Singhal Bharat, Kiss István Z, Li Jr-Shin
Electrical and Systems Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA.
Department of Chemistry, Saint Louis University, St. Louis, Missouri 63103, USA.
SIAM J Appl Dyn Syst. 2023;22(3):2180-2205. doi: 10.1137/22m1521201.
We develop a framework to design optimal entrainment signals that entrain an ensemble of heterogeneous nonlinear oscillators, described by phase models, at desired phases. We explicitly take into account heterogeneity in both oscillation frequency and the type of oscillators characterized by different Phase Response Curves. The central idea is to leverage the Fourier series representation of periodic functions to decode a phase-selective entrainment task into a quadratic program. We demonstrate our approach using a variety of phase models, where we entrain the oscillators into distinct phase patterns. Also, we show how the generalizability gained from our formulation enables us to meet a wide range of design objectives and constraints, such as minimum-power, fast entrainment, and charge-balanced controls.
我们开发了一个框架，用于设计最优的同步信号，该信号能使由相位模型描述的一组异构非线性振荡器在期望的相位上实现同步。我们明确考虑了振荡频率的异质性以及由不同相位响应曲线表征的振荡器类型的异质性。核心思想是利用周期函数的傅里叶级数表示，将相位选择性同步任务解码为一个二次规划问题。我们使用各种相位模型来演示我们的方法，在这些模型中，我们将振荡器同步到不同的相位模式。此外，我们展示了从我们的公式中获得的通用性如何使我们能够满足广泛的设计目标和约束条件，例如最小功率、快速同步和电荷平衡控制。
