二维最优控制系统的曲率与反馈分类
On curvature and feedback classification of two-dimensional optimal control systems
摘要：
本文的目的是利用Cartan的活动标架方法将二维黎曼曲面的高斯曲率的经典概念推广到具有标量输入的二维最优控制系统。这个概念已经由A. A. Agrachev和R. V.Gamkrelidze使用纯变分方法的更一般的控制系统。然后我们将看到，类似于高斯曲率的“控制”反映了极值流的类似的内在性质。特别是当曲率为负时，任意长的极值段都是局部最优的。最后，我们将定义和刻画平坦控制系统。
英文摘要：
The goal of this paper is to extend to two-dimensional optimal control systems with scalar input the classical notion of Gaussian curvature of two-dimensional Riemannian surface using the Cartan's moving frame method. This notion was already introduced by A. A. Agrachev and R. V. Gamkrelidze for more general control systems using a purely variational approach. Then we will see that the ``control'' analogue to Gaussian curvature reflects similar intrinsic properties of the extremal flow. In particular if the curvature is negative, arbitrarily long segment of extremals are locally optimal. Finally, we will define and characterize flat control systems.
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。
