On the Regret of Recursive Methods for Discrete-Time Adaptive Control with Matched Uncertainty
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866915198921605120 |
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| author | Karapetyan, Aren Balta, Efe C. Tsiamis, Anastasios Iannelli, Andrea Lygeros, John |
| author_facet | Karapetyan, Aren Balta, Efe C. Tsiamis, Anastasios Iannelli, Andrea Lygeros, John |
| contents | Continuous-time adaptive controllers for systems with a matched uncertainty often comprise an online parameter estimator and a corresponding parameterized controller to cancel the uncertainty. However, such methods are often impossible to implement directly, as they depend on an unobserved estimation error. We consider the equivalent discrete-time setting with a causal information structure, and propose a novel, online proximal point method-based adaptive controller, that under a sufficient excitation (SE) condition is asymptotically stable and achieves finite regret, scaling only with the time required to fulfill the SE. We show the same also for the widely-used recursive least squares with exponential forgetting controller under a stronger persistence of excitation condition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_02023 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Regret of Recursive Methods for Discrete-Time Adaptive Control with Matched Uncertainty Karapetyan, Aren Balta, Efe C. Tsiamis, Anastasios Iannelli, Andrea Lygeros, John Systems and Control Continuous-time adaptive controllers for systems with a matched uncertainty often comprise an online parameter estimator and a corresponding parameterized controller to cancel the uncertainty. However, such methods are often impossible to implement directly, as they depend on an unobserved estimation error. We consider the equivalent discrete-time setting with a causal information structure, and propose a novel, online proximal point method-based adaptive controller, that under a sufficient excitation (SE) condition is asymptotically stable and achieves finite regret, scaling only with the time required to fulfill the SE. We show the same also for the widely-used recursive least squares with exponential forgetting controller under a stronger persistence of excitation condition. |
| title | On the Regret of Recursive Methods for Discrete-Time Adaptive Control with Matched Uncertainty |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2404.02023 |