Random Spatiotemporal Sampled-Data Control for Reaction-Diffusion Neural Networks With Dwell-Time-Based Sojourn...

Area of Science:

• Control Theory
• Computational Neuroscience
• Network Science

Background:

• Reaction-diffusion neural networks (RDNNs) are crucial for modeling complex spatio-temporal dynamics.
• Synchronization of RDNNs is challenging due to stochastic switching and communication constraints.
• Existing methods often require precise transition probabilities or constant sojourn probabilities, limiting their applicability.

Purpose of the Study:

• To address the mean-square exponential synchronization of RDNNs under stochastic switching and communication limitations.
• To develop a more tractable characterization of random mode evolution using dwell-time-dependent sojourn probabilities.
• To reduce communication burden via a random adaptive event-triggered protocol (RAETP) and a random spatiotemporal sampled-data control (RSTSDC) scheme.

Main Methods:

• A dwell-time-dependent sojourn-probability switching rule for characterizing random mode evolution.
• A random adaptive event-triggered protocol (RAETP) with online threshold adjustment.
• A random spatiotemporal sampled-data control (RSTSDC) scheme integrating random sampling and switching gains.
• Derivation of sufficient conditions for mean-square exponential synchronization.

Main Results:

• The proposed switching rule offers a more tractable approach to random mode evolution.
• The RAETP effectively reduces communication load by adjusting triggering thresholds dynamically.
• The RSTSDC scheme successfully integrates various random elements into the RDNN synchronization framework.
• Sufficient conditions guaranteeing mean-square exponential synchronization were established.

Conclusions:

• The developed methods ensure mean-square exponential synchronization for RDNNs with stochastic switching and communication constraints.
• The proposed approach demonstrates superior performance in terms of convergence speed and communication efficiency compared to benchmark strategies.
• This work provides a robust framework for designing controllers for complex neural network systems under realistic operational conditions.