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Time-optimal neural feedback control of nilpotent systems as a binary classification problem
Nelly Villamizar 
,
Samuel Gue,
Dante Kalise ,
Sara Bicego
,
Samuel Gue,
Dante Kalise ,
Sara Bicego
Communications on Applied Mathematics and Computation
Swansea University Authors:
Nelly Villamizar , 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...
| Published in: | Communications on Applied Mathematics and Computation |
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| Published: |
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa71999 |
| 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 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. |
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| College: |
Faculty of Science and Engineering |