In this paper we estimate the minimal controllability time for a class of non-linear control systems with a bounded convex state constraint. An explicit expression is given for the controllability time if the image of the control matrix is of co-dimension one. A lower bound for the controllability time is given in the general case. The technique is based on finding a lower dimension system with the similar controllability properties as the original system. The controls corresponding to the minimal time, or time close to the minimal one, are discussed and computed analytically. The effectiveness of the proposed approach is illustrated by a few examples.

中文翻译：

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紧凸状态约束下具有非线性漂移的系统的最小可控时间

在本文中，我们估计了一类具有有界凸状态约束的非线性控制系统的最小可控时间。如果控制矩阵的图像是一维的，则给出可控制时间的明确表达式。在一般情况下，给出了可控制时间的下限。该技术基于找到具有与原始系统相似的可控性的低维系统。讨论并分析了与最小时间或接近最小时间的控件。举几个例子说明了该方法的有效性。