The notion of a local infimum for the optimal control problem, which generalizes the notion of an optimal trajectory, is introduced. For a local infimum the existence theorem is proved and necessary conditions in the form of a family of ‘maximum principles’ are derived. The meaningfulness of the necessary conditions, which generalize and strengthen Pontryagin’s maximum principle, is illustrated by examples. Bibliography: 9 titles.

中文翻译：

---

最优控制中的局部极小值和最大原则族

引入了关于最优控制问题的局部极小值的概念，该概念概括了最优轨迹的概念。对于局部极小，证明了存在定理，并以“最大原理”族的形式导出了必要条件。实例说明了必要条件的意义，该条件概括并加强了庞特里亚金的最大原理。参考书目：9种。