TY - GEN

T1 - On the optimal synchronization of oscillator networks via sparse interconnection graphs

AU - Fardad, Makan

AU - Lin, Fu

AU - Jovanovic, Mihailo R.

PY - 2012/11/26

Y1 - 2012/11/26

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.

KW - Convex relaxation

KW - optimization

KW - oscillator synchronization

KW - reweighted l minimization

KW - semidefinite programming

KW - sparse communication architecture

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M3 - Conference contribution

AN - SCOPUS:84869455235

SN - 9781457710957

T3 - Proceedings of the American Control Conference

SP - 4777

EP - 4782

BT - 2012 American Control Conference, ACC 2012

T2 - 2012 American Control Conference, ACC 2012

Y2 - 27 June 2012 through 29 June 2012

ER -