Optimal experimental design and some related control problems

TL;DR

This paper explores the connection between optimal experimental design and control, highlighting their mathematical foundations and applications in parameter estimation, adaptive control, and statistical learning.

Contribution

It provides a comprehensive overview of the mathematical basis of optimal experimental design and its role in control and estimation, including both parametric and nonparametric models.

Findings

Optimal inputs improve parameter estimation accuracy.

Perturbations in adaptive control enhance system robustness.

Experimental design influences estimator asymptotic properties.

Abstract

This paper traces the strong relations between experimental design and control, such as the use of optimal inputs to obtain precise parameter estimation in dynamical systems and the introduction of suitably designed perturbations in adaptive control. The mathematical background of optimal experimental design is briefly presented, and the role of experimental design in the asymptotic properties of estimators is emphasized. Although most of the paper concerns parametric models, some results are also presented for statistical learning and prediction with nonparametric models.