论文标题
使用多个轨迹对线性动力学系统的非反应鉴定
Non-asymptotic Identification of Linear Dynamical Systems Using Multiple Trajectories
论文作者
论文摘要
本文考虑了使用输入/输出数据的线性时间不变（LTI）系统标识的问题。最近的工作为使用单个轨迹的部分观察到的LTI系统识别提供了非肿瘤结果，但仅适用于稳定系统。我们为学习Markov参数提供有限的时间分析，该参数基于普通最小二乘（OLS）的估计器，使用多个轨迹涵盖稳定和不稳定的系统。对于不稳定的系统，我们的结果表明，在存在过程噪声的情况下，马尔可夫参数更难估计。没有过程噪声，我们对估计误差的上限独立于系统动力学的光谱半径，概率很高。这两个功能与完全观察到的LTI系统不同，该系统最近的工作表明，光谱半径较大的不稳定系统更容易估计。广泛的数值实验证明了我们的OLS估计量的性能。
This paper considers the problem of linear time-invariant (LTI) system identification using input/output data. Recent work has provided non-asymptotic results on partially observed LTI system identification using a single trajectory but is only suitable for stable systems. We provide finite-time analysis for learning Markov parameters based on the ordinary least-squares (OLS) estimator using multiple trajectories, which covers both stable and unstable systems. For unstable systems, our results suggest that the Markov parameters are harder to estimate in the presence of process noise. Without process noise, our upper bound on the estimation error is independent of the spectral radius of system dynamics with high probability. These two features are different from fully observed LTI systems for which recent work has shown that unstable systems with a bigger spectral radius are easier to estimate. Extensive numerical experiments demonstrate the performance of our OLS estimator.
