Regularization for Covariance Parameterization of Direct Data-Driven LQR Control
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Date
2025
Publication Type
Journal Article
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yes
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Abstract
As the benchmark of data-driven control methods, the linear quadratic regulator (LQR) problem has gained significant attention. A growing trend is direct LQR design, which finds the optimal LQR gain directly from raw data and bypassing system identification. To achieve this, our previous work develops a direct LQR formulation parameterized by sample covariance. In this letter, we propose a regularization method for the covariance-parameterized LQR. We show that the regularizer accounts for the uncertainty in both the steady-state covariance matrix corresponding to closed-loop stability, and the LQR cost function corresponding to averaged control performance. With a positive or negative coefficient, the regularizer can be interpreted as promoting either exploitation or exploration, which are well-known trade-offs in reinforcement learning. In simulations, we observe that our covariance-parameterized LQR with regularization can significantly outperform the certainty-equivalence LQR in terms of both the optimality gap and the robust stability.
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published
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Journal / series
Volume
9
Pages / Article No.
961 - 966
Publisher
IEEE
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Subject
Linear quadratic regulator; linear system; data-driven control; system identification
Organisational unit
09478 - Dörfler, Florian / Dörfler, Florian