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Fixed-time pinning-controlled synchronization for coupled delayed neural networks with discontinuous activations
Hui Lü1, Wangli He2, Qing-Long Han3
1School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200072, China.
Summary
This study addresses fixed-time synchronization for neural networks with delays and discontinuous activations using pinning control. Controllers are designed to achieve synchronization in a predictable time, regardless of initial states.
Area of Science:
- Control Theory
- Neural Networks
- Dynamical Systems
Background:
- Coupled delayed neural networks are crucial in complex systems.
- Achieving synchronization in finite or fixed time is a significant challenge.
Purpose of the Study:
- To investigate the fixed-time synchronization problem for coupled delayed neural networks with discontinuous activations.
- To design novel discontinuous controllers for achieving synchronization.
Main Methods:
- Utilizing pinning control strategies.
- Developing discontinuous controllers for finite-time and fixed-time synchronization.
- Employing a topology-dependent Lyapunov function for analysis.
Main Results:
- A discontinuous controller guarantees finite-time synchronization.
- A discontinuous fixed-time controller ensures synchronization with an estimated settling time.
- Criteria for finite- and fixed-time synchronization are derived.
Conclusions:
- The proposed controllers effectively achieve finite- and fixed-time synchronization.
- The settling time is independent of initial conditions with the fixed-time controller.
- Numerical examples validate the controllers' performance.
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