应用数学2017，Vol.30Issue(2)：445-456,12.
一类不带线性结构的随机最优控制问题的最大值原理
The Maximum Principle for a Stochastic Optimal Control System in the Absence of Linear Structure
摘要
Abstract
The Pontryagin's maximum principle for a stochastic optimal control system has been proved in this paper,under the assumptions that the diffusion coefficient does not contain the control variable,but the control domain has no linear structure.We also obtain the variational equation,adjoint equation and the Hamilton system for our problem.Furthermore,by the additional conditions,a second-order necessary condition is given,where the "second-order" is in the sense of that the forward Pontryagin's maximum principle is viewed as a first-order necessary optimality condition.关键词
Pontryagin最大值原理/最优控制/随机Hamilton系统/线性结构Key words
Pontryagin's maximum principle/Optimal control/Stochastic Hamilton system/Linear structure分类
数理科学引用本文复制引用
王维峰,汪宝彬,杨怀奎..一类不带线性结构的随机最优控制问题的最大值原理[J].应用数学,2017,30(2):445-456,12.基金项目
Supported by the National Natural Science Foundation of China(11526195) and the special fund of basic scientific research of central colleges(CZQ14021) （11526195）
