集合卡尔曼滤波与模型预测控制在混沌系统中的结合
Ensemble Kalman filter meets model predictive control in chaotic systems
AI总结：
本文揭示地球科学数据同化与模型预测控制在最小化二次代价函数上的相似性，提出基于集合卡尔曼滤波的时空混沌系统控制方法，并通过Lorenz 63模型验证其能以较小扰动将系统约束在蝴蝶吸引子单侧翼上。
摘要：
尽管数据同化起源于控制理论，但地球科学中的现代数据同化方法与模型预测控制之间的关系尚未得到广泛探索。在本文中，我讨论指出，地球科学中的现代数据同化方法与模型预测控制本质上是在最小化相似的二次代价函数。受这一相似性的启发，我提出了一种新的基于集合卡尔曼滤波（EnKF）的方法，用于控制时空混沌系统，该方法可应用于高维和非线性的地球系统。在该方法中，作为控制目标的参考向量通过集合卡尔曼平滑器被同化到状态空间中，作为伪观测，从而获得需要施加到系统中的适当扰动。文中给出了一个使用Lorenz 63模型的概念验证实验。系统被约束在蝴蝶吸引子的一个翼上，而不会翻转到另一侧，所使用的控制扰动合理地小，并与先前工作中的扰动幅度相当。
英文摘要：
Although data assimilation originates from control theory, the relationship between modern data assimilation methods in geoscience and model predictive control has not been extensively explored. In the present paper, I discuss that the modern data assimilation methods in geoscience and model predictive control essentially minimize the similar quadratic cost functions. Inspired by this similarity, I propose a new ensemble Kalman filter (EnKF)-based method for controlling spatio-temporally chaotic systems, which can be applied to high-dimensional and nonlinear Earth systems. In this method, the reference vector, which serves as the control target, is assimilated into the state space as a pseudo-observation by ensemble Kalman smoother to obtain the appropriate perturbation to be added to a system. A proof-of-concept experiment using the Lorenz 63 model is presented. The system is constrained in one wing of the butterfly attractor without tipping to the other side by reasonably small control perturbations which are comparable with previous works.
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