论文标题
一个维椭圆形分布的最佳控制问题，带有点式衍生约束
A One Dimensional Elliptic Distributed Optimal Control Problem with Pointwise Derivative Constraints
论文作者
论文摘要
我们考虑一个一维椭圆分布的最佳控制问题，并在状态的导数上进行了点数的约束。通过利用最佳状态的导数满足的变异不平等，我们在适当的数据假设下获得了最佳状态的较高规律性。我们还通过$ C^1 $有限元方法解决了最佳控制问题作为第四阶变异不等式，并将误差分析与数值结果一起介绍。
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain higher regularity for the optimal state under appropriate assumptions on the data. We also solve the optimal control problem as a fourth order variational inequality by a $C^1$ finite element method, and present the error analysis together with numerical results.
