求解源于连续H_∞预演控制的偏微分方程组(英文)  

Solve PDEs from continuous-time H_∞ preview control

作　　者：王宏霞[1] 张焕水[2] 

机构地区：[1]哈尔滨工业大学深圳研究生院,深圳518055 [2]山东大学控制科学与工程学院,济南250061

出　　处：《黑龙江大学自然科学学报》2011年第5期630-639,共10页Journal of Natural Science of Heilongjiang University

基　　金：Supported by National Science Foundation for Distinguished Young Scholars of China(60825304)

摘　　要：通过完全平方的方法研究连续系统的H∞预演控制问题,并以一组耦合的微分方程组(一个微分Riccati方程和两个偏微分方程)的解来刻画所设计的控制器。但是,求解这类方程组或者是给出其数值解都相当困难。这类方程还经常出现在其它时滞系统的控制及估计问题的解的刻画中,通过解耦的方法提供这类方程组的解析解,该方法还为探讨该方程组的数值解提供了思路,也能够求解时滞系统最优控制、H∞控制及估计问题。The H∞ preview control problem for the continuous-time systems is discussed.The problem will be solved via the completion of square.Its solution will be characterized by coupled differential equations,a differential Riccati equation as well as two partial differential equations.It is very difficult to solve them even though a numerical approach is applied.Such coupled equations always appear in solving control and estimate problems for delay or preview systems.The aim is to propose an idea to decouple these equations such that an analytic solution is reached.The idea also provides a numerical approach to solve the equations.It should be noted that the decoupling idea can be applied to the quadratic index control and estimate problems for delay or preview systems.

关 键 词：H∞预演控制 RICCATI方程 时滞 偏微分方程 连续时间 

分 类 号：O189.1[理学—数学]