本项目是随机分析、最优控制和时滞微分代数系统的交叉课题，是基于随机时滞系统和随机最优控制理论，定性研究随机时滞微分代数系统（SDDAS）最优控制若干问题。主要是：研究SDDAS线性二次最优控制问题的指标准则，以及SDDAS具有限时区和无限时区线性二次最优控制问题，建立新的理论与方法，克服时滞所带来的困难；建立具指标2的SDDAS最优控制问题局部极小值原理的必要条件，弥补这方面研究的不足；研究具高指标的SDDAS最优控制问题一阶近似和必要最优条件；研究非线性SDDAS最优控制问题相对应的Hamilton-Jacobi-Bellman方程，继而得到其值函数性质和粘性解的惟一性；研究具任意指标的SDDAS的 Pontryagin最大值原理及其数值实现方法。本项目研究内容的实现将有助于了解随机和时滞对微分代数系统最优控制的影响，必将丰富最优控制理论及其应用。

This project is a intersect project for stochastic analysis, optimal control and delay differential-Algebraic systems, Be based on stochastic delay systems and stochastic optimal control theory, to study some problems for optimal control of stochastic delay differential-algebraic systems(SDDAS). The project will mainly study the following several problems: Index criteria for the SDDAS arising from linear-quadratic optimal control problems, finite-time horizon and infinite-time horizon linear-quadratic optimal control problems for the SDDAS, to establish new theory and methodas well as to overcome the difficulty arising from delay; The necessary conditions of local minimun principle for optimal control problems subject to the SDDAS with index two, and to mak up the shortcoming; First-order approximations and necessary optimality conditions of optimal control problems for the SDDAS with higher index; The Hamilton-Jacobi-Bellman equation corresponding with optimal control problem for the SDDAS, to obtain the property and unicity of viscosity solution; Pontryagin maximum principle and mumerical method for the SDDAS with arbitrary index. The completion for this research contrent will help us to understand the influence for delay and stochastics to optimal control of differential-algebraic systems, and it is doubtless to widen and develop optimal control theory and its applications.