We investigate nondegenerate and normal forms of the maximum principle for general, free end-time, impulsive optimal control problems with state and endpoint constraints. We introduce constraint qualifications sufficient to avoid degeneracy or abnormality phenomena, which do not require any convexity and impose the existence of an inward pointing velocity just on the subset of times, in which the extended optimal trajectory has an outward pointing velocity (w.r.t. the state constraint). These conditions extend to impulsive problems some conditions, recently proposed by F. Fontes and H. Frankowska, for conventional optimization problems. The nontriviality of this extension is illustrated through some examples.

中文翻译：

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状态约束下最优脉冲控制中最大原理的正态性和非简并性

我们研究了具有状态和端点约束的一般、自由结束时间、脉冲最优控制问题的最大原理的非退化和正规形式。我们引入了足以避免退化或异常现象的约束条件，这些条件不需要任何凸性，并且仅在时间子集上强加向内指向速度的存在，其中扩展的最优轨迹具有向外指向速度（wrt 状态约束）。这些条件扩展到脉冲问题一些条件，最近由 F. Fontes 和 H. Frankowska 提出，用于常规优化问题。通过一些示例说明了此扩展的非平凡性。