Time-optimal neural feedback control of nilpotent systems as a binary classification problem
File(s)
Accepted 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 Acceptance
2026-05-19
Citation
Communications on Applied Mathematics and Computation
ISSN
2096-6385
Publisher
Springer
Journal / Book Title
Communications on Applied Mathematics and Computation
Copyright Statement
Copyright This paper is embargoed until publication. Once published the author’s accepted manuscript will be made available under a CC-BY License in accordance with Imperial’s Research Publications Open Access policy (www.imperial.ac.uk/oa-policy).
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Publication Status
Accepted