Phase balancing in globally connected networks of Liénard oscillators

Mohit Sinha, Florian Dorfler, Brian Johnson, Sairaj Dhople

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

We synthesize a feedback for a fully connected network of identical Liénard-type oscillators such that the phase-balanced equilibrium - the mode where the centroid of the coupled oscillators in polar coordinates is at the origin - is asymptotically stable, and the phase-synchronized equilibrium is unstable. Our approach hinges on a coordinate transformation of the oscillator dynamics to polar coordinates, and periodic averaging theory to simplify the examination of multiple time-scale behavior. Using Lyapunov- and linearization-based arguments, we demonstrate that the oscillator dynamics have the same radii and balanced phases in steady state for a large set of initial conditions. Numerical simulation results are presented to validate the analyses.

Original languageEnglish (US)
Title of host publication2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages595-600
Number of pages6
ISBN (Electronic)9781509028733
DOIs
StatePublished - Jan 18 2018
Externally publishedYes
Event56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia
Duration: Dec 12 2017Dec 15 2017

Publication series

Name2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume2018-January

Other

Other56th IEEE Annual Conference on Decision and Control, CDC 2017
CountryAustralia
CityMelbourne
Period12/12/1712/15/17

Bibliographical note

Funding Information:
M. Sinha and S. V. Dhople were supported in part by the National Science Foundation under the CAREER award, ECCS-CAR-1453921, and grant ECCS-1509277. F. Dörfler was supported by ETH Zürich funds and the SNF Assistant Professor Energy Grant #160573. B. Johnson was supported by the U.S. Department of Energy (DOE) Solar Energy Technologies Office under Contract No. DE-EE0000-1583 and by the DOE under Contract No. DE-AC36-08-GO28308 with NREL.

Fingerprint Dive into the research topics of 'Phase balancing in globally connected networks of Liénard oscillators'. Together they form a unique fingerprint.

Cite this