Infimal Convolution and Optimal Time Control Problem III: Minimal Time Projection Set
研究了巴拿赫空间上具有凸常值动力学和下半连续目标函数的最小时间问题，给出了最小时间投影集的显式描述及其非空、单值和Lipschitz性质的条件。
We continue the investigation of a general minimal time problem with a convex constant dynamics and a lower semicontinuous extended real-valued target function defined on a Banach space. In this paper we obtain an explicit description of the minimal time projection set in terms of the Legendre--Fenchel conjugate function and provide some sufficient conditions for this set to be nonempty. The single valuedness and Lipschitz property of the minimal time projection are also investigated.