基于相位-幅度坐标的自适应大输入振荡定时和夹带的最优控制
Optimal Control of Oscillation Timing and Entrainment Using Large Magnitude Inputs: An Adaptive Phase-Amplitude-Coordinate-Based Approach
摘要：
鉴于许多振荡动力系统的高维性和潜在的复杂性，相位减少通常是控制应用中的必要的第一步，其中振荡定时和夹带是感兴趣的。不幸的是，大多数相位缩减框架对允许输入的幅度进行了严格的限制，从而在许多情况下限制了所得到的相位降阶模型的实际效用。在这项工作中，动机的搜索控制策略，以加快恢复时差引起的快速旅行通过多个时区，最近开发的自适应相位振幅降低的功效被认为是操纵振荡定时在存在的大幅度夹带刺激。自适应相位-幅度简化方程允许数值上易于处理的最优控制配方和相关的最优刺激显着优于那些从先前提出的最优控制配方。此外，数据驱动的技术，以确定必要的条款的自适应相位振幅减少提出和验证使用一个模型描述了一个大人口的耦合极限环振荡器的总振荡。这种数据驱动的模型简化算法在底层模型方程不可靠或不可用的情况下是必不可少的。
英文摘要：
Given the high dimensionality and underlying complexity of many oscillatory dynamical systems, phase reduction is often an imperative first step in control applications where oscillation timing and entrainment are of interest. Unfortunately, most phase reduction frameworks place restrictive limitations on the magnitude of allowable inputs, limiting the practical utility of the resulting phase reduced models in many situations. In this work, motivated by the search for control strategies to hasten recovery from jet-lag caused by rapid travel through multiple time zones, the efficacy of the recently developed adaptive phase-amplitude reduction is considered for manipulating oscillation timing in the presence of a large magnitude entraining stimulus. The adaptive phase-amplitude reduced equations allow for a numerically tractable optimal control formulation and the associated optimal stimuli significantly outperform those resulting from from previously proposed optimal control formulations. Additionally, a data-driven technique to identify the necessary terms of the adaptive phase-amplitude reduction is proposed and validated using a model describing the aggregate oscillations of a large population of coupled limit cycle oscillators. Such data-driven model reduction algorithms are essential in situations where the underlying model equations are either unreliable or unavailable.
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