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Time-optimal neural feedback control of nilpotent systems as a binary classification problem

Nelly Villamizar Orcid Logo, Samuel Gue, Dante Kalise Orcid Logo, Sara Bicego Orcid Logo

Communications on Applied Mathematics and Computation

Swansea University Authors: Nelly Villamizar Orcid Logo, Samuel Gue

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DOI (Published version): 10.1007/s42967-026-00619-1

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-dependentpolynomial system for the control...

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Published in: Communications on Applied Mathematics and Computation
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URI: https://cronfa.swan.ac.uk/Record/cronfa71999
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last_indexed 2026-06-03T06:27:05Z
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spelling 2026-06-02T17:39:32.8641805 v2 71999 2026-06-01 Time-optimal neural feedback control of nilpotent systems as a binary classification problem 41572bcee47da6ba274ecd1828fbfef4 0000-0002-8741-7225 Nelly Villamizar Nelly Villamizar true false 644aee46b5525107f1ac670b2fac63fc Samuel Gue Samuel Gue true false 2026-06-01 MACS 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-dependentpolynomial 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 ofreal roots to be found. In the second part of this 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. Journal Article Communications on Applied Mathematics and Computation 0 0 0 0001-01-01 10.1007/s42967-026-00619-1 COLLEGE NANME Mathematics and Computer Science School COLLEGE CODE MACS Swansea University Another institution paid the OA fee 2026-06-02T17:39:32.8641805 2026-06-01T13:44:34.8149818 Faculty of Science and Engineering School of Mathematics and Computer Science - Mathematics Nelly Villamizar 0000-0002-8741-7225 1 Samuel Gue 2 Dante Kalise 0000-0003-2327-1957 3 Sara Bicego 0000-0002-9284-7115 4
title Time-optimal neural feedback control of nilpotent systems as a binary classification problem
spellingShingle Time-optimal neural feedback control of nilpotent systems as a binary classification problem
Nelly Villamizar
Samuel Gue
title_short Time-optimal neural feedback control of nilpotent systems as a binary classification problem
title_full Time-optimal neural feedback control of nilpotent systems as a binary classification problem
title_fullStr Time-optimal neural feedback control of nilpotent systems as a binary classification problem
title_full_unstemmed Time-optimal neural feedback control of nilpotent systems as a binary classification problem
title_sort Time-optimal neural feedback control of nilpotent systems as a binary classification problem
author_id_str_mv 41572bcee47da6ba274ecd1828fbfef4
644aee46b5525107f1ac670b2fac63fc
author_id_fullname_str_mv 41572bcee47da6ba274ecd1828fbfef4_***_Nelly Villamizar
644aee46b5525107f1ac670b2fac63fc_***_Samuel Gue
author Nelly Villamizar
Samuel Gue
author2 Nelly Villamizar
Samuel Gue
Dante Kalise
Sara Bicego
format Journal article
container_title Communications on Applied Mathematics and Computation
institution Swansea University
doi_str_mv 10.1007/s42967-026-00619-1
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Mathematics and Computer Science - Mathematics{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Mathematics and Computer Science - Mathematics
document_store_str 0
active_str 0
description 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-dependentpolynomial 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 ofreal roots to be found. In the second part of this 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.
published_date 0001-01-01T06:39:47Z
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score 11.108426

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