Event-triggered topology identification of stochastic delayed hypernetworks via output coupling

Xueyi Zhao; Na Li; Anjing Fan; Xueyi Zhao; Na Li; Anjing Fan

doi:10.3934/math.20261340

AIMS Mathematics

2026, Volume 11, Issue 10: 34341-34359. doi: 10.3934/math.20261340

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Research article

Event-triggered topology identification of stochastic delayed hypernetworks via output coupling

1.
School of Mathematics and Statistics, Hanjiang Normal University, Shiyan 442000, China
2.
Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, China
3.
School of Mathematics and Statistics, Henan University, Kaifeng 475000, China
4.
School of Computer and Information Engineering, Anyang Normal University, Anyang 455000, China

Received: 24 August 2026 Revised: 25 September 2026 Accepted: 15 October 2026 Published: 22 October 2026
MSC : 93A16, 93C65, 34K50, 60H10, 93C40

This paper investigated the topology identification of stochastic delayed hypernetworks using only output variables. To overcome the limitation that full state information is often unmeasurable in practice, an adaptive drive-response framework was constructed. Considering the complexity of realistic network environments, multiple interaction delays and stochastic perturbations were explicitly incorporated into the system model. We designed robust output-feedback controllers and parameter updating laws under both continuous-time and event-triggered communication schemes. Particularly, the proposed event-triggered mechanism (ETM) effectively reduced the communication frequency among network nodes while strictly excluding Zeno behavior. Based on the stochastic Lyapunov stability theory, we rigorously proved that the synchronization and identification errors were uniformly ultimately bounded almost surely, ensuring the accurate reconstruction of unknown multilayer topological matrices. Finally, numerical simulations were provided to verify the effectiveness and communication efficiency of the proposed theoretical results.
- topology identification,
- event-triggered mechanism,
- output coupling,
- stochastic delayed hypernetworks,
- multiple time delays
Citation: Xueyi Zhao, Na Li, Anjing Fan. Event-triggered topology identification of stochastic delayed hypernetworks via output coupling[J]. AIMS Mathematics, 2026, 11(10): 34341-34359. doi: 10.3934/math.20261340

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Abstract

This paper investigated the topology identification of stochastic delayed hypernetworks using only output variables. To overcome the limitation that full state information is often unmeasurable in practice, an adaptive drive-response framework was constructed. Considering the complexity of realistic network environments, multiple interaction delays and stochastic perturbations were explicitly incorporated into the system model. We designed robust output-feedback controllers and parameter updating laws under both continuous-time and event-triggered communication schemes. Particularly, the proposed event-triggered mechanism (ETM) effectively reduced the communication frequency among network nodes while strictly excluding Zeno behavior. Based on the stochastic Lyapunov stability theory, we rigorously proved that the synchronization and identification errors were uniformly ultimately bounded almost surely, ensuring the accurate reconstruction of unknown multilayer topological matrices. Finally, numerical simulations were provided to verify the effectiveness and communication efficiency of the proposed theoretical results.

References

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