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Event-triggered delayed impulsive control for nonlinear systems with application to complex neural networks.

Mingzhu Wang1, Xiaodi Li2, Peiyong Duan3

  • 1School of Mathematics and Statistics, Shandong Normal University, Ji'nan, 250014, PR China.

Neural Networks : the Official Journal of the International Neural Network Society
|March 22, 2022
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Summary

This study introduces event-triggered delayed impulsive control (ETDIC) for nonlinear systems and neural networks. It demonstrates that time delays in impulses can positively impact system stability and synchronization, reducing resource waste.

Keywords:
Complex neural networksEvent-triggered delayed impulsive controlNonlinear systemStabilitySynchronization

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Area of Science:

  • Control Theory
  • Nonlinear Systems Analysis
  • Computational Neuroscience

Background:

  • Event-triggered impulse control (ETIC) reduces resource consumption by activating control only at specific instants.
  • Traditional methods often overlook or inadequately address time delays within impulse control systems.
  • Complex neural networks require robust control strategies for stable and synchronized operation.

Purpose of the Study:

  • To develop and analyze event-triggered delayed impulsive control (ETDIC) for nonlinear systems.
  • To investigate the impact of time delays in impulses on system stability and performance.
  • To apply ETDIC strategies to achieve synchronization in complex neural networks.

Main Methods:

  • Lyapunov-based event-triggered mechanism (ETM) to define impulse time sequences and avoid Zeno behavior.
  • Dynamic analysis integrating the effects of time delays within impulses.
  • Development of sufficient conditions for global asymptotic stability and network synchronization.

Main Results:

  • Sufficient conditions for global asymptotic stability of nonlinear systems under ETDIC.
  • Demonstration that time delays in impulses can have a stabilizing effect and improve performance.
  • Effective application of ETDIC for achieving synchronization in complex neural networks, considering impulse time delays.

Conclusions:

  • The proposed ETDIC framework offers an efficient approach to control, minimizing resource usage.
  • Time delays in impulses are shown to be beneficial for system stabilization and synchronization.
  • The study provides a validated theoretical framework with numerical examples for practical application.