Distributionally Robust System Level Synthesis With Output Feedback Affine Control Policy
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918156157583360 |
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| author | Li, Yun Shi, Jicheng Jones, Colin N. Yorke-Smith, Neil Keviczky, Tamas |
| author_facet | Li, Yun Shi, Jicheng Jones, Colin N. Yorke-Smith, Neil Keviczky, Tamas |
| contents | This paper studies the finite-horizon robust optimal control of constrained linear systems subject to model mismatch and additive stochastic disturbances. Utilizing the system level synthesis (SLS) parameterization, we propose a novel SLS design using an output-feedback affine control policy and extend it to a distributionally robust setting to improve system resilience by minimizing the cost function while ensuring constraint satisfaction against the worst-case uncertainty distribution. The scopes of model mismatch and stochastic disturbances are quantified using the 1-norm and a Wasserstein metric-based ambiguity set, respectively. For the closed-loop dynamics, we analyze the distributional shift between the predicted output-input response -- computed using nominal parameters and empirical disturbance samples -- and the actual closed-loop distribution, highlighting its dependence on model mismatch and SLS parameterization. Assuming convex and Lipschitz continuous cost functions and constraints, we derive a tractable reformulation of the distributionally robust SLS (DR-SLS) problem by leveraging tools from robust control and distributionally robust optimization (DRO). Numerical experiments validate the performance and robustness of the proposed approach. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_05466 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributionally Robust System Level Synthesis With Output Feedback Affine Control Policy Li, Yun Shi, Jicheng Jones, Colin N. Yorke-Smith, Neil Keviczky, Tamas Optimization and Control Systems and Control This paper studies the finite-horizon robust optimal control of constrained linear systems subject to model mismatch and additive stochastic disturbances. Utilizing the system level synthesis (SLS) parameterization, we propose a novel SLS design using an output-feedback affine control policy and extend it to a distributionally robust setting to improve system resilience by minimizing the cost function while ensuring constraint satisfaction against the worst-case uncertainty distribution. The scopes of model mismatch and stochastic disturbances are quantified using the 1-norm and a Wasserstein metric-based ambiguity set, respectively. For the closed-loop dynamics, we analyze the distributional shift between the predicted output-input response -- computed using nominal parameters and empirical disturbance samples -- and the actual closed-loop distribution, highlighting its dependence on model mismatch and SLS parameterization. Assuming convex and Lipschitz continuous cost functions and constraints, we derive a tractable reformulation of the distributionally robust SLS (DR-SLS) problem by leveraging tools from robust control and distributionally robust optimization (DRO). Numerical experiments validate the performance and robustness of the proposed approach. |
| title | Distributionally Robust System Level Synthesis With Output Feedback Affine Control Policy |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2508.05466 |