无限维系统最优控制器的解析设计

This project studied LQ problems for some partial differential equations with boundary controls or pointwise controls.and stochastic differential equations, and the weighted operators in the quadratic cost functionals allowed to be indefinite. It were established the relations among the wellposedness of LQ problems, the.solvability of LQ problems, the associated Riccati equation and the frequency characteristic; and it were also given the feedback synthesis of optimal controls and the frequency type conditions for the wellposedness and solvability of LQ problems.

本项目拟对由几类偏微分方程边界控制和点控制支配的线性二次最优控制问题进行研究，其中二次性能指标具有不定号的加权算子。建立起这些问题的适定性、可解性、相应黎卡提方程和频率特征相互的关系；给出最优控制的状态反馈表示和适定性、可解性的频率条件；并运用这些结果建立非线性系统绝对稳定性的频率判据。