有限样本下基于误设有限模型集的LTI系统辨识
Finite-Sample LTI System Identification from a Misspecified Finite Model Set
Nicolas Chatzikiriakos, Andrea Iannelli
AI 速览：研究真实LTI系统不在有限假设类内时，有限样本辨识的估计目标、失败概率下界及指数加权算法的鲁棒性上界。
We consider the problem of finite-sample identification of an unknown LTI system from a finite hypothesis class. In contrast to existing results that assume the hypothesis class contains the true system, we consider the misspecified setting, where the true system does not belong to the hypothesis class. We first characterize the resulting estimation target and its dependence on the data-generation scheme. We then establish a finite-sample lower bound on the failure probability that any identification algorithm must incur. Finally, we analyze the robustness of an existing exponential weighting-based identification algorithm to the misspecification and derive a finite-sample upper bound on its failure probability. Our results illustrate when using a misspecified finite hypothesis class can provide an advantage over identification without prior knowledge of the candidate systems.