Adaptive tracking synchronization for coupled reaction-diffusion neural networks with parameter mismatches.

Area of Science:

• Control Systems Engineering
• Computational Neuroscience
• Applied Mathematics

Background:

• Coupled reaction-diffusion neural networks are essential for modeling complex spatio-temporal dynamics.
• Achieving tracking synchronization in these networks is challenging due to parameter mismatches and uncertainties.
• Existing methods often require boundedness assumptions for parameter mismatches, limiting their applicability.

Purpose of the Study:

• To investigate tracking synchronization for reaction-diffusion neural networks with potentially unbounded parameter mismatches.
• To design novel controllers that compensate for parameter uncertainties using only local network information.
• To demonstrate the effectiveness of the proposed control strategies through theoretical analysis and numerical simulations.

Main Methods:

• Design of parameter-dependent and parameter-independent adaptive controllers for known parameter mismatches.
• Development of a distributed adaptive controller for unknown network parameters and mismatches.
• Application of partial differential equation theories and differential inequality techniques for error analysis.

Main Results:

• The proposed controllers ensure that tracking synchronization errors are uniformly ultimately bounded.
• Synchronization errors are proven to converge exponentially to adjustable bounded domains.
• Controllers effectively compensate for parameter mismatches, including unbounded cases, using local information.

Conclusions:

• The developed control strategies effectively achieve tracking synchronization in coupled reaction-diffusion neural networks despite parameter mismatches.
• The theoretical framework guarantees robust performance and convergence, even under unbounded uncertainties.
• Numerical examples validate the practical applicability and effectiveness of the proposed controllers.