Exit Time Problems in Optimal Control and Vanishing Viscosity Method
Exit Time Problems in Optimal Control and Vanishing Viscosity Method
复制标题
最优控制和消失粘度法中的退出时间问题
DOI：
10.1137/0326063
复制
发表时间：
1988
影响因子：
2.2
通讯作者：
B. Perthame
中科院分区：
文献类型：
--
作者：
G. Barles;B. Perthame
研究了一阶Hamilton Jacobi（HJ）方程的确定性出口时间控制问题与边界上可能的不连续粘性解之间的联系。这个方程承认一个最大值和一个最小值的解决方案，是价值的功能相关的停止时间问题的边界。当这些解相等时，可以通过消失粘性法得到。最后，当HJ方程有连续解时，证明了它是区域第一次出射时刻的值函数。特别是在某些大偏差问题中，也会出现消失粘性极限。
The authors study the connections between deterministic exit time control problems and possibly discontinuous viscosity solutions of a first-order Hamilton-Jacobi (HJ) equation up to the boundary. This equation admits a maximum and a minimum solution that are the value functions associated to stopping time problems on the boundary. When these solutions are equal, they can be obtained through the vanishing viscosity method. Finally, when the HJ equation has a continuous solution, it is proved to be the value function for the first exit time of the domain. It is also the vanishing viscosity limit arising, in particular, in some large deviations problems.