关于随机控制的最佳控制不存在问题

The Unexistance of a Class of Stochastic Optimal Control Problem

利用最优控制理论和随机过程理论,讨论了一类带停时的随机控制的折扣费用模型,将原模型中费用结构中的R-S积分的被积函数由1推广为满足某些条件的一般函数,推广后的模型更具一般性。针对不同参数,当最佳控制存在时,给出在不同初始状态下,最优控制策略的结构及最佳费用函数的形式,尤其当最佳控制不存在时,给出具体详细的证明。

By employing the optimal control theory and the stochastic process method, this paper discussed a class of discounted model of singular stochastic control with stopping, in which the integrand of the R-S integral in cost structure is generated from 1 to the general function which satisfied some conditions. Thus ,the discounted model was extended to more general form. When the optimal control exists, we give the corresponding optimal strategies and the corresponding maximal cost functions under different original states. When the optimal control does not exist, we also give the detailed prove.