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arXiv · 2007.02398

Truncated Hausdorff Moment Problem and Analytic Solution of the Time-Optimal Problem for One Class of Nonlinear Control Systems

Grigory M. Sklyar·Svetlana Yu. Ignatovich
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Abstract

A complete analytic solution for the time-optimal control problem for nonlinear control systems of the form $\dot x_1=u$, $\dot x_j=x_1^{j-1}$, $j=2,\ldots,n$, is obtained for arbitrary $n$. The main goal of the paper is to present the following surprising observation: this nonlinear optimality problem leads to a truncated Hausdorff moment problem, which is applied essentially for finding the optimal time and optimal controls.

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Grigory M. Sklyar, Svetlana Yu. Ignatovich. 2020-07-05. Truncated Hausdorff Moment Problem and Analytic Solution of the Time-Optimal Problem for One Class of Nonlinear Control Systems. https://arxiv.org/abs/2007.02398

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