| Issue |
ESAIM: COCV
Volume 28, 2022
|
|
|---|---|---|
| Article Number | 15 | |
| Number of page(s) | 26 | |
| DOI | https://doi.org/10.1051/cocv/2022007 | |
| Published online | 24 February 2022 | |
Hausdorff moment problem and nonlinear time optimality*
1
Institute of Mathematics, University of Szczecin,
Wielkopolska str. 15,
Szczecin
70-451, Poland.
2
Faculty of Computer Science and Information Technology, West Pomeranian University of Technology in Szczecin,
Żołnierska 49,
71-210
Szczecin, Poland.
3
Department of Applied Mathematics, V.N. Karazin Kharkiv National University,
Svobody sqr. 4,
Kharkiv
61022, Ukraine.
** Corresponding author: ignatovich@ukr.net
Received:
1
January
2021
Accepted:
26
January
2022
A complete analytic solution for the time-optimal control problem for nonlinear control systems of the form ẋ1 = u, ẋj = ẋ1j−1, j = 2, …, n, is obtained for arbitrary n. In the paper we present the following surprising observation: this nonlinear optimality problem leads to a truncated Hausdorff moment problem, which gives analytic tools for finding the optimal time and optimal controls. Being homogeneous, the mentioned system approximates affine systems from a certain class in the sense of time optimality. Therefore, the obtained results can be used for solving the time-optimal control problem for systems from this class.
Mathematics Subject Classification: 49K15 / 44A60 / 93C10
Key words: Nonlinear control system / time-optimal control problem / truncated Hausdorff moment problem
© The authors. Published by EDP Sciences, SMAI 2022
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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