论文标题
来自多个轨迹数据的乘法噪声下的线性系统识别
Linear System Identification Under Multiplicative Noise from Multiple Trajectory Data
论文作者
论文摘要
乘法噪声模型的研究在控制理论中具有悠久的历史，但在具有基于学习的控制的复杂网络系统和系统的背景下重新出现。我们考虑来自多个状态输入轨迹数据的乘法噪声的线性系统识别。我们提出探索性输入信号以及最小二乘算法，以同时估计名义系统参数和乘法噪声协方差矩阵。通过分析系统的第一和第二矩动力学，证明了最小二乘估计器的协方差结构和渐近一致性的可识别性。结果通过数值模拟说明。
The study of multiplicative noise models has a long history in control theory but is re-emerging in the context of complex networked systems and systems with learning-based control. We consider linear system identification with multiplicative noise from multiple state-input trajectory data. We propose exploratory input signals along with a least-squares algorithm to simultaneously estimate nominal system parameters and multiplicative noise covariance matrices. Identifiability of the covariance structure and asymptotic consistency of the least-squares estimator are demonstrated by analyzing first and second moment dynamics of the system. The results are illustrated by numerical simulations.
