In this paper we show that, for optimal control problems involving equality and inequality constraints on the control function, the notions of normality and properness (or the Mangasarian–Fromovitz constraint qualification) of a trajectory relative to the set of constraints are equivalent. This is in contrast with some differences recently obtained between the theories of mathematical programming and optimal control, and it provides an important insight in the derivation of first and second order necessary optimality conditions for infinite dimensional problems.

中文翻译：

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最优控制的常态，可控性和适当性

在本文中，我们表明，对于在控制功能上涉及相等和不等式约束的最优控制问题，相对于约束集合的轨迹的正则性和正确性（或Mangasarian-Fromovitz约束资格）概念是等效的。这与最近在数学程序设计和最优控制理论之间获得的一些差异形成对比，它为推导无限维问题的一阶和二阶必要最优性条件提供了重要的见识。