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Saturated impulsive control for synchronization of coupled delayed neural networks
Shuchen Wu1, Xiaodi Li2, Yanhui Ding3
1School of Mathematics and Statistics, Shandong Normal University, Ji'nan, 250014, PR China.
Summary
This study addresses the synchronization of coupled neural networks with impulsive control and mixed delays. Researchers developed a new method to ensure synchronization even with saturation in control actions.
Area of Science:
- Computational Neuroscience
- Control Theory
- Systems Engineering
Background:
- Coupled neural networks are crucial for complex computations but face synchronization challenges.
- Impulsive control and mixed delays (transmission and coupled) complicate network synchronization.
- Saturation in control actions is a practical limitation that must be addressed.
Purpose of the Study:
- To investigate the exponential synchronization of coupled neural networks with saturated impulsive control.
- To develop novel conditions for achieving synchronization under mixed delays.
- To maximize the domain of attraction for synchronization.
Main Methods:
- Utilized a sector condition based on a new set-inclusion constraint.
- Replaced saturation nonlinearity with a dead-zone function for analysis.
- Employed Lyapunov stability theory and domain of attraction estimation.
- Solved an optimization problem to enlarge the domain of attraction.
Main Results:
- Derived a sufficient condition for exponential synchronization of the addressed neural networks.
- Demonstrated that synchronization is achievable within the framework of saturated impulses.
- Proposed an optimized, enlarged domain of attraction for synchronization.
Conclusions:
- The proposed methods effectively achieve synchronization in coupled delayed neural networks with saturated impulses.
- The results provide a robust framework for designing stable and synchronized neural network systems.
- Numerical simulations confirm the theoretical findings and the practical applicability of the approach.
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