A case study in ensemble optimal control for Bayesian input design
Optimization and Control
2025-11-21 v1
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.
Cite
@article{arxiv.2511.16251,
title = {A case study in ensemble optimal control for Bayesian input design},
author = {Ludovic Sacchelli and Alessandro Scagliotti},
journal= {arXiv preprint arXiv:2511.16251},
year = {2025}
}