Volume 28, 2022
|Number of page(s)||26|
|Published online||24 February 2022|
Hausdorff moment problem and nonlinear time optimality*
Institute of Mathematics, University of Szczecin,
Wielkopolska str. 15,
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: email@example.com
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
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