Noise Sensitivity of the Semidefinite Programs for Direct Data-Driven LQR
成果类型：
Article
署名作者：
Zeng, Xiong; Bako, Laurent; Ozay, Necmiye
署名单位：
University of Michigan System; University of Michigan; Inria; Universite de Lille; Centre National de la Recherche Scientifique (CNRS); Centrale Lille; CNRS - Institute for Information Sciences & Technologies (INS2I)
刊物名称：
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
ISSN/ISSBN：
0018-9286
DOI：
10.1109/TAC.2025.3641444
发表日期：
2026
关键词：
摘要：
In this article, we study the noise sensitivity of the semidefinite program (SDP) proposed for direct data-driven infinite-horizon linear quadratic regulator (LQR) problem for discrete-time linear time-invariant systems. While this SDP is shown to find the true LQR controller in the noise-free setting, we show that it leads to a trivial solution with zero gain matrices when data are corrupted by noise, even when the noise is arbitrarily small. We then study a variant of the SDP that includes a robustness-promoting regularization term, and prove that regularization does not fully eliminate the sensitivity issue. In particular, the solution of the regularized SDP converges in probability also to a trivial solution.