Quantized Sampled-Data Synchronization of Delayed Reaction-Diffusion Neural Networks Under Spatially Point...

Area of Science:

• Control Theory
• Neural Networks
• Dynamical Systems

Background:

• Reaction-diffusion neural networks (RDNNs) are crucial in modeling complex spatio-temporal phenomena.
• Synchronization of delayed RDNNs is challenging due to inherent delays and communication constraints.
• Existing methods often lack consideration for quantized sampled-data control and limited spatial measurements.

Purpose of the Study:

• To investigate the synchronization problem of delayed RDNNs under quantized sampled-data (SD) control using spatially point measurements (SPMs).
• To develop novel synchronization criteria that account for communication limitations like quantization and variable sampling.
• To ensure the exponential stability of the synchronization error system.

Main Methods:

• Utilized inequality techniques and Lyapunov-Krasovskii functional to establish synchronization criteria.
• Formulated criteria in the form of linear matrix inequalities (LMIs).
• Employed quantized sampled-data control based on spatially point measurements.

Main Results:

• Established synchronization criteria for delayed RDNNs under quantized SD control with SPMs.
• Demonstrated that the proposed criteria guarantee exponential stability of the synchronization error system.
• The synchronization method is applicable even with distributed and discrete delays.

Conclusions:

• The proposed quantized SD control strategy effectively achieves synchronization for delayed RDNNs.
• The established LMIs provide a feasible approach for designing controllers.
• Numerical examples validate the efficacy and robustness of the developed synchronization method.