Synchronization of a class of nonlinear multiple neural networks with delays via a dynamic event-triggered impulsive control strategy

Chengbo Yi; Jiayi Cai; Rui Guo; Chengbo Yi; Jiayi Cai; Rui Guo

doi:10.3934/era.2024208

Electronic Research Archive

2024, Volume 32, Issue 7: 4581-4603. doi: 10.3934/era.2024208

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Research article

Synchronization of a class of nonlinear multiple neural networks with delays via a dynamic event-triggered impulsive control strategy

1.
School of Undergraduate Education, Shenzhen Polytechnic University, Shenzhen 518060, China
2.
School of Mathematics and Statistics, Guizhou University of Finance and Economics, Guiyang 550025, China
3.
School of Mathematical Sciences, Shenzhen University, Shenzhen 518060, China
† The authors contributed equally to this work.

Received: 09 June 2024 Revised: 03 July 2024 Accepted: 12 July 2024 Published: 25 July 2024

In this paper, the impulsive synchronization of a class of nonlinear multiple neural networks (MNNs) with multi-delays was considered under a dynamic event-based mechanism. To achieve a more comprehensive synchronization outcome and mitigate the conservativeness of impulsive control due to predetermined time sequences, we integrated a dynamic event-triggered strategy. This approach formed a novel control framework for generalized MNNs, where impulsive inputs were applied only under specific conditions governed by event-triggering rules. Towards the above objectives, the impulsive jumping system, resulting from dynamic component, and matrix measure method were invoked to directly increase the computational simplicity and extensibility of the study. As the outcome, the synchronization criteria for the MNNs could be achieved, and the exponential convergence rate is resolved by considering both the generalized comparison principle regarding impulsive systems and the variable parameter formula. Moreover, Zeno-freeness of the achieved triggering regulation is ensured. Finally, two numerical examples confirmed the validity of the designed approach.
- synchronization,
- delayed neural networks,
- impulsive control,
- dynamic event-triggered
Citation: Chengbo Yi, Jiayi Cai, Rui Guo. Synchronization of a class of nonlinear multiple neural networks with delays via a dynamic event-triggered impulsive control strategy[J]. Electronic Research Archive, 2024, 32(7): 4581-4603. doi: 10.3934/era.2024208

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Abstract

In this paper, the impulsive synchronization of a class of nonlinear multiple neural networks (MNNs) with multi-delays was considered under a dynamic event-based mechanism. To achieve a more comprehensive synchronization outcome and mitigate the conservativeness of impulsive control due to predetermined time sequences, we integrated a dynamic event-triggered strategy. This approach formed a novel control framework for generalized MNNs, where impulsive inputs were applied only under specific conditions governed by event-triggering rules. Towards the above objectives, the impulsive jumping system, resulting from dynamic component, and matrix measure method were invoked to directly increase the computational simplicity and extensibility of the study. As the outcome, the synchronization criteria for the MNNs could be achieved, and the exponential convergence rate is resolved by considering both the generalized comparison principle regarding impulsive systems and the variable parameter formula. Moreover, Zeno-freeness of the achieved triggering regulation is ensured. Finally, two numerical examples confirmed the validity of the designed approach.

References

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