Design of optimal coupling gains for synchronization of nonlinear oscillators

Victor Purba; Xiaofan Wu; Mohit Sinha; Sairaj V. Dhople; Mihailo R. Jovanovic

doi:10.1109/CDC.2015.7402392

Design of optimal coupling gains for synchronization of nonlinear oscillators

Victor Purba, Xiaofan Wu, Mohit Sinha, Sairaj V. Dhople, Mihailo R. Jovanovic

Electrical and Computer Engineering

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

2 Scopus citations

Abstract

This paper develops a structured optimal-control framework to design coupling gains for synchronization of weakly nonlinear oscillator circuits connected in resistive networks with arbitrary topologies. The oscillators are modeled as weakly nonlinear Liénard-type circuits, and the coupling gain amounts to the current gain which scales the output current of the oscillator. The structured optimal-control problem allows us to seek a decentralized control strategy (equivalently, a diagonal feedback matrix) that precludes communications between oscillators. To this end, a sparsity-promoting optimal control algorithm is developed to tune the optimal diagonal feedback-gain matrix with minimal performance sacrifice. This involves solving an ?2 optimal control problem with ℓ₁ regularization by applying the alternating direction method of multipliers (ADMM). Simulation studies with application to voltage regulation in islanded networks composed of power-electronic inverters are provided to validate the approach.

Original language	English (US)
Title of host publication	54rd IEEE Conference on Decision and Control,CDC 2015
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1310-1315
Number of pages	6
ISBN (Electronic)	9781479978861
DOIs	https://doi.org/10.1109/CDC.2015.7402392
State	Published - Feb 8 2015
Event	54th IEEE Conference on Decision and Control, CDC 2015 - Osaka, Japan Duration: Dec 15 2015 → Dec 18 2015

Publication series

Name	Proceedings of the IEEE Conference on Decision and Control
Volume	54rd IEEE Conference on Decision and Control,CDC 2015
ISSN (Print)	0743-1546

Other

Other	54th IEEE Conference on Decision and Control, CDC 2015
Country	Japan
City	Osaka
Period	12/15/15 → 12/18/15

Keywords

Alternating direction method of multipliers
sparsity-promoting optimal control
synchronization
weakly nonlinear oscillators

Access

10.1109/CDC.2015.7402392

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Purba, V., Wu, X., Sinha, M., Dhople, S. V., & Jovanovic, M. R. (2015). Design of optimal coupling gains for synchronization of nonlinear oscillators. In 54rd IEEE Conference on Decision and Control,CDC 2015 (pp. 1310-1315). [7402392] (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2015.7402392

Design of optimal coupling gains for synchronization of nonlinear oscillators. / Purba, Victor; Wu, Xiaofan; Sinha, Mohit; Dhople, Sairaj V.; Jovanovic, Mihailo R.

54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc., 2015. p. 1310-1315 7402392 (Proceedings of the IEEE Conference on Decision and Control; Vol. 54rd IEEE Conference on Decision and Control,CDC 2015).

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

Purba, V, Wu, X, Sinha, M, Dhople, SV & Jovanovic, MR 2015, Design of optimal coupling gains for synchronization of nonlinear oscillators. in 54rd IEEE Conference on Decision and Control,CDC 2015., 7402392, Proceedings of the IEEE Conference on Decision and Control, vol. 54rd IEEE Conference on Decision and Control,CDC 2015, Institute of Electrical and Electronics Engineers Inc., pp. 1310-1315, 54th IEEE Conference on Decision and Control, CDC 2015, Osaka, Japan, 12/15/15. https://doi.org/10.1109/CDC.2015.7402392

Purba V, Wu X, Sinha M, Dhople SV, Jovanovic MR. Design of optimal coupling gains for synchronization of nonlinear oscillators. In 54rd IEEE Conference on Decision and Control,CDC 2015. Institute of Electrical and Electronics Engineers Inc. 2015. p. 1310-1315. 7402392. (Proceedings of the IEEE Conference on Decision and Control). https://doi.org/10.1109/CDC.2015.7402392

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abstract = "This paper develops a structured optimal-control framework to design coupling gains for synchronization of weakly nonlinear oscillator circuits connected in resistive networks with arbitrary topologies. The oscillators are modeled as weakly nonlinear Li{\'e}nard-type circuits, and the coupling gain amounts to the current gain which scales the output current of the oscillator. The structured optimal-control problem allows us to seek a decentralized control strategy (equivalently, a diagonal feedback matrix) that precludes communications between oscillators. To this end, a sparsity-promoting optimal control algorithm is developed to tune the optimal diagonal feedback-gain matrix with minimal performance sacrifice. This involves solving an ?2 optimal control problem with ℓ1 regularization by applying the alternating direction method of multipliers (ADMM). Simulation studies with application to voltage regulation in islanded networks composed of power-electronic inverters are provided to validate the approach.",

keywords = "Alternating direction method of multipliers, sparsity-promoting optimal control, synchronization, weakly nonlinear oscillators",

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N2 - This paper develops a structured optimal-control framework to design coupling gains for synchronization of weakly nonlinear oscillator circuits connected in resistive networks with arbitrary topologies. The oscillators are modeled as weakly nonlinear Liénard-type circuits, and the coupling gain amounts to the current gain which scales the output current of the oscillator. The structured optimal-control problem allows us to seek a decentralized control strategy (equivalently, a diagonal feedback matrix) that precludes communications between oscillators. To this end, a sparsity-promoting optimal control algorithm is developed to tune the optimal diagonal feedback-gain matrix with minimal performance sacrifice. This involves solving an ?2 optimal control problem with ℓ1 regularization by applying the alternating direction method of multipliers (ADMM). Simulation studies with application to voltage regulation in islanded networks composed of power-electronic inverters are provided to validate the approach.

AB - This paper develops a structured optimal-control framework to design coupling gains for synchronization of weakly nonlinear oscillator circuits connected in resistive networks with arbitrary topologies. The oscillators are modeled as weakly nonlinear Liénard-type circuits, and the coupling gain amounts to the current gain which scales the output current of the oscillator. The structured optimal-control problem allows us to seek a decentralized control strategy (equivalently, a diagonal feedback matrix) that precludes communications between oscillators. To this end, a sparsity-promoting optimal control algorithm is developed to tune the optimal diagonal feedback-gain matrix with minimal performance sacrifice. This involves solving an ?2 optimal control problem with ℓ1 regularization by applying the alternating direction method of multipliers (ADMM). Simulation studies with application to voltage regulation in islanded networks composed of power-electronic inverters are provided to validate the approach.

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