论文标题
Moreau-Yosida正则化，以最佳控制具有状态限制的分数PDE：抛物线案例
Moreau-Yosida regularization for optimal control of fractional PDEs with state constraints: parabolic case
论文作者
论文摘要
本文考虑了具有状态和控制约束的分数抛物线PDE的最佳控制。关键挑战是如何处理状态约束。同样，对于椭圆情况，在本文中，我们在抛物线环境中建立了几种新的数学工具，这些工具引起了广泛关注。例如，存在针对分数抛物线方程的解决方案，并具有右侧的测量数据。我们采用Moreau-Yosida正规化来处理国家限制。我们将正则最佳控制问题的融合（速率）与原始问题建立。数值实验证实了我们在理论上证明了什么。
This paper considers optimal control of fractional parabolic PDEs with both state and control constraints. The key challenge is how to handle the state constraints. Similarly, to the elliptic case, in this paper, we establish several new mathematical tools in the parabolic setting that are of wider interest. For example, existence of solution to the fractional parabolic equation with measure data on the right-hand-side. We employ the Moreau-Yosida regularization to handle the state constraints. We establish convergence, with rate, of the regularized optimal control problem to the original one. Numerical experiments confirm what we have proven theoretically.
