一类非线性控制系统的截断Hausdorff矩问题及时间最优问题的分析解
Truncated Hausdorff Moment Problem and Analytic Solution of the Time-Optimal Problem for One Class of Nonlinear Control Systems
摘要：
对于任意的$n$，得到了形式为$\dot x_1=u$，$\dot x_j=x_1^{j-1}$，$j=2,\ldots,n$的非线性控制系统时间最优控制问题的完全分析解.本文的主要目标是提出以下令人惊讶的观察：这个非线性最优性问题导致截断Hausdorff矩问题，这是基本上适用于寻找最优时间和最优控制。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
