Research on synchronized assets of multiple individuals based on delayed feedback control

Huaiqin Yu; Qiang Fu; Xiaohuan Wang; Huaiqin Yu; Qiang Fu; Xiaohuan Wang

doi:10.3934/era.2026047

Electronic Research Archive

2026, Volume 34, Issue 2: 1017-1043. doi: 10.3934/era.2026047

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Research on synchronized assets of multiple individuals based on delayed feedback control

1.
Business Administration, JOONGBU University, South Korea
2.
School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received: 25 November 2025 Revised: 08 January 2026 Accepted: 16 January 2026 Published: 29 January 2026

From a theoretical perspective, it is worthwhile to use the idea of control to synchronize multiple individual assets. We regard personal assets as multi-agent systems, i.e., second-order multi-agent systems (SOMAS). The delayed feedback control for consensus and average quasi-consensus of delayed SOMAS is studied. First, two weight matrices are studied, where the interactions are not entirely cooperative into the SOMAS with mixed time-varying delays (the delay varies with time). Second, a delayed feedback control is designed based on two weight matrices where the interactions are cooperative to get the consensus about followers and the average quasi-consensus about leader and followers. The consensus and average quasi-consensus of the delayed SOMAS are established by the graph-theoretic technique and Lyapunov functions. Finally, some numerical simulations is given to verify the theory.
- delayed feedback control,
- consensus,
- average quasi-consensus,
- SOMAS,
- graph-theoretic technique,
- mixed time-varying delays
Citation: Huaiqin Yu, Qiang Fu, Xiaohuan Wang. Research on synchronized assets of multiple individuals based on delayed feedback control[J]. Electronic Research Archive, 2026, 34(2): 1017-1043. doi: 10.3934/era.2026047

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Abstract

From a theoretical perspective, it is worthwhile to use the idea of control to synchronize multiple individual assets. We regard personal assets as multi-agent systems, i.e., second-order multi-agent systems (SOMAS). The delayed feedback control for consensus and average quasi-consensus of delayed SOMAS is studied. First, two weight matrices are studied, where the interactions are not entirely cooperative into the SOMAS with mixed time-varying delays (the delay varies with time). Second, a delayed feedback control is designed based on two weight matrices where the interactions are cooperative to get the consensus about followers and the average quasi-consensus about leader and followers. The consensus and average quasi-consensus of the delayed SOMAS are established by the graph-theoretic technique and Lyapunov functions. Finally, some numerical simulations is given to verify the theory.

References

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