论文标题
与有限度量控制的最佳控制问题应用的变异离散方法
Variational discretization approach applied to an optimal control problem with bounded measure controls
论文作者
论文摘要
我们考虑具有初始测量控制的抛物线最佳控制问题。成本功能由对应于最终观察状态的跟踪术语组成。我们遵循E. casas和K. Kunisch的方法，而不是成本功能中的正规化项，并考虑了初始控制的度量规范的束缚。问题的变异离散以及最佳条件会引起初始控制的最大离散稀疏性，即空间中的狄拉克度量。我们提出数值实验来说明我们的方法。
We consider a parabolic optimal control problem with an initial measure control. The cost functional consists of a tracking term corresponding to the observation of the state at final time. Instead of a regularization term in the cost functional, we follow an approach by E. Casas and K. Kunisch and consider a bound on the measure norm of the initial control. The variational discretization of the problem together with the optimality conditions induce maximal discrete sparsity of the initial control, i.e. Dirac measures in space. We present numerical experiments to illustrate our approach.
