不依赖稳定性假设，给出线性系统识别的样本复杂度上下界。
Sample Complexity Bounds for Linear System Identification from a Finite Set
- 用最大似然估计识别LTI系统，避免传统稳定性限制。
- 推导出样本复杂度上界，与真实系统轨迹数据量相关。
- 信息论工具支持下界分析，适用于任意估计方法。
本文从有限样本视角研究基于轨迹数据从有限候选系统集中识别LTI系统的问题。采用最大似然估计器识别真实系统，并给出了其样本复杂度的上界。关键在于该上界不依赖于可能具有限制性的稳定性假设。此外，利用信息论工具，给出了独立于具体估计器的样本复杂度下界。所推导的上下界通过解析与数值方式进行了分析。
原文摘要 · Abstract (English)
This paper considers a finite sample perspective on the problem of identifying an LTI system from a finite set of possible systems using trajectory data. To this end, we use the maximum likelihood estimator to identify the true system and provide an upper bound for its sample complexity. Crucially, the derived bound does not rely on a potentially restrictive stability assumption. Additionally, we leverage tools from information theory to provide a lower bound to the sample complexity that holds independently of the used estimator. The derived sample complexity bounds are analyzed analytically and numerically.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。