A case study in ensemble optimal control for Bayesian input design

TL;DR

This paper explores optimal control strategies for Bayesian input design in linear systems, comparing traditional and ensemble-inspired approaches to reduce parameter estimation uncertainty.

Contribution

It introduces a novel ensemble control-inspired method for Bayesian input design and derives a generalized Pontryagin's maximum principle for Gaussian distributions.

Findings

Ensemble control approach averages the cost over the prior after computation.

Derived a generalized Pontryagin's maximum principle for Gaussian distributions.

Compared traditional and ensemble control methods in 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.