一类带停时的最优控制策略研究

The Research on a Class of Optimal Control Strategy Problem with Stopping

利用随机分析的知识及最优控制理论,讨论了一类带停时随机控制的折扣费用模型,将原模型中费用结构中的R-S积分的被积函数同上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,证明了最佳控制的存在性,并刻划了不同初始状态下,最优控制策略的结构及最佳费用函数的形式.

By employing the optimal control theory and the stochastic analysis 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. We proved the existence of the optimal control under different parameters, and we also give the corresponding optimal strategies and the corresponding maximal cost functions under different original states.