Phase balancing in globally connected networks of Liénard oscillators

Mohit Sinha; Florian Dorfler; Brian Johnson; Sairaj Dhople

doi:10.1109/CDC.2017.8263726

Phase balancing in globally connected networks of Liénard oscillators

Mohit Sinha, Florian Dorfler, Brian Johnson, Sairaj Dhople

Electrical and Computer Engineering

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

10 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 language	English (US)
Title of host publication	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	595-600
Number of pages	6
ISBN (Electronic)	9781509028733
DOIs	https://doi.org/10.1109/CDC.2017.8263726
State	Published - Jun 28 2017
Event	56th IEEE Annual Conference on Decision and Control, CDC 2017 - Melbourne, Australia Duration: Dec 12 2017 → Dec 15 2017

Publication series

Name	2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017
Volume	2018-January

Other

Other	56th IEEE Annual Conference on Decision and Control, CDC 2017
Country/Territory	Australia
City	Melbourne
Period	12/12/17 → 12/15/17

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.

Publisher Copyright:
© 2017 IEEE.

Publisher link

10.1109/CDC.2017.8263726

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Sinha, M., Dorfler, F., Johnson, B., & Dhople, S. (2017). Phase balancing in globally connected networks of Liénard oscillators. In 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017 (pp. 595-600). (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2017.8263726

Phase balancing in globally connected networks of Liénard oscillators. / Sinha, Mohit; Dorfler, Florian; Johnson, Brian et al.
2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 595-600 (2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017; Vol. 2018-January).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Sinha, M, Dorfler, F, Johnson, B & Dhople, S 2017, Phase balancing in globally connected networks of Liénard oscillators. in 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017. 2017 IEEE 56th Annual Conference on Decision and Control, CDC 2017, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 595-600, 56th IEEE Annual Conference on Decision and Control, CDC 2017, Melbourne, Australia, 12/12/17. https://doi.org/10.1109/CDC.2017.8263726

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abstract = "We synthesize a feedback for a fully connected network of identical Li{\'e}nard-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.",

author = "Mohit Sinha and Florian Dorfler and Brian Johnson and Sairaj Dhople",

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. D{\"o}rfler was supported by ETH Z{\"u}rich 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. Publisher Copyright: {\textcopyright} 2017 IEEE.; 56th IEEE Annual Conference on Decision and Control, CDC 2017 ; Conference date: 12-12-2017 Through 15-12-2017",

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N1 - 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. Publisher Copyright: © 2017 IEEE.

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N2 - 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.

AB - 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.

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Phase balancing in globally connected networks of Liénard oscillators

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