Observer-Based Boundary Stabilization of Coupled Semilinear Reaction-Diffusion Neural Networks With Spatially Varying...

Area of Science:

• Control Theory
• Applied Mathematics
• Computational Neuroscience

Background:

• Coupled semilinear reaction-diffusion neural networks are crucial in modeling complex systems.
• Stabilizing these networks, especially with spatially varying coefficients, presents significant challenges.
• Existing control strategies may require frequent updates, impacting efficiency.

Purpose of the Study:

• To propose an observer-based event-triggered Robin boundary control strategy.
• To achieve exponential stabilization of coupled semilinear reaction-diffusion neural networks.
• To minimize control law updates while maintaining system stability.

Main Methods:

• Design of an observer to estimate system states from available measurements.
• Development of an event-triggered boundary control law using the observer.
• Application of the backstepping method for explicit control formula derivation.
• Exclusion of Zeno behavior in the event-triggered control design.

Main Results:

• The proposed strategy successfully achieves exponential stabilization of the neural networks.
• The event-triggered approach significantly reduces the frequency of control law updates.
• The observer effectively estimates system states, enabling robust control.
• Numerical simulations confirm the method's effectiveness and performance.

Conclusions:

• The observer-based event-triggered boundary control is effective for stabilizing reaction-diffusion neural networks.
• This approach offers improved control efficiency through reduced updates.
• The method provides a robust framework for complex neural network systems.