论文标题
一类非线性控制系统的时间优势问题的Hausdorff力矩问题和分析解决方案
Truncated Hausdorff Moment Problem and Analytic Solution of the Time-Optimal Problem for One Class of Nonlinear Control Systems
论文作者
论文摘要
对于$ \ dot x_1 = u $，$ \ dot x_j = x_1^{J-1} $，$ j = 2，$ j = 2，\ ldots，n $的完整分析解决方案，用于$ \ dot x_1 = u $，$ \ dot x_1 = u $，$ \ dot x_1 = u $。本文的主要目的是介绍以下令人惊讶的观察：这个非线性的最优问题导致截断的Hausdorff Moment问题，该问题基本上用于查找最佳时间和最佳控制。
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.
