Mean square synchronization for stochastic delayed neural networks via pinning impulsive control

Yilin Li; Jianwen Feng; Jingyi Wang; Yilin Li; Jianwen Feng; Jingyi Wang

doi:10.3934/era.2022161

Electronic Research Archive

2022, Volume 30, Issue 9: 3172-3192. doi: 10.3934/era.2022161

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Mean square synchronization for stochastic delayed neural networks via pinning impulsive control

College of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China

Received: 26 April 2022 Revised: 26 May 2022 Accepted: 29 May 2022 Published: 20 June 2022

The mean square synchronization for a class of general stochastic delayed neural networks is explored in this paper using pinning impulsive control (PIC). It is evident that PIC combines the profits of pinning control and impulsive control. Considering that there is a time delay between the allocation and execution of impulsive instructions in practice, the idea of average impulsive delay (AID) is brought to describe this kind of delay. Furthermore, in actuality, neural networks with internal delay and stochastic disturbance are more general. Accordingly, some appropriate criteria are derived using the Lyapunov stability theory and the Fubini theorem to ensure mean square synchronization in two different cases, namely when the controller is designed with and without the impulsive delay. Finally, some numerical examples are afforded to validate the efficiency of theoretical results.
- stochastic delayed neural networks,
- mean square synchronization,
- pinning impulsive control,
- average impulsive delay
Citation: Yilin Li, Jianwen Feng, Jingyi Wang. Mean square synchronization for stochastic delayed neural networks via pinning impulsive control[J]. Electronic Research Archive, 2022, 30(9): 3172-3192. doi: 10.3934/era.2022161

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Abstract

The mean square synchronization for a class of general stochastic delayed neural networks is explored in this paper using pinning impulsive control (PIC). It is evident that PIC combines the profits of pinning control and impulsive control. Considering that there is a time delay between the allocation and execution of impulsive instructions in practice, the idea of average impulsive delay (AID) is brought to describe this kind of delay. Furthermore, in actuality, neural networks with internal delay and stochastic disturbance are more general. Accordingly, some appropriate criteria are derived using the Lyapunov stability theory and the Fubini theorem to ensure mean square synchronization in two different cases, namely when the controller is designed with and without the impulsive delay. Finally, some numerical examples are afforded to validate the efficiency of theoretical results.

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