基于算子的数据嵌入：从含噪数据出发的连续时间系统数据驱动控制
Operator-based data embedding for data-driven control of continuous-time systems from noisy data
浏览论文内容
中文总结 AI 辅助
该研究针对含噪数据提出基于算子的数据嵌入方法，刻画与数据一致的系统集合，推导数据可辨识性条件并构造反馈增益，得到连续时间信号重构误差上界，用于连续时间系统的数据驱动控制。
中文摘要 AI 辅助
我们提出一种用于设计状态反馈增益的数据驱动方法，该方法可实现连续时间系统的镇定、$H_2$控制与$H_\infty$控制。假设状态输入数据受过程噪声、测量噪声及输入干扰污染，我们首先采用基于算子的数据嵌入刻画与含噪数据一致的所有系统集合，该刻画在某类噪声下给出数据可辨识性的充要条件，这些条件被表述为线性矩阵不等式，反馈增益由其解构造。为实现从含噪采样数据直接设计连续时间系统控制器，我们还得到了连续时间信号重构误差的上界。
英文摘要
We propose a data-driven method for designing state-feedback gains that achieve stabilization, $H_2$-control, and $H_\infty$-control for continuous-time systems. The state-input data are assumed to be corrupted by process noise, measurement noise, and input disturbances. We first characterize the set of all systems consistent with the noisy data using operator-based data embedding. This characterization yields necessary and sufficient conditions for data informativity under a certain class of noise. These conditions are formulated as linear matrix inequalities, and the feedback gains are constructed from their solutions. To enable direct controller design from noisy sampled data for continuous-time systems, we also obtain an upper bound on the reconstruction error of continuous-time signals.
