摘要
讨论了由Teugel鞅和多维独立布朗运动共同驱动的随机微分方程的线性二次最优控制问题,其中Teugel鞅是和Lévy过程相关的一类具有可料表示性的强正规鞅序列.通过凸变分理论建立了最优控制的存在性和唯一性,其次利用对偶技术建立了最优控制的Hamilton随机系统对偶表示,最后利用动态规划原理和Riccati方程,获得了最优控制的状态反馈表示.这里的Hamilton随机系统是由状态方程、对偶方程以及最优性条件构成的Teugel鞅和多维独立布朗运动共同驱动的正倒向随机微分方程,Riccati方程是一个高阶非线性的常微分方程.
This paper mainly studies a linear quadratic optimal control problem for the stochastic differential equation driven by Teugels martingale and an independent multi-dimensional Brownian motion.Here Teugels martingales are a family of pairwise strongly orthonormal martingales associated with Lévy processes.Firstly,the existence and uniqueness of optimal control is established by convex variation theory,secondly,the dual characterization of the optimal control is obtained by the stochastic Hamilton system,in the end the state feedback presentation of optimal control is established by the dynamical programming principle and Riccati equation.Here the stochastic Hamilton system is a linear forward-backward stochastic differential equation driven by Teugels martingales and an independent multi-dimensional Brownian motion,consisting of state equation,adjoint equation and the dual presentation of the optimal control.Riccati equation is a highly nonlinear ordinary differential equation.
出处
《湖州师范学院学报》
2016年第8期13-23,共11页
Journal of Huzhou University
基金
浙江省新苗人才计划项目(2015R427023)
湖州师范学院大学生创新创业项目(2015-99)
