SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 2093-2120, January 2021.
We derive necessary conditions for optimality for control problems with smooth mixed constraints in the absence of regularity conditions. We show that the lack of regularity is reflected by the appearance of purely finitely additive set functions as multipliers corresponding to the mixed constraints. We illustrate with examples the rule of such set functions. Additionally, we show how our approach allows to treat regular mixed constraints and pure state constraints as particular cases; for the latter, we also provide a connection to well-established results involving only countably additive measures.

中文翻译：

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具有非规则混合约束的最优控制：一种优化方法

SIAM Journal on Control and Optimization，第 59 卷，第 3 期，第 2093-2120 页，2021 年 1 月。
我们推导出了在没有规律性条件的情况下，具有平滑混合约束的控制问题的最优性的必要条件。我们表明，作为与混合约束相对应的乘数的纯有限加性集合函数的出现反映了缺乏规律性。我们举例说明这种集合函数的规则。此外，我们展示了我们的方法如何允许将常规混合约束和纯状态约束视为特殊情况；对于后者，我们还提供了与仅涉及可数附加措施的完善结果的联系。