论文标题
在状态限制下，最佳冲动控制中没有最大的差距和正常性
No infimum gap and normality in optimal impulsive control under state constraints
论文作者
论文摘要
在本文中，我们考虑了具有无限控制的最佳控制问题的冲动扩展，但要受端点和状态约束。我们表明，对于约束最大原则而言，这是正常的极端态度的扩展最小化器的存在，可确保原始问题的INSIMA及其扩展之间没有差距。此外，我们以约束和终点资格的形式将这种关系转化为可验证的足够条件。以前，对于没有状态限制的问题，已经探索过脉冲控制中的临界差距和正态性之间的联系。本文在存在状态限制的情况下建立了此类链接，并为局部Lipschitz的连续数据提供了额外的普通控制。
In this paper we consider an impulsive extension of an optimal control problem with unbounded controls, subject to endpoint and state constraints. We show that the existence of an extended-sense minimizer that is a normal extremal for a constrained Maximum Principle ensures that there is no gap between the infima of the original problem and of its extension. Furthermore, we translate such relation into verifiable sufficient conditions for normality in the form of constraint and endpoint qualifications. Links between existence of an infimum gap and normality in impulsive control have previously been explored for problems without state constraints. This paper establishes such links in the presence of state constraints and of an additional ordinary control, for locally Lipschitz continuous data.
