We present existence of solution and necessary conditions for an optimal control problem with a particular case of sweeping processes with constant sweeping set. Using a sequence of approximating problems we prove existence of solution and necessary conditions. The special feature of our approach resides on the nature of the approximating problems: in contrast with other literature these problems do not rely on distance functions to the sweeping set.

中文翻译：

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涉及清扫过程的最优控制

我们针对具有恒定清扫集的清扫过程的特定情况，提出了最优控制问题的解决方案和必要条件的存在。使用一系列近似问题，我们证明了解的存在和必要条件。我们的方法的特殊之处在于近似问题的性质：与其他文献相比，这些问题不依赖于距离集的距离函数。