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

• URL: http://arxiv.org/abs/2503.17581v1
• Date: Fri, 21 Mar 2025 23:36:20 GMT
• Title: Time-optimal neural feedback control of nilpotent systems as a binary classification problem
• Authors: Sara Bicego, Samuel Gue, Dante Kalise, Nelly Villamizar,
• Abstract summary: computational method for synthesis of time-optimal feedback control laws.<n>System is sampled and solved to generate a dataset for the construction of a time-optimal deep neural network.<n>Tests assess the accuracy, robustness, and real-time-control capabilities of the approximate control law.
• Score: 0.6999740786886538
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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