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arXiv · 2507.06446

On Regular Regressors in Adaptive Control

Erick Mejia Uzeda·Mireille E. Broucke
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Abstract

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.

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Erick Mejia Uzeda, Mireille E. Broucke. 2025-07-08. On Regular Regressors in Adaptive Control. https://doi.org/10.1109/lcsys.2025.3573124

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