A case study in ensemble optimal control for Bayesian input design
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909915447033856 |
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| author | Sacchelli, Ludovic Scagliotti, Alessandro |
| author_facet | Sacchelli, Ludovic Scagliotti, Alessandro |
| contents | We discuss the problem of input design for uncertainty reduction in a parameter estimation procedure. Assuming a linear continuous-time control system with noisy measurements, we formulate an objective of variance reduction in a Bayesian Gaussian setting as an optimal control problem and analyze it from a geometric control perspective. The resulting cost functional depends on the unknown parameter, we compare the optimal control approach with a non-standard alternative inspired by ensemble control, where the cost is averaged over the prior distribution after computation, rather than before. This requires the statement of a generalized Pontryagin's maximum principle adapted to Gaussian distributions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_16251 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A case study in ensemble optimal control for Bayesian input design Sacchelli, Ludovic Scagliotti, Alessandro Optimization and Control We discuss the problem of input design for uncertainty reduction in a parameter estimation procedure. Assuming a linear continuous-time control system with noisy measurements, we formulate an objective of variance reduction in a Bayesian Gaussian setting as an optimal control problem and analyze it from a geometric control perspective. The resulting cost functional depends on the unknown parameter, we compare the optimal control approach with a non-standard alternative inspired by ensemble control, where the cost is averaged over the prior distribution after computation, rather than before. This requires the statement of a generalized Pontryagin's maximum principle adapted to Gaussian distributions. |
| title | A case study in ensemble optimal control for Bayesian input design |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2511.16251 |