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<p>This paper investigates the problem of tracking synchronization control for higher-order complex networks (HOCNs) that include both pairwise and group interactions, in which the considered HOCNs are modeled based on hypergraph theory. Different from the existing results that either ignore the input of target node or rely on the global parameters such as the sizes and topologies of global networks to design control protocols, a novel synchronization strategy is proposed to achieve the tracking synchronization of HOCNs with a target node of bounded input and without requiring any global information. By employing the hypergraph theory, boundary layering concept and <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\sigma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>σ</mi> </math></EquationSource> </InlineEquation>-modification technique, the synchronization errors are guaranteed to converge to a relatively small and adjustable set without chattering phenomenon. Meanwhile, by designing the suitable distributed adaptive laws of coupling strengths for different nodes, the developed tracking synchronization protocol can be operated in a fully distributed scenario. Finally, the validity of the achieved theoretical results is demonstrated through a network composed of Chua’s circuits.</p>

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Distributed adaptive tracking synchronization control for higher-order networks

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • Binrui Wang,
  • SaSa Chen,
  • Dan Liu,
  • Xiaohang Li,
  • Kaibo Shi

摘要

This paper investigates the problem of tracking synchronization control for higher-order complex networks (HOCNs) that include both pairwise and group interactions, in which the considered HOCNs are modeled based on hypergraph theory. Different from the existing results that either ignore the input of target node or rely on the global parameters such as the sizes and topologies of global networks to design control protocols, a novel synchronization strategy is proposed to achieve the tracking synchronization of HOCNs with a target node of bounded input and without requiring any global information. By employing the hypergraph theory, boundary layering concept and \(\sigma \) σ -modification technique, the synchronization errors are guaranteed to converge to a relatively small and adjustable set without chattering phenomenon. Meanwhile, by designing the suitable distributed adaptive laws of coupling strengths for different nodes, the developed tracking synchronization protocol can be operated in a fully distributed scenario. Finally, the validity of the achieved theoretical results is demonstrated through a network composed of Chua’s circuits.