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Distributed adaptive robust containment control for reaction-diffusion neural networks with external disturbances

Qian Qiu1, Housheng Su2

  • 1School of Artificial Intelligence and Automation, Image Processing and Intelligent Control Key Laboratory of Education Ministry of China, Huazhong University of Science and Technology, Wuhan 430074, China; School of Artificial Intelligence, Henan University, Zhengzhou 450046, China.

Neural Networks : the Official Journal of the International Neural Network Society
|May 13, 2024
PubMed
Summary

This study introduces a novel distributed adaptive controller for robust synchronization in reaction-diffusion neural networks (RDNNs). The controller prevents parameter drift and ensures reliable tracking synchronization despite external disturbances.

Keywords:
Adaptive controlDirected graphsExternal disturbancesMultiple leadersRDNNs

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Area of Science:

  • Control Theory
  • Applied Mathematics
  • Computational Neuroscience

Background:

  • Reaction-diffusion neural networks (RDNNs) are crucial for modeling complex spatio-temporal dynamics.
  • Synchronization in complex networks is a fundamental problem with applications in various fields.
  • Existing methods often struggle with parameter drift and external disturbances in directed network topologies.

Purpose of the Study:

  • To address the leader-follower robust synchronization problem for RDNNs with multiple leaders and external disturbances.
  • To develop a novel distributed adaptive controller that overcomes limitations of previous approaches.
  • To ensure robust containment and tracking synchronization under directed graph settings.

Main Methods:

  • Utilizing the σ modification approach to design a distributed adaptive controller.
  • Introducing a novel term to mitigate parameter drift, ensuring adaptive parameters remain bounded.
  • Developing a new function χi(t) to enhance design freedom and achieve robust containment against external disturbances.

Main Results:

  • A novel distributed adaptive controller is proposed for robust synchronization in RDNNs.
  • The controller effectively prevents parameter drift, a common issue in adaptive control.
  • Robust tracking synchronization is guaranteed for RDNNs with one leader under bounded L² norm external disturbances.
  • Numerical simulations confirm the theoretical results, demonstrating the controller's efficacy.

Conclusions:

  • The proposed adaptive controller effectively achieves robust leader-follower synchronization in RDNNs under directed graphs.
  • The method provides a robust solution for handling external disturbances and preventing parameter drift.
  • This work contributes to the theoretical understanding and practical application of synchronization in complex neural network systems.