Noise Sensitivity of the Semidefinite Programs for Direct Data-Driven LQR
Optimization and Control
2024-12-30 v1 Systems and Control
Systems and Control
Abstract
In this paper, 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 is 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.
Cite
@article{arxiv.2412.19705,
title = {Noise Sensitivity of the Semidefinite Programs for Direct Data-Driven LQR},
author = {Xiong Zeng and Laurent Bako and Necmiye Ozay},
journal= {arXiv preprint arXiv:2412.19705},
year = {2024}
}