Lukas Markolf and Olaf Stursberg: Guaranteed constraint satisfaction and asymptotic closed-loop stability in learning of control laws.
Int. Journal of Dynamics and Control, Vol. 13, No. 271, 2025.
Abstract
This paper considers the problem of selecting control laws with guaranteed closed-loop properties from a set of functions represented by deep neural networks or other parametric approximators. The task is addressed for time-varying linear systems with multiplicative uncertainties and polytopic state and input constraints. Based on ellipsoidal control-invariant and -contractive sets, which can be computed offline for this system class, the paper shows how safe and stabilizing sets of control laws can be defined and computed. In particular, a closed-form transformation of the control laws is proposed as a tailored output layer, ensuring the satisfaction of the constraints and asymptotic stability of the origin for all possible parameterizations.
BibTex
@article{markolf2025,
abstract = {This paper considers the problem of selecting control laws with guaranteed closed-loop properties from a set of functions represented by deep neural networks or other parametric approximators. The task is addressed for time-varying linear systems with multiplicative uncertainties and polytopic state and input constraints. Based on ellipsoidal control-invariant and -contractive sets, which can be computed offline for this system class, the paper shows how safe and stabilizing sets of control laws can be defined and computed. In particular, a closed-form transformation of the control laws is proposed as a tailored output layer, ensuring the satisfaction of the constraints and asymptotic stability of the origin for all possible parameterizations.},
author = {Markolf, Lukas and Stursberg, Olaf},
journal = {Int. Journal of Dynamics and Control},
number = {Vol.13},
pages = {TBD},
title = {Guaranteed constraint satisfaction and asymptotic closed-loop stability in learning of control laws},
year = 2025
}
DOI