Regularization for Covariance Parameterization of Direct Data-Driven LQR Control
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| Format: | Preprint |
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2025
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| _version_ | 1866910859133976576 |
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| author | Zhao, Feiran Chiuso, Alessandro Dörfler, Florian |
| author_facet | Zhao, Feiran Chiuso, Alessandro Dörfler, Florian |
| contents | 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 closed-loop stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02985 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Regularization for Covariance Parameterization of Direct Data-Driven LQR Control Zhao, Feiran Chiuso, Alessandro Dörfler, Florian Systems and Control Optimization and Control 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 closed-loop stability. |
| title | Regularization for Covariance Parameterization of Direct Data-Driven LQR Control |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2503.02985 |