2022, 164: 102832. [3] OLFF H, ALONSO D, BERG M P, et al. Parallel ecological networks in ecosystems[J]. Philosophical Transactions of the Royal Society B: Biological Sciences, 2009, 364(1524): 17551779. [4] SHI Y, WANG Y, TUO J. Distributed secure state estimation of multi-agent systems under homologous sensor attacks[J]. IEEE/CAA Journal of Automatica Sinica, 2022, 10(1): 6777. [5] SOLTAN S, MAZAURIC D, Zussman G. Analysis of failures in power grids[J]. IEEE Transactions on Control of Network Systems, 2015, 4(2): 288300. [6] FARZA M, M′SAAD M, ROSSIGNOL L. Observer design for a class of MIMO nonlinear systems[J]. Automatica, 2004, 40(1): 135143. [7] TARGUI B, FRIKEL M, M′SAAD M, et al. Observer design for the state estimation of a class of communication networks[C]//18th Mediterranean Conference on Control and Automation, MED′10. Marrakech, Morocco: IEEE, 2010: 495499. [8] FAN C X, JIANG G P. State estimation of complex dynamical network under noisy transmission channel[C]//2012 IEEE International Symposium on Circuits and Systems(ISCAS). Seoul, Korea(South): IEEE, 2012: 21072110. [9] ZHU H, LEUNG H. A maximum likelihood approach to state estimation of complex dynamical networks with unknown noisy transmission channel[C]//2013 IEEE International Symposium on Circuits and Systems(ISCAS). Beijing, China: IEEE, 2013: 25212524. [10] PATANIA A, PETRI G, VACCARINO F. The shape of collaborations[J]. EPJ Data Science, 2017, 6: 116. [11] FAN Z, WU X. Identifying partial topology of simplicial complexes[J]. Chaos: an Interdisciplinary Journal of Nonlinear Science, 2022, 32(11): 113128. [12] LI K, SHI C. Synchronization-based topology identification of multilink hypergraphs: a verifiable linear independence[J]. Nonlinear Dynamics, 2024, 112(4): 27812794. [13] LI K, LIN Y, Wang J. Synchronization of multi-directed hypergraphs via adaptive pinning control[J]. Chaos, Solitons & Fractals, 2024, 184: 115000. [14] SHAFI S Y, ARCAK M. Adaptive synchronization of diffusively coupled systems[J]. IEEE Transactions on Control of Network Systems, 2014, 2(2): 131141. [15] NDOW F K, AMINZARE Z. Global synchronization analysis of non-diffusively coupled networks through Contraction Theory[DB/OL].[20240624]. http://doi.org/10.48550/arXiv.2307.00030. [16] ZHANG Y, LATORA V, MOTTER A E. Unified treatment of synchronization patterns in generalized networks with higher-order, multilayer, and temporal interactions[J]. Communications Physics, 2021, 4(1): 195. [17] WU C W, CHUA L O. Synchronization in an array of linearly coupled dynamical systems[J]. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1995, 42(8): 430447. [18] GAMBUZZA L V, DI PATTI F, GALLO L, et al. Stability of synchronization in simplicial complexes[J]. Nature communications, 2021, 12(1): 1255. [19] LI J N, BAO W D, LI S B, et al. Exponential synchronization of discrete-time mixed delay neural networks with actuator constraints and stochastic missing data[J]. Neurocomputing, 2016, 207: 700707. [20] BOYD S, EL GHAOUI L, FERON E, et al. Linear matrix inequalities in system and control theory[M]. Society for Industrial and Applied Mathematics, 1994.
