随机分布参数系统控制理论

本项目拟研究随机分布参数系统的能控能观性、最优控制等问题。其主要科学目标如下： 1）建立随机微局部分析与随机偏微分方程的奇性传播理论，并给出其在随机分布参数系统能控能观性中的应用；2）给出一般向量值、算子值、张量值或多重线性算子值倒向随机发展方程的适定性，及其在随机分布参数系统最优控制理论中的应用；3）给出一般情形随机分布参数系统最优控制问题的动态规划方法，尤其是相应的无穷维倒向随机Hamilton-Jacobi-Bellman方程的粘性解理论。

This project is addressed to a study of controllability, observability, optimal control problems and so on for stochastic distributed parameter systems. The main scientific aims are as follows: 1) To establish the theory of stochastic microlocal analysis and singularity propagation for stochastic partial differential equations, and give their applications in controllability and observability for some stochastic distributed parameter systems; 2) To give the well-posedness of general vector/operator/tensor/multilinear operator valued stochastic evolution equations, and their applications in optimal control theory for stochastic distributed parameter systems; and 3) To introduce the dynamic programming method to solve optimal control problems for stochastic distributed parameter systems in the general case, in particular the viscosity solution theory for the corresponding backward stochastic Hamilton-Jacobi-Bellman equations in infinite dimensions.