具有点态控制约束热方程的时间与范数最优控制问题的等价性

摘要

In this paper, we study the problem of the equivalence of the heat equation with pointwise control constraints. By making use of the uniqueness of time optimal control, controllability properties and the characterization of norm optimal controls through variational methods, we establish the equivalence between time and norm optimal control problems of the heat equation with pointwise control constraints, and extend the results in the related literature.%本文研究了具有点态控制热方程的等价性问题。利用变分法分析时间最优控制的唯一性，能控性以及范数最优控制的特征，获得了具有点态控制约束热方程的时间与范数最优控制问题之间的等价性，推广了现有文献的结果。