论文标题
瞬时半拉格朗日式方法，用于熔化问题的边界控制
An instantaneous semi-Lagrangian approach for boundary control of a melting problem
论文作者
论文摘要
在本文中，研究了一个自由边界问题的次优边界控制策略。该模型由非平滑对流扩散方程式描述。基于特征方法的瞬时策略解决了控制问题。由此产生的时间独立控制问题作为功能空间优化问题，并具有互补性约束。在每个时间步骤中，都证明了一个最佳解决方案的存在，并为惩罚性的调查版本得出了带有常规Lagrange乘数的一阶最佳条件。总体方法的性能由数值示例说明。
In this paper, a sub-optimal boundary control strategy for a free boundary problem is investigated. The model is described by a non-smooth convection-diffusion equation. The control problem is addressed by an instantaneous strategy based on the characteristics method. The resulting time independent control problems are formulated as function space optimization problems with complementarity constraints. At each time step, the existence of an optimal solution is proved and first-order optimality conditions with regular Lagrange multipliers are derived for a penalized-regularized version. The performance of the overall approach is illustrated by numerical examples.
