A New Looped Functional to Synchronize Neural Networks With Sampled-Data Control

Area of Science:

• Control Systems Engineering
• Computational Neuroscience
• Applied Mathematics

Background:

• Neural networks are crucial for complex computations.
• Synchronization of dynamical systems is essential for distributed computing and signal processing.
• Sampled-data control introduces challenges due to discrete-time information.

Purpose of the Study:

• To address the sampled-data-based synchronization of neural networks.
• To develop a control strategy that accounts for time delays.
• To ensure robust synchronization between master and slave neural network systems.

Main Methods:

• A novel looped Lyapunov functional incorporating multiple state points (e(t_k), e(t), e(t_k+1), e(t_k-τ_c), e(t-τ_c), and e(t_k+1-τ_c)) was constructed.
• A generalized free-matrix-based integral inequality (GFMBII) was employed.
• Linear matrix inequality (LMI) techniques were used to design the sampled-data controller.

Main Results:

• Sufficient conditions were derived to guarantee synchronization.
• The proposed method effectively synchronizes the slave system with the master system, even in the presence of time delays.
• Numerical examples validated the effectiveness and advantages of the proposed approach.

Conclusions:

• The novel looped functional and GFMBII provide a powerful framework for sampled-data synchronization of neural networks.
• The LMI-based controller ensures reliable synchronization with time delays.
• The method offers a valid and advantageous solution for neural network synchronization problems.