Time-optimal neural feedback control of nilpotent systems as a binary classification problem
File(s)
Published online version
Author(s)
Bicego, Sara
Gue, Samuel
Kalise, Dante
Villamizar, Nelly
Type
Journal Article
Abstract
A computational method for the synthesis of time-optimal feedback control laws for linear nilpotent systems is proposed. The method is based on the use of the bang-bang theorem, which leads to a characterization of the time-optimal trajectory as a parameter dependent polynomial system for the control switching sequence. A deflated Newton’s method is then applied to exhaust all the real roots of the polynomial system. The root
finding procedure is informed by the Hermite quadratic form, which provides a sharp estimate on the number of real roots to be found. In the second part of the paper, the polynomial systems are sampled and solved to generate a synthetic dataset for the construction of a
time-optimal deep neural network-interpreted as a binary classifier- via supervised learning. Numerical tests in integrators of increasing dimension assess the accuracy, robustness, and real-time-control capabilities of the approximate control law.
finding procedure is informed by the Hermite quadratic form, which provides a sharp estimate on the number of real roots to be found. In the second part of the paper, the polynomial systems are sampled and solved to generate a synthetic dataset for the construction of a
time-optimal deep neural network-interpreted as a binary classifier- via supervised learning. Numerical tests in integrators of increasing dimension assess the accuracy, robustness, and real-time-control capabilities of the approximate control law.
Date Issued
2026-09-25
Date Acceptance
2026-05-19
Citation
Communications on Applied Mathematics and Computation, 2026
ISSN
2096-6385
Publisher
Springer
Journal / Book Title
Communications on Applied Mathematics and Computation
Copyright Statement
© The Author(s) 2026. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Identifier
10.1007/s42967-026-00619-1
Subjects
Time-optimal control
Feedback control
Supervised learning
Deep neural networks (NNs)
Nilpotent systems
Hermite quadratic forms Mathematics Subject Classification 93B52
93C05
68T07
14P10
Publication Status
Published online
Date Publish Online
2026-09-25