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Fixed-Time Synchronization of Coupled Oscillator Networks with a Pacemaker
Xiufeng Guo1, Pengchun Rao1, Zhaoyan Wu2
1School of Science, East China Jiaotong University, Nanchang 330013, China.
Sensors (Basel, Switzerland)
|December 11, 2022
Summary
This study achieves fixed-time synchronization for Kuramoto oscillator networks using cyber-physical systems. Synchronization occurs in a time independent of initial conditions, verified by simulations.
Area of Science:
- Complex Systems
- Network Science
- Control Theory
Background:
- Kuramoto oscillator networks are fundamental models for studying synchronization phenomena.
- Cyber-physical systems (CPS) offer a framework for analyzing distributed control strategies.
- Achieving synchronization in a finite, predictable time is crucial for many applications.
Purpose of the Study:
- To investigate the fixed-time synchronization problem for a Kuramoto-oscillator network with a pacemaker.
- To develop fixed-time synchronization criteria for both identical and non-identical oscillators within a CPS framework.
- To determine upper bounds for the synchronization time.
Main Methods:
- Utilizing Lyapunov stability analyses to derive sufficient conditions for synchronization.
- Applying distributed control strategies to achieve phase and frequency agreement.
- Employing theoretical analysis and numerical simulations to validate the findings.
Main Results:
- Sufficient conditions for fixed-time phase and frequency synchronization were established.
- The derived synchronization time is independent of the initial phases and frequencies of the oscillators.
- Upper bounds for the synchronization time were successfully obtained.
Conclusions:
- The proposed distributed control strategies effectively achieve fixed-time synchronization in Kuramoto oscillator networks.
- The theoretical results are validated through numerical simulations, confirming the effectiveness of the approach.
- This research contributes to the understanding and control of synchronized dynamics in complex networks.
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