论文标题
在树结构上针对最佳控制问题的反馈重建技术
Feedback reconstruction techniques for optimal control problems on a tree structure
论文作者
论文摘要
使用动态编程方程进行反馈控制的计算是一项艰巨的任务，因为维度的诅咒。树结构算法是最近引入的方法来减轻此问题的方法。该方法计算避免使用空间网格的构建以及使用一组离散控件的插值技术的需求。但是，将控件的计算严格链接到在树的计算中选择的控制集。在这里，我们扩展并完成选择反馈计算中设置的较好控制设置的方法。这需要使用插值方法进行散射数据，这使我们能够重建不属于树的节点的值函数。该方法的有效性通过数值示例显示。
The computation of feedback control using Dynamic Programming equation is a difficult task due the curse of dimensionality. The tree structure algorithm is one the methods introduced recently that mitigate this problem. The method computes the value function avoiding the construction of a space grid and the need for interpolation techniques using a discrete set of controls. However, the computation of the control is strictly linked to control set chosen in the computation of the tree. Here, we extend and complete the method selecting a finer control set in the computation of the feedback. This requires to use an interpolation method for scattered data which allows us to reconstruct the value function for nodes not belonging to the tree. The effectiveness of the method is shown via a numerical example.
