{"ID":2839029,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.16251","arxiv_id":"2511.16251","title":"A case study in ensemble optimal control for Bayesian input design","abstract":"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.","short_abstract":"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 con...","url_abs":"https://arxiv.org/abs/2511.16251","url_pdf":"https://arxiv.org/pdf/2511.16251v1","authors":"[\"Ludovic Sacchelli\",\"Alessandro Scagliotti\"]","published":"2025-11-20T11:28:38Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}