On the optimal synchronization of oscillator networks via sparse interconnection graphs

Makan Fardad; Fu Lin; Mihailo R. Jovanovic

doi:10.1109/acc.2012.6315116

On the optimal synchronization of oscillator networks via sparse interconnection graphs

Makan Fardad, Fu Lin, Mihailo R. Jovanovic

Department of Electrical Engineering & Computer Science

Research output: Chapter in Book/Entry/Poem › Conference contribution

9 Scopus citations

Abstract

We study the optimal design of a conductance network as a means for synchronizing a given set of oscillators. By considering the conductance that connects two oscillators as the measure of the amount of communication between them, we formulate an optimal control problem that addresses the trade-off between synchronization performance and communication. Additionally, we promote the sparsity of the network by penalizing the number of interconnection links. For identical oscillators, we establish convexity and show that the design problem can be formulated as a semidefinite program. For non-identical oscillators, that can be considered as perturbations around a central (average) oscillator, we show that it is meaningful to design an optimal conductance network by assuming that all oscillators are identical to the central oscillator. Finally, for special classes of oscillator networks we derive explicit formulas for the optimal conductance values.

Original language	English (US)
Title of host publication	2012 American Control Conference, ACC 2012
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	4777-4782
Number of pages	6
ISBN (Print)	9781457710957
DOIs	https://doi.org/10.1109/acc.2012.6315116
State	Published - 2012
Event	2012 American Control Conference, ACC 2012 - Montreal, QC, Canada Duration: Jun 27 2012 → Jun 29 2012

Publication series

Name	Proceedings of the American Control Conference
ISSN (Print)	0743-1619

Other

Other	2012 American Control Conference, ACC 2012
Country/Territory	Canada
City	Montreal, QC
Period	6/27/12 → 6/29/12

Keywords

Convex relaxation
optimization
oscillator synchronization
semidefinite programming
sparse communication architecture

ASJC Scopus subject areas

Electrical and Electronic Engineering

Access to Document

10.1109/acc.2012.6315116

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On the optimal synchronization of oscillator networks via sparse interconnection graphs. / Fardad, Makan; Lin, Fu; Jovanovic, Mihailo R.
2012 American Control Conference, ACC 2012. Institute of Electrical and Electronics Engineers Inc., 2012. p. 4777-4782 6315116 (Proceedings of the American Control Conference).

Research output: Chapter in Book/Entry/Poem › Conference contribution

Fardad, M, Lin, F & Jovanovic, MR 2012, On the optimal synchronization of oscillator networks via sparse interconnection graphs. in 2012 American Control Conference, ACC 2012., 6315116, Proceedings of the American Control Conference, Institute of Electrical and Electronics Engineers Inc., pp. 4777-4782, 2012 American Control Conference, ACC 2012, Montreal, QC, Canada, 6/27/12. https://doi.org/10.1109/acc.2012.6315116

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N2 - We study the optimal design of a conductance network as a means for synchronizing a given set of oscillators. By considering the conductance that connects two oscillators as the measure of the amount of communication between them, we formulate an optimal control problem that addresses the trade-off between synchronization performance and communication. Additionally, we promote the sparsity of the network by penalizing the number of interconnection links. For identical oscillators, we establish convexity and show that the design problem can be formulated as a semidefinite program. For non-identical oscillators, that can be considered as perturbations around a central (average) oscillator, we show that it is meaningful to design an optimal conductance network by assuming that all oscillators are identical to the central oscillator. Finally, for special classes of oscillator networks we derive explicit formulas for the optimal conductance values.

AB - We study the optimal design of a conductance network as a means for synchronizing a given set of oscillators. By considering the conductance that connects two oscillators as the measure of the amount of communication between them, we formulate an optimal control problem that addresses the trade-off between synchronization performance and communication. Additionally, we promote the sparsity of the network by penalizing the number of interconnection links. For identical oscillators, we establish convexity and show that the design problem can be formulated as a semidefinite program. For non-identical oscillators, that can be considered as perturbations around a central (average) oscillator, we show that it is meaningful to design an optimal conductance network by assuming that all oscillators are identical to the central oscillator. Finally, for special classes of oscillator networks we derive explicit formulas for the optimal conductance values.

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KW - optimization

KW - oscillator synchronization

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KW - sparse communication architecture

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On the optimal synchronization of oscillator networks via sparse interconnection graphs

Abstract

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Keywords

ASJC Scopus subject areas

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