Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reduction
Non-asymptotic Closed-Loop System Identification using Autoregressive Processes and Hankel Model Reduction
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DOI：
10.1109/cdc42340.2020.9304468
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发表时间：
2019-09
期刊：
影响因子：
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通讯作者：
Bruce Lee;Andrew G. Lamperski
中科院分区：
文献类型：
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作者：
Bruce Lee;Andrew G. Lamperski
系统识别的主要挑战之一是确定需要多少数据才能充分适应模型。系统辨识方法性能的非渐近表征提供了这方面的知识。这种表征可用于执行开环识别的几种算法。然而，通常情况下，数据是在闭环中收集的。将开环辨识方法应用于闭环数据会导致估计偏差。消除这些偏差的一种方法是首先拟合一个长期自回归模型，然后进行模型约简。这类算法的渐近行为具有很好的特征，但其非渐近行为却没有很好的特征。这项工作提供了这些算法的一个特定变体的非渐近表征。更具体地说，我们提供了所产生模型泛化误差的非渐近上界，以及所产生模型与有限水平卡尔曼滤波器之间差异的高概率界。
One of the primary challenges of system identification is determining how much data is necessary to adequately fit a model. Non-asymptotic characterizations of the performance of system identification methods provide this knowledge. Such characterizations are available for several algorithms performing open-loop identification. Often times, however, data is collected in closed-loop. Application of open-loop identification methods to closed-loop data can result in biased estimates. One method to eliminate these biases involves first fitting a long-horizon autoregressive model and then performing model reduction. The asymptotic behavior of such algorithms is well characterized, but the non-asymptotic behavior is not. This work provides a non-asymptotic characterization of one particular variant of these algorithms. More specifically, we provide non-asymptotic upper bounds on the generalization error of the produced model, as well as high probability bounds on the difference between the produced model and the finite horizon Kalman Filter.