受控于Poisson过程的脉冲型随机控制问题  

Impulse stochastic control determined by Poisson process

作　　者：田绍琳[1] 王军[1] 牛红丽[1] 

机构地区：[1]北京交通大学理学院,北京100044

出　　处：《哈尔滨工程大学学报》2013年第4期536-540,共5页Journal of Harbin Engineering University

基　　金：国家自然科学基金资助项目(71271026;10971010)

摘　　要：为探讨脉冲型随机控制问题,建立了状态过程受控于Poisson过程,目标函数为满足更一般条件的随机控制模型,采用随机分析、鞅论、Ito公式等理论和方法,证明了模型最优控制的存在性.在特殊条件下,刻画了最优控制的解析解.模型的主要特点是,干扰时间是离散的、随机的,并且由Poisson过程决定的,这是系统内生的,即决策者不能随意地干扰系统,只能依赖于Poisson过程给的某个信息实施控制.模型得到了最优控制ξ*,该最优控制实质上为一脉冲控制,并在一条件下得到最优目标函数v(x)的表达式,从而解决了一类脉冲型随机控制模型最优解的问题.To investigate the problem associated with impulse stochastic control,an investigation of a stochastic control model,governed by a Poisson process and objective function for a more general condition,was conducted.The existence of this model's optimal control was proved by applying the stochastic analysis,martingale theory,Ito formula,and other more theories and methods.Under special conditions,the analytical solution of the optimal control was achieved.The main feature of this model was the fact that the interference time was discrete,random,and determined by a Poisson process.This process was viewed as being endogenous rather than exogenous,that is,decision-makers can not arbitrarily interfere with the system,but can only implement control of some information given by the Poisson process.The obtained optimal control was an impulse control essentially.Under certain conditions,the optimal control ξ* and the optimal objective function v(x) was obtained.So we find the optimal solution of a class of impulse stochastic control.

关 键 词：脉冲型随机控制 变分不等式 Ito 公式 POISSON 过程 最优控制 停时 

分 类 号：O211.6[理学—概率论与数理统计]