Impulse Control of Piecewise Deterministic Markov Processes
Impulse Control of Piecewise Deterministic Markov Processes
复制标题
分段确定性马尔可夫过程的脉冲控制
DOI：
10.1214/aoap/1177004771
复制
发表时间：
1995
影响因子：
1.8
通讯作者：
J. Ye
中科院分区：
文献类型：
--
作者：
M. Dempster;J. Ye
本文研究了分段确定马尔可夫过程的最优脉冲控制问题。将动态控制加脉冲控制的PDP最优（全）控制问题转化为等价的动态控制问题。利用新的动态控制问题的值函数，得到了PDP完全控制问题的最优完全控制的存在性和广义Bellman{汉密尔顿{Jacobi（BHJ））最优性必要条件.证明了原PDP最优完全控制问题的值函数是Lipschitz连续的，并且满足一个带边界条件的广义拟变分不等式。对于原完全控制问题，给出了一个用值函数表示的最优性充要条件。
This paper concerns the optimal impulse control of piecewise determinis-tic Markov processes (PDPs). The PDP optimal (full) control problem with dynamic control plus impulse control is transformed to an equivalent dynamic control problem. The existence of an optimal full control and a generalized Bellman{Hamilton{Jacobi (BHJ) necessary and suucient optimality condition for the PDP full control problem in terms of the value function for the new dynamic control problem are derived. It is shown that the value function of the original PDP optimal full control problem is Lipschitz continuous and satisses a generalized quasi-variational inequality with a boundary condition. A necessary and suucient optimality condition in terms of the value function for the original full control problem is also given.