标题： 关于集值映射可构造可提取的可测选择 显示英文标题

标题： On constructive extractability of measurable selectors of set-valued maps

摘要： 本文研究了从可能在可行性理论、最优控制、不连续系统等中常见的集值映射中构造性地提取可测选择的可能性。 例如，某些微分包含解的存在性通常需要迭代地提取可测选择。 接下来，最优控制通常不是唯一的，这自然导致了一个最优集值函数。 最后，一般来说，可行的控制律可以看作是一个选择。 已知选择定理是不可构造的，因此选择不能总是被提取。 在本工作中，我们分析在哪些特定条件下可以选择器可以被构造性地提取。 从定理中推导出一个算法，并应用于一个三轮机器人模型的计算研究中。 显示英文摘要

摘要： This paper investigates the possibility of constructive extraction of measurable selector from set-valued maps which may commonly arise in viability theory, optimal control, discontinuous systems etc. For instance, existence of solutions to certain differential inclusions, often requires iterative extraction of measurable selectors. Next, optimal controls are in general non-unique which naturally leads to an optimal set-valued function. Finally, a viable control law can be seen, in general, as a selector. It is known that selector theorems are non-constructive and so selectors cannot always be extracted. In this work, we analyze under which particular conditions selectors are constructively extractable. An algorithm is derived from the theorem and applied in a computational study with a three-wheel robot model.