Design of optimal sparse interconnection graphs for synchronization of oscillator networks

TL;DR

This paper presents a convex optimization framework for designing sparse interconnection graphs that optimize synchronization performance in oscillator networks, balancing coupling strength and network sparsity.

Contribution

It introduces a convex semidefinite programming approach for optimal sparse interconnection design, including explicit solutions for certain network classes.

Findings

Convex formulation of the sparse interconnection design problem.

Explicit solutions for specific oscillator network classes.

Trade-off analysis between synchronization performance and network sparsity.

Abstract

We study the optimal design of a conductance network as a means for synchronizing a given set of oscillators. Synchronization is achieved when all oscillator voltages reach consensus, and performance is quantified by the mean-square deviation from the consensus value. We formulate optimization problems that address the trade-off between synchronization performance and the number and strength of oscillator couplings. We promote the sparsity of the coupling network by penalizing the number of interconnection links. For identical oscillators, we establish convexity of the optimization problem and demonstrate that the design problem can be formulated as a semidefinite program. Finally, for special classes of oscillator networks we derive explicit analytical expressions for the optimal conductance values.