论文标题
从异质数据中学习最小能量控制
Learning Minimum-Energy Controls from Heterogeneous Data
论文作者
论文摘要
在本文中，我们研究了从异质数据学习线性系统的最小能量控制的问题。具体而言，我们考虑使用具有不同时间范围和任意初始条件的实验收集的输入，初始和最终状态测量的数据集。在这种情况下，我们首先根据可用数据建立系统的输入和采样状态轨迹的一般表示。然后，我们利用这种基于数据的表示形式来得出最小能量控制的封闭形式数据驱动的表达式，以范围内的多种控制范围。此外，我们表征重建最小能源输入所需的最小数据数量，并讨论表达式的数值属性。最后，我们研究了噪声对数据驱动公式的影响，并且在具有已知二阶统计的噪声的情况下，我们提供了校正的表达式，这些表达式渐近地融合到真正的最佳控制输入。
In this paper we study the problem of learning minimum-energy controls for linear systems from heterogeneous data. Specifically, we consider datasets comprising input, initial and final state measurements collected using experiments with different time horizons and arbitrary initial conditions. In this setting, we first establish a general representation of input and sampled state trajectories of the system based on the available data. Then, we leverage this data-based representation to derive closed-form data-driven expressions of minimum-energy controls for a wide range of control horizons. Further, we characterize the minimum number of data required to reconstruct the minimum-energy inputs, and discuss the numerical properties of our expressions. Finally, we investigate the effect of noise on our data-driven formulas, and, in the case of noise with known second-order statistics, we provide corrected expressions that converge asymptotically to the true optimal control inputs.
