分布参数系统控制理论及应用

本项目拟综合研究有重要实际意义的几类典型的确定性和随机分布参数系统的模型与结构分析、最优控制与反馈控制等，以及其中部分问题的离散化、特别是数值实现。研究内容包括：1）一些耦合偏微分方程组以及高阶偏微分方程的稳定性、能控性与这些问题的数值方法；2）一些拟线性偏微分方程的能控性与反馈镇定问题，以及非线性色散波方程的非齐次边值问题、边界控制问题以及输入输出的连续依赖性；3）随机偏微分方程的能控性问题；4）较为一般的扩散项含控制的随机偏微分方程的最优控制问题与数值方法等。

This project is addressed to a systematic study of the model and structural analysis, optimal control and feedback control for several typical deterministic/stochastic distributed parameter systems with significant physical background, and their numerical solutions. The main research topics include: 1) Stability and controllability for some coupled PDEs and some PDEs of higher order, and the numerical approach for these problems; 2) Controllability and stabilization of some quasilinear PDEs, and the nonhomogeneous boundary problem, boundary controllability and continuous dependence of the input-output map for nonlinear dispersive wave equations; 3) Controllability of stochastic PDEs; and 4) Optimal control problem and its numerical method for the general stochastic controlled PDEs with controls appeared in the difussion term.