Synchronization for singularity-perturbed complex networks via event-triggered impulsive control

Kun Liang; Wangli He; Yang Yuan; Liyu Shi

doi:10.3934/dcdss.2022068

Article Contents

2022, Volume 15, Issue 11: 3205-3221. Doi: 10.3934/dcdss.2022068

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Synchronization for singularity-perturbed complex networks via event-triggered impulsive control

Key Laboratory of Smart Manufacturing in Energy Chemical Processes, Ministry of Education, East China University of Science and Technology, 200237 Shanghai, China

^* Corresponding author: Wangli He
^* Corresponding author: Wangli He

Received: October 31, 2021

Revised: December 31, 2021

Early access: March 2022

Published: September 2022

This work is supported by National Natural Science Foundation of China (61922030), Shanghai International Science Technology Cooperation Program (21550712400) and Fundamental Research Funds for the Central Universities (222202217006)

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Abstract

This paper studies synchronization of singularity-perturbed complex networks (SPCNs) with a small singular perturbation parameter (SPP) via event-triggered impulsive control (ETIC). A novel dynamic event-triggered mechanism is proposed where an auxiliary impulse parameter is introduced to regulate the triggering threshold dynamically for saving the network resource. Based on SPP-dependent Lyapunov function, some sufficient conditions involving the impulsive gain, triggering parameters and singular perturbation parameter (SPP) are obtained to synchronize the SPCNs, and the upper bound of SPP is also determined. Moreover, it proves that the Zeno behavior can be excluded. Finally, two simulations are provided to demonstrate the validity of the obtained results.

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Mathematics Subject Classification: Primary: 93D23, 93D50; Secondary: 93C27.

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Figure 1. Framework of the SPCN with ETIC strategy

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Figure 2. Lyapunov function

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Figure 3. Trajectories of $ \eta_{is} $ ($ i = 1, 2, 3, 4, 5, s = 1, 2, 3 $) of error system (5) without dynamic ETIC

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Figure 4. Trajectories of $ \eta_{is} $ ($ i = 1, 2, 3, 4, 5, s = 1, 2, 3 $) of the error system (5) with dynamic ETIC

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Table 1. The relationship between the upper bound of SPP $ \bar{\varepsilon} $ and the nonlinear function $ f\left( x_{i}\left( t\right) \right) $

$ h $ 0.65 0.70 0.75 0.85 0.90

$ \bar{\varepsilon} $ 1.5737 0.9119 0.2226 0.0305 infeasible

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Table 2. The number of triggering times

$ \beta $ 0.06 0.05 0.04 0.03 0.02 0.01 0.00

number 17 19 21 26 30 39 50

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