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Fixed/Prescribed-Time Synchronization and Energy Consumption for Kuramoto-Oscillator Networks.

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Summary

This study introduces fixed-time synchronization (FxTS) and prescribed-time synchronization (PTS) for Kuramoto oscillator networks. It also estimates energy consumption, offering insights into system efficiency and control time.

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Area of Science:

Complex Systems
Control Theory
Network Science

Background:

Kuramoto oscillator networks are fundamental models for studying synchronization phenomena in coupled systems.
Evaluating energy consumption and control time is crucial for practical applications of synchronization control.

Purpose of the Study:

To investigate fixed-time synchronization (FxTS) and prescribed-time synchronization (PTS) in Kuramoto oscillator networks.
To estimate the energy consumption associated with FxTS and PTS.
To analyze the impact of control strategies on synchronization time and energy efficiency.

Main Methods:

Development of two sufficient conditions for achieving FxTS in Kuramoto networks.
Design of a prescribed-time controller incorporating a time-varying function for PTS.
Derivation of energy consumption bounds for both FxTS and PTS control processes.
Simulation using a 5-node Kuramoto oscillator network to validate the proposed methods.

Main Results:

Sufficient conditions for FxTS (phase and frequency agreement) were established.
A novel PTS controller was proposed, achieving synchronization independent of initial conditions and controller parameters.
Energy consumption bounds were derived for FxTS and PTS, aiding in system working time evaluation.
Effectiveness of FxTS and PTS was demonstrated through a 5-node network example.

Conclusions:

The study successfully demonstrated FxTS and PTS for Kuramoto oscillator networks.
The proposed methods provide a framework for energy-efficient and time-bound synchronization control.
The independence of setting-time in PTS enhances its applicability in diverse systems.