随机最优控制的二阶必要条件综述

张海森,张旭

系统科学与数学 ›› 2019, Vol. 39 ›› Issue (2) : 228-265.

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系统科学与数学 ›› 2019, Vol. 39 ›› Issue (2) : 228-265. DOI: 10.12341/jssms13585
论文

随机最优控制的二阶必要条件综述

    张海森1,张旭2
作者信息 +

A Survey of Second Order Necessary Conditions for Stochastic Optimal Controls

    ZHANG Haisen1 ,ZHANG Xu2
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摘要

文章介绍作者(含合作)近期在随机最优控制的二阶必要条件方面的工作. 首先, 在凸控制约束情况下给出经典意义下随机奇异最优控制的逐点型二阶必要条件. 其次, 利用针状变分获得具有非凸控制约束的~Pontryagin 最大值原理意义下随机奇异最优控制的逐点型二阶必要条件. 最后利用变分分析的工具进一步改进非凸控制约束情形的结果, 并将其推广到具有状态约束的情形.

Abstract

In this paper, we present some of our recent results (partially joint with our collaborator) on the second order necessary conditions for stochastic optimal controls. Firstly, we establish the pointwise second order necessary conditions for stochastic singular optimal controls in the classical sense under the condition that the control regions are convex. Then using the needle variation, we obtain the pointwise second order necessary conditions for stochastic singular optimal controls in the sense of Pontryagin maximum principle when the control regions are allowed to be nonconvex. By means of the variational analysis approach, the results for nonconvex control constraints are further developed and extended also to the state constrained cases.

关键词

随机最优控制 / 二阶必要条件 / 针状变分 / 变分分析 / Malliavin 分析.

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张海森 , 张旭. 随机最优控制的二阶必要条件综述. 系统科学与数学, 2019, 39(2): 228-265. https://doi.org/10.12341/jssms13585
ZHANG Haisen , ZHANG Xu. A Survey of Second Order Necessary Conditions for Stochastic Optimal Controls. Journal of Systems Science and Mathematical Sciences, 2019, 39(2): 228-265 https://doi.org/10.12341/jssms13585
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