Department of Physics, The Hong Kong University of Science and Technology, Hong Kong.
Phys Rev E. 2017 Jan;95(1-1):012207. doi: 10.1103/PhysRevE.95.012207. Epub 2017 Jan 13.
Maintaining the stability of synchronization state is crucial for the functioning of many natural and artificial systems. In this study, we develop methods to optimize the synchronization stability of the Kuramoto model by minimizing the dominant Lyapunov exponent. Using the recently proposed cut-set space approximation of the steady states, we greatly simplify the objective function, and further derive its gradient and Hessian with respect to natural frequencies, which leads to an efficient algorithm with the quasi-Newton's method. The optimized systems are demonstrated to achieve better synchronization stability for the Kuramoto model with or without inertia in certain regimes. Hence our method is applicable in improving the stability of power grids. It is also viable to adjust the coupling strength of each link to improve the stability of the system. Various operational constraints can also be easily integrated into our scope by employing the interior point method in convex optimization. The properties of the optimized networks are also discussed.
维持同步状态的稳定性对于许多自然和人工系统的运行至关重要。在本研究中，我们通过最小化主导李雅普诺夫指数来开发优化 Kuramoto 模型同步稳定性的方法。利用最近提出的稳态的割集空间逼近，我们极大地简化了目标函数，并进一步推导出其关于自然频率的梯度和 Hessian，这导致了一种具有拟牛顿法的高效算法。优化后的系统在惯性存在或不存在的某些情况下，证明了它们在 Kuramoto 模型中的同步稳定性更好。因此，我们的方法适用于提高电网的稳定性。调整每个链路的耦合强度也可以提高系统的稳定性。通过在凸优化中使用内点法，各种操作约束也可以很容易地纳入我们的范围。还讨论了优化网络的特性。
