Synchronization of Coupled Harmonic Oscillators Using Quantized Sampled Position Data

Xinjing Wang,Peipei He

doi:10.1155/2017/3949428

Abstract

For coupled harmonic oscillators (CHO), the paper studies the synchronization problem by using the quantized current sampled position data. The logarithmic quantizer is adopted here to quantize the information transmitted; thus the quantization error of the sampled position data can be illustrated as the uncertainty according to the sector bound property. On the basis of that, the synchronization problem is converted into the asymptotical stability of the subsystems and even the solving problem of characteristic equation. Some sufficient conditions ensuring the synchronization of CHO are obtained relating to coupling strength, sampling period, and quantizer parameter. The usefulness of the theoretical result is shown by an example at the end.

Highlights

As a special multiagent system, coupled harmonic oscillators (CHO) has gotten much attention
When the CHO is affected by controller loss and communication time-delays, an algorithm is proposed in [2] to ensure the synchronization of the system and a brief procedure of the convergence analysis for such algorithm is given
A sufficient condition for the synchronized oscillatory motions of CHO is given by the influence of noise for the strongly connected directed graph

Summary

Introduction

As a special multiagent system, CHO has gotten much attention. By assuming that the undirected network is not connectivity, literature [1] shows that the CHO is able to achieve synchronization. Literature [8] proposes a distributed control method just using the outdated position states For both positive and negative coupling strengths, it derives some necessary and sufficient conditions (NSCs) for the synchronization of CHO. Summarized above, the synchronization of CHO and quantized consensus for the general multiagent systems have received enough attention, respectively. There are few results relating to the synchronization of CHO affected by data quantization, which is the problem studied in our paper. By adopting the logarithmic quantizer, the quantization error of the sampled position data can be illustrated as the uncertainty according to the sector bound property With this setup, some sufficient conditions relating to coupling strength, sampling period, and quantizer parameter are obtained for synchronized CHO.

Problem Formulation

The Sufficient Conditions for Synchronization

Simulation

Conclusion