Controller design for global fixed-time synchronization of delayed neural networks with discontinuous activations

Area of Science:

• Control Systems Engineering
• Computational Neuroscience
• Applied Mathematics

Background:

• Delayed neural networks (DNNs) are crucial for modeling complex dynamics but face synchronization challenges.
• Discontinuous activation functions in DNNs complicate controller design and stability analysis.
• Achieving synchronization within a fixed, predictable time is essential for real-time applications.

Purpose of the Study:

• To design controllers for global fixed-time synchronization of DNNs with discontinuous activations.
• To ensure the synchronization settling time is independent of the initial states.
• To provide easily verifiable conditions for achieving fixed-time synchronization.

Main Methods:

• Design of adaptive control and state feedback control laws.
• Utilizing two specific lemmas to prove system stability.
• Analysis of the error system for global asymptotic and fixed-time stability.

Main Results:

• Global fixed-time synchronization for DNNs with discontinuous activations is achieved.
• Derived conditions for fixed-time synchronization are sufficient and easy to check.
• The settling time is independent of the initial conditions of the drive and response systems.
• Finite-time synchronization results are shown as special cases of the fixed-time results.

Conclusions:

• The proposed control strategies effectively guarantee global fixed-time synchronization for the studied DNNs.
• The independence of settling time from initial conditions offers robustness and predictability.
• The findings extend existing synchronization theory and have practical implications for complex network systems.