Distributed Adaptive Containment Control for Coupled Reaction-Diffusion Neural Networks With Directed Topology

Area of Science:

• Control Theory
• Neural Networks
• Dynamical Systems

Background:

• Reaction-diffusion neural networks (RDNNs) present complex dynamics due to spatial variables and nonlinearities.
• Coordinating distributed systems with directed communication topologies poses significant control challenges.

Purpose of the Study:

• To develop a distributed adaptive control protocol for leader-follower coordination of RDNNs.
• To address the containment control problem for RDNNs under multiple leaders and directed networks.

Main Methods:

• Design of a novel adaptive control protocol tailored for RDNNs.
• Utilizing Lyapunov functional construction and prior knowledge for stability analysis.
• Theoretical proof of containment stability for coupled RDNNs.

Main Results:

• A novel adaptive control protocol effectively solves the containment control problem for RDNNs.
• The stability of containment for coupled RDNNs with directed communication is theoretically guaranteed.
• A corollary is presented for leader-follower synchronization in RDNNs.

Conclusions:

• The proposed adaptive control protocol ensures stable containment for RDNNs under directed networks.
• The findings extend leader-follower coordination strategies to complex partial differential systems.
• Numerical examples validate the effectiveness of the theoretical results.