振荡器网络同步的最优稀疏互连图设计
Design of optimal sparse interconnection graphs for synchronization of oscillator networks
AI总结：
研究通过优化电导网络设计实现振荡器同步，提出权衡同步性能与耦合稀疏性的凸优化问题，并给出半定规划形式及特殊情形下的解析解。
摘要：
我们研究电导网络的最优设计，作为同步一组给定振荡器的手段。当所有振荡器电压达到一致时实现同步，性能通过相对于一致值的均方偏差来量化。我们制定了优化问题，以解决同步性能与振荡器耦合数量和强度之间的权衡。通过惩罚互连链路的数量来促进耦合网络的稀疏性。对于相同的振荡器，我们建立了优化问题的凸性，并证明该设计问题可以表述为半定规划。最后，对于特殊类别的振荡器网络，我们推导出最优电导值的显式解析表达式。
英文摘要：
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.
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