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Observer-based event-triggered impulsive control of delayed reaction-diffusion neural networks.

Luyao Li1, Licheng Fang1, Huan Liang2

  • 1School of Mathematics and Information Sciences, Yantai University, Yantai 264005, China.

Mathematical Biosciences and Engineering : MBE
|July 18, 2025
PubMed
Summary

This study introduces an event-triggered impulsive control for delayed neural networks with unmeasurable states. The novel observer-based strategy ensures global exponential stability with reduced control frequency.

Keywords:
event-triggered impulsive controlimpulsive observerneural networksreaction-diffusion

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Area of Science:

  • Control Systems Engineering
  • Computational Neuroscience
  • Applied Mathematics

Background:

  • Delayed reaction-diffusion neural networks (DRDnn) are crucial in modeling complex spatio-temporal dynamics.
  • Impulsive perturbations and unmeasurable states pose significant challenges in controlling these networks.
  • Existing control strategies often require continuous state monitoring or high triggering frequencies.

Purpose of the Study:

  • To develop a novel observer-based event-triggered impulsive control strategy for DRDnn.
  • To ensure global exponential stability for DRDnn with time delays and impulsive perturbations.
  • To address the challenge of unmeasurable states in control design.

Main Methods:

  • An event-triggered impulsive control mechanism is designed, where control instants are event-driven.
  • An impulsive observer is utilized to estimate system states for control signal generation.
  • Lyapunov stability criteria and linear matrix inequalities (LMIs) are employed to establish stability conditions.

Main Results:

  • The proposed strategy achieves global exponential stability for the delayed reaction-diffusion neural networks.
  • The event-triggered approach significantly reduces control signal frequency compared to traditional methods.
  • The control strategy is effective even when the network states are not directly measurable.

Conclusions:

  • The novel observer-based event-triggered impulsive control is effective for delayed neural networks.
  • This method offers advantages in reduced control frequency and applicability to systems with unmeasurable states.
  • The theoretical findings are validated through a numerical simulation, demonstrating practical effectiveness.