Deterministic control of randomly-terminated processes
Deterministic control of randomly-terminated processes
复制标题
随机终止过程的确定性控制
DOI：
10.4171/ifb/312
复制
发表时间：
2013
影响因子：
1
通讯作者：
A. Vladimirsky
中科院分区：
文献类型：
--
作者：
J. Andrews;A. Vladimirsky
我们考虑离散和连续的“不确定时域”确定性控制过程，其中终止时间是一个随机变量。我们研究动态规划方程的价值函数的过程，探讨其连接到无限地平线和最优停止问题，并推导出充分条件的非迭代（标签设置）方法的适用性。在连续的情况下，所得到的偏微分方程有一个自由边界，所有的特征曲线都起源于此。因果性质的“不确定的地平线”的问题，可以利用设计有效的数值算法：我们推导出因果半拉格朗日和欧拉离散的各向同性随机终止的问题，并使用它们来建立一个修改后的版本的快速推进方法。我们说明了我们的方法使用数值例子，从最佳的空闲时间处理和预期的响应时间最小化。
We consider both discrete and continuous "uncertain horizon" deterministic control processes, for which the termination time is a random variable. We examine the dynamic programming equations for the value function of such processes, explore their connections to infinite-horizon and optimal-stopping problems, and derive sufficient conditions for the applicability of non-iterative (label-setting) methods. In the continuous case, the resulting PDE has a free boundary, on which all characteristic curves originate. The causal properties of "uncertain horizon" problems can be exploited to design efficient numerical algorithms: we derive causal semi-Lagrangian and Eulerian discretizations for the isotropic randomly-terminated problems, and use them to build a modified version of the Fast Marching Method. We illustrate our approach using numerical examples from optimal idle-time processing and expected response-time minimization.