Optimal Control of a Biharmonic Obstacle Problem
Optimal Control of a Biharmonic Obstacle Problem
复制标题
双调和障碍问题的最优控制
DOI：
10.1007/978-1-4419-1345-6_1
复制
发表时间：
2010
影响因子：
1.4
通讯作者：
S. Lenhart
中科院分区：
文献类型：
--
作者：
D. Adams;V. Hrynkiv;S. Lenhart
考虑一类障碍型变分不等式，其中偏微分算子是双调和算子。我们考虑一个最优控制问题，其中系统的状态由变分不等式的解给出，障碍物是一个控制。对于给定的目标轮廓，我们希望找到一个障碍，使得变分不等式的相应解接近目标轮廓，而障碍的范数在适当的空间中不会变得太大。我们证明了最优控制的存在性，并利用逼近技巧导出了最优性系统。即变分不等式和目标泛函分别用半线性偏微分方程和相应的逼近泛函逼近。
We consider a variational inequality of the obstacle type where the underlying partial differential operator is biharmonic. We consider an optimal control problem where the state of the system is given by the solution of the variational inequality and the obstacle is taken to be a control. For a given target profile we want to find an obstacle such that the corresponding solution to the variational inequality is close the target profile while the norm of the obstacle does not get too large in the appropriate space. We prove the existence of an optimal control and derive the optimality system by using approximation techniques. Namely, the variational inequality and the objective functional are approximated by a semilinear partial differential equation and the corresponding approximating functional respectively.