2025/11/20 by Ludovic Sacchelli, Sacchelli, Ludovic, Alessandro Scagliotti +1
Engineering · Computer Science · Decision Sciences · #Control Systems and Identification #Gaussian Processes and Bayesian Inference #Probabilistic and Robust Engineering Design
paper · pdf · doi:10.48550/arxiv.2511.16251
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.