This paper addresses a shortcoming in adaptive control, that the property of a regressor being persistently exciting (PE) is not well-behaved. One can construct regressors that upend the commonsense notion that excitation should not be created out of nothing. To amend the situation, a notion of regularity of regressors is needed. We are naturally led to a broad class of regular regressors that enjoy the property that their excitation is always confined to a subspace, a foundational result called the PE decomposition. A geometric characterization of regressor excitation opens up new avenues for adaptive control, as we demonstrate by formulating a number of new adaptive control problems.
Cite
@article{arxiv.2507.06446,
title = {On Regular Regressors in Adaptive Control},
author = {Erick Mejia Uzeda and Mireille E. Broucke},
journal= {arXiv preprint arXiv:2507.06446},
year = {2025}
}