Year: 2025
Type: article
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 paper, 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.
Source: IEEE Control Systems Letters
Institutions: ETH Zurich, University of Padua
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4411203181