Synchronization of Networked Harmonic Oscillators via Quantized Sampled Velocity Feedback

TL;DR

This paper introduces a quantized sampled velocity feedback protocol for synchronizing harmonic oscillators over a network, ensuring convergence to a neighborhood of synchronized states with adjustable zooming parameters.

Contribution

It presents a novel quantized coupling protocol with fixed and adjustable zooming, providing conditions for synchronization in networked harmonic oscillators.

Findings

Oscillators converge to a bounded neighborhood of synchronization

The protocol works with fixed and adjustable zooming parameters

Numerical examples confirm effectiveness

Abstract

In this technical note, we propose a practicable quantized sampled velocity data coupling protocol for synchronization of a set of harmonic oscillators. The coupling protocol is designed in a quantized way via interconnecting the velocities encoded by a uniform quantizer with a zooming parameter in either a fixed or an adjustable form over a directed communication network. We establish sufficient conditions for the networked harmonic oscillators to converge to a bounded neighborhood of the synchronized orbits with a fixed zooming parameter. We ensure the oscillators to achieve synchronization by designing the quantized coupling protocol with an adjustable zooming parameter. Finally, we show two numerical examples to illustrate the effectiveness of the proposed coupling protocol.