SIAM Journal on Control and Optimization, Volume 58, Issue 6, Page 3212-3236, January 2020.
We introduce the concept of local controllability for a control system of ordinary differential equations with free time and provide sufficient conditions for its controllability. As a direct consequence, for time-optimal problems, we obtain necessary conditions for a local infimum---this notion generalizes that of an optimal trajectory. These conditions constitute a family of relations, each of which has the form of a maximum principle. Examples are given to demonstrate the meaningfulness of the necessary conditions obtained in the present paper, which generalize and strengthen the Pontryagin maximum principle.

中文翻译：

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空闲时间最优控制问题的局部可控性和最大原理族

SIAM控制与优化杂志，第58卷，第6期，第3212-3236页，2020年1月。
我们引入具有自由时间的常微分方程控制系统的局部可控性概念，并为其控制性提供了充分条件。直接的结果是，对于时间最优的问题，我们获得了局部极小值的必要条件-这个概念概括了最优轨迹的概念。这些条件构成了一系列关系，每种关系都具有最大原则的形式。举例说明了本文所获得的必要条件的意义，它推广并加强了庞特里亚金最大原理。