Optimality of Linear Policies for Distributionally Robust Linear Quadratic Gaussian Regulator with Stationary Distributions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909587320340480 |
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| author | Lanzetti, Nicolas Terpin, Antonio Dörfler, Florian |
| author_facet | Lanzetti, Nicolas Terpin, Antonio Dörfler, Florian |
| contents | We prove that output-feedback linear policies remain optimal for solving the Linear Quadratic Gaussian regulation problem in the face of worst-case process and measurement noise distributions when these are independent, stationary, and known to be within a radius (in the Wasserstein sense) to some reference zero-mean Gaussian noise distributions. Additionally, we establish the existence of a Nash equilibrium of the zero-sum game between a control engineer, who minimizes control cost, and a fictitious adversary, who chooses the noise distributions that maximize this cost. For general (possibly non-Gaussian) reference noise distributions, we establish a quasi closed-form solution for the worst-case distributions against linear policies. Our work provides a less conservative alternative compared to recent work in distributionally robust control. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22826 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Optimality of Linear Policies for Distributionally Robust Linear Quadratic Gaussian Regulator with Stationary Distributions Lanzetti, Nicolas Terpin, Antonio Dörfler, Florian Optimization and Control We prove that output-feedback linear policies remain optimal for solving the Linear Quadratic Gaussian regulation problem in the face of worst-case process and measurement noise distributions when these are independent, stationary, and known to be within a radius (in the Wasserstein sense) to some reference zero-mean Gaussian noise distributions. Additionally, we establish the existence of a Nash equilibrium of the zero-sum game between a control engineer, who minimizes control cost, and a fictitious adversary, who chooses the noise distributions that maximize this cost. For general (possibly non-Gaussian) reference noise distributions, we establish a quasi closed-form solution for the worst-case distributions against linear policies. Our work provides a less conservative alternative compared to recent work in distributionally robust control. |
| title | Optimality of Linear Policies for Distributionally Robust Linear Quadratic Gaussian Regulator with Stationary Distributions |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2410.22826 |