Online Nonstochastic Control with Convex Safety Constraints
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866913670916734976 |
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| author | Jiang, Nanfei Hutchinson, Spencer Alizadeh, Mahnoosh |
| author_facet | Jiang, Nanfei Hutchinson, Spencer Alizadeh, Mahnoosh |
| contents | This paper considers the online nonstochastic control problem of a linear time-invariant system under convex state and input constraints that need to be satisfied at all times. We propose an algorithm called Online Gradient Descent with Buffer Zone for Convex Constraints (OGD-BZC), designed to handle scenarios where the system operates within general convex safety constraints. We demonstrate that OGD-BZC, with appropriate parameter selection, satisfies all the safety constraints under bounded adversarial disturbances. Additionally, to evaluate the performance of OGD-BZC, we define the regret with respect to the best safe linear policy in hindsight. We prove that OGD-BZC achieves $\tilde{O} (\sqrt{T})$ regret given proper parameter choices. Our numerical results highlight the efficacy and robustness of the proposed algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_18039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Online Nonstochastic Control with Convex Safety Constraints Jiang, Nanfei Hutchinson, Spencer Alizadeh, Mahnoosh Optimization and Control Systems and Control This paper considers the online nonstochastic control problem of a linear time-invariant system under convex state and input constraints that need to be satisfied at all times. We propose an algorithm called Online Gradient Descent with Buffer Zone for Convex Constraints (OGD-BZC), designed to handle scenarios where the system operates within general convex safety constraints. We demonstrate that OGD-BZC, with appropriate parameter selection, satisfies all the safety constraints under bounded adversarial disturbances. Additionally, to evaluate the performance of OGD-BZC, we define the regret with respect to the best safe linear policy in hindsight. We prove that OGD-BZC achieves $\tilde{O} (\sqrt{T})$ regret given proper parameter choices. Our numerical results highlight the efficacy and robustness of the proposed algorithm. |
| title | Online Nonstochastic Control with Convex Safety Constraints |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2501.18039 |