基于非稳态频域数据的分布鲁棒频率响应估计
Distributionally Robust Frequency Response Estimation Using Non-Steady-State Frequency-Domain Data
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中文总结 AI 辅助
本文提出一种分布鲁棒优化框架，利用非稳态频域数据估计线性时不变系统的频率响应函数，通过最小化凸上界实现鲁棒估计，并证明误差受DRO最优值约束，数值实验显示在重尾噪声下性能更优。
中文摘要 AI 辅助
本文针对未知线性时不变系统，利用重复的非稳态输入输出含噪测量数据，开发了一种用于辨识频率响应函数（FRF）的分布鲁棒优化（DRO）框架。基于近期Willems基本引理的频域扩展，我们将FRF估计表述为一个DRO问题，其中鲁棒性是针对生成含噪数据的未知概率分布而言的。所提出的估计器通过最小化DRO成本的凸上界来计算FRF估计，并允许对Wasserstein度量进行频率相关的校准；该可处理的凸上界由一个经验拟合项和一个正则化项组成，后者惩罚对谱扰动的最大的加权灵敏度。在适当的假设下，我们证明了FRF估计误差以DRO问题的最优值为上界。通过一个简单的数值研究验证了该方法，结果表明在严重重尾噪声下性能有所提升。
英文摘要
This paper develops a distributionally robust optimization (DRO) framework for identifying the frequency response function (FRF) of an unknown linear time-invariant system from repeated noisy non-steady-state input-output measurements. Building on a recent frequency-domain extension of Willems' fundamental lemma, we formulate FRF estimation as a DRO problem, wherein robustness is desired with respect to the unknown probability distribution generating the noisy data. The proposed estimator computes FRF estimates by minimizing a convex upper bound on the DRO cost and allows for frequency-dependent calibration of the Wasserstein metric; the tractable upper bound consists of an empirical fit and a regularizer that penalizes the largest weighted sensitivity to spectral perturbations. Under suitable assumptions, we prove that the FRF estimation error is upper bounded by the optimal value of the DRO problem. The method is validated via a simple numerical study, which demonstrates improved performance under severely heavy-tailed noise.
发表机构
- University of Toronto（多伦多大学）
- University of British Columbia（不列颠哥伦比亚大学）
机构由 AI 辅助整理，请以论文原文为准。
