项目名称: 部分可观测信息下的双重随机最优控制理论及其应用
项目编号: No.11301298
项目类型: 青年科学基金项目
立项/批准年度: 2014
项目学科: 数理科学和化学
项目作者: 朱庆峰
作者单位: 山东财经大学
项目金额: 22万元
中文摘要: 本项目旨在深入研究部分可观测信息下的双重随机系统,解决倒向双重随机系统和正倒向双重随机系统在部分可观测信息下的最优控制问题。在控制域为非凸的情形下,结合Girsanov定理和针状变分方法,建立部分可观测信息下正倒向双重随机最优控制问题的最大值原理和最优性的充分条件;在带有状态约束的情形下,建立部分可观测信息下正倒向双重随机最优控制问题的最大值原理;作为最大值原理的应用,我们研究一类部分可观测的线性二次最优控制问题。在风险敏感情形下,研究一类部分可观测信息的倒向双重随机最优控制问题,得到部分可观测信息的倒向双重随机最优控制问题的一般随机最大值原理。作为部分可观测信息的特例,我们讨论完全可观测的风险敏感双重随机最优控制问题的一般最大值原理。研究一类部分可观测的线性二次非零和双重随机微分对策问题,获得开环Nash均衡点存在的必要的和充分的最优条件。
中文关键词: 部分可观测;随机最优控制;随机微分对策;倒向重随机微分方程;正倒向重随机微分方程
英文摘要: This research program concerns partially observed doubly stochastic systems, which includes partially observed optimal control problem of backward doubly stochastic systems and forward-backward doubly stochastic systems. Combining Girsanov's theory and the spike variational method, the maximum principle and sufficient condition for partially-observed optimal control of forward-backward doubly stochastic systems are obtained on the assumption that the control domain is not necessarily convex. By Ekeland's variational principle, the maximum principle for partially observed optimal control of forward-backward doubly stochastic systems with state constraints are given. As an application of the maximum priciple, one kind of partially observed linear quadratic optimal control problem is studied. The maximum principle for partially observed risk-sensitive optimal control of backward doubly stochastic systems are given. As a special case of partial information, the general stochastic maximum principle for fully observed risk-sensitive optimal control problem is obtained. One kind of partially-observed linear-quadratic non-zero sum doubly stochastic differential game is studied. The Nash equilibrium point of this kind of game problem is obtained.
英文关键词: Partially-observed;stochastic optimal control;stochastic differential game;backward doubly stochastic differential equations;forward-backward doubly stochastic systems