Fixed-time synchronization control of fuzzy inertial neural networks with mismatched parameters and structures

Jingyang Ran; Tiecheng Zhang; Jingyang Ran; Tiecheng Zhang

doi:10.3934/math.20241525

AIMS Mathematics

2024, Volume 9, Issue 11: 31721-31739. doi: 10.3934/math.20241525

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Research article

Fixed-time synchronization control of fuzzy inertial neural networks with mismatched parameters and structures

Jingyang Ran ,
Tiecheng Zhang ^,

Huangshi Key Laboratory of Metaverse and Virtual Simulation, School of Mathematics and Statistics, Hubei Normal University, Huangshi, Hubei 435002, China

Received: 21 September 2024 Revised: 16 October 2024 Accepted: 23 October 2024 Published: 07 November 2024
MSC : 93D09, 93D20, 93D23

This research addressed the issue of fixed-time synchronization between random neutral-type fuzzy inertial neural networks and non-random neutral-type fuzzy inertial neural networks. Notably, it should be emphasized that the parameters of the drive and reaction systems did not correspond. Initially, additional free parameters were introduced to reduce the order of the error system. Subsequently, considering the influence of memory on system dynamics, a piecewise time-delay fixed time controller was developed to compensate for the influence of the time delay on the system. Utilizing stochastic analysis techniques and Lyapunov functions, sufficient conditions were derived to ensure the random fixed-time synchronization of the two neural networks. Furthermore, the settling time for system synchronization was assessed using stochastic finite-time inequalities. As a particular case, the necessary criteria for achieving fixed-time synchronization were established when the strength of the random disturbances was equal to zero. Finally, simulation results were provided to demonstrate the effectiveness of the proposed approach.
- inertial neural network,
- mismatched parameters,
- fixed-time synchronization
Citation: Jingyang Ran, Tiecheng Zhang. Fixed-time synchronization control of fuzzy inertial neural networks with mismatched parameters and structures[J]. AIMS Mathematics, 2024, 9(11): 31721-31739. doi: 10.3934/math.20241525

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Abstract

This research addressed the issue of fixed-time synchronization between random neutral-type fuzzy inertial neural networks and non-random neutral-type fuzzy inertial neural networks. Notably, it should be emphasized that the parameters of the drive and reaction systems did not correspond. Initially, additional free parameters were introduced to reduce the order of the error system. Subsequently, considering the influence of memory on system dynamics, a piecewise time-delay fixed time controller was developed to compensate for the influence of the time delay on the system. Utilizing stochastic analysis techniques and Lyapunov functions, sufficient conditions were derived to ensure the random fixed-time synchronization of the two neural networks. Furthermore, the settling time for system synchronization was assessed using stochastic finite-time inequalities. As a particular case, the necessary criteria for achieving fixed-time synchronization were established when the strength of the random disturbances was equal to zero. Finally, simulation results were provided to demonstrate the effectiveness of the proposed approach.

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