Conformal Prediction for Distribution-free Optimal Control of Linear Stochastic Systems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916512401457152 |
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| author | Vlahakis, Eleftherios E. Lindemann, Lars Sopasakis, Pantelis Dimarogonas, Dimos V. |
| author_facet | Vlahakis, Eleftherios E. Lindemann, Lars Sopasakis, Pantelis Dimarogonas, Dimos V. |
| contents | We address an optimal control problem for linear stochastic systems with unknown noise distributions and joint chance constraints using conformal prediction. Our approach involves designing a feedback controller to maintain an error system within a prediction region (PR). We define PRs as sublevel sets of a nonconformity score over error trajectories, enabling the handling of joint chance constraints. We propose two methods to design feedback control and PRs: one through direct optimization over error trajectory samples, and the other indirectly using the $S$-procedure with a disturbance ellipsoid obtained from data. By tightening constraints with PRs, we solve a relaxed problem to synthesize a feedback policy. Our method ensures reliable probabilistic guarantees based on marginal coverage, independent of data size. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_19132 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Conformal Prediction for Distribution-free Optimal Control of Linear Stochastic Systems Vlahakis, Eleftherios E. Lindemann, Lars Sopasakis, Pantelis Dimarogonas, Dimos V. Systems and Control We address an optimal control problem for linear stochastic systems with unknown noise distributions and joint chance constraints using conformal prediction. Our approach involves designing a feedback controller to maintain an error system within a prediction region (PR). We define PRs as sublevel sets of a nonconformity score over error trajectories, enabling the handling of joint chance constraints. We propose two methods to design feedback control and PRs: one through direct optimization over error trajectory samples, and the other indirectly using the $S$-procedure with a disturbance ellipsoid obtained from data. By tightening constraints with PRs, we solve a relaxed problem to synthesize a feedback policy. Our method ensures reliable probabilistic guarantees based on marginal coverage, independent of data size. |
| title | Conformal Prediction for Distribution-free Optimal Control of Linear Stochastic Systems |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2411.19132 |