论文标题
耦合振荡器同步的随机方法
A stochastic approach to the synchronization of coupled oscillators
论文作者
论文摘要
本文讨论了与库拉莫托模型相关的最佳控制问题，该模型描述了耦合振荡器网络的动力学行为。我们的目的是设计合适的控制功能，使我们能够将系统引导到同步配置，其中所有振荡器在同一阶段对齐。通过最小化与所考虑的动力学相关的给定成本功能来计算此控制。为了最小化，我们提出了一种基于标准梯度下降（GD）方法与最近开发的随机批次方法（RBM）的组合的新方法，以有效地对集体动力学进行数值近似。我们的模拟表明，RBM的使用改善了GD算法的性能，从而降低了最小化过程的计算复杂性，并允许进行更有效的控制计算。
This paper deals with an optimal control problem associated to the Kuramoto model describing the dynamical behavior of a network of coupled oscillators. Our aim is to design a suitable control function allowing us to steer the system to a synchronized configuration in which all the oscillators are aligned on the same phase. This control is computed via the minimization of a given cost functional associated with the dynamics considered. For this minimization, we propose a novel approach based on the combination of a standard Gradient Descent (GD) methodology with the recently-developed Random Batch Method (RBM) for the efficient numerical approximation of collective dynamics. Our simulations show that the employment of RBM improves the performances of the GD algorithm, reducing the computational complexity of the minimization process and allowing for a more efficient control calculation.
