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

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.