A case study in ensemble optimal control for Bayesian input design

Ludovic Sacchelli; Alessandro Scagliotti

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arXiv · 2511.16251

A case study in ensemble optimal control for Bayesian input design

Ludovic Sacchelli·Alessandro Scagliotti

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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.

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Ludovic Sacchelli, Alessandro Scagliotti. 2025-11-20. A case study in ensemble optimal control for Bayesian input design. https://arxiv.org/abs/2511.16251

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