黑龙江大学自然科学学报
黑龍江大學自然科學學報
흑룡강대학자연과학학보
JOURNAL OF NATURAL SCIENCE OF HEILONGJIANG UNIVERSITY
2011年
5期
630-639
,共10页
H∞预演控制%Riccati方程%时滞%偏微分方程%连续时间
H∞預縯控製%Riccati方程%時滯%偏微分方程%連續時間
H∞예연공제%Riccati방정%시체%편미분방정%련속시간
H∞ preview control%Riccati equation%delay%partial differential equation%continuous - time
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.
通過完全平方的方法研究連續繫統的H∞預縯控製問題,併以一組耦閤的微分方程組(一箇微分Riccati方程和兩箇偏微分方程)的解來刻畫所設計的控製器.但是,求解這類方程組或者是給齣其數值解都相噹睏難.這類方程還經常齣現在其它時滯繫統的控製及估計問題的解的刻畫中,通過解耦的方法提供這類方程組的解析解,該方法還為探討該方程組的數值解提供瞭思路,也能夠求解時滯繫統最優控製、H∞控製及估計問題.
통과완전평방적방법연구련속계통적H∞예연공제문제,병이일조우합적미분방정조(일개미분Riccati방정화량개편미분방정)적해래각화소설계적공제기.단시,구해저류방정조혹자시급출기수치해도상당곤난.저류방정환경상출현재기타시체계통적공제급고계문제적해적각화중,통과해우적방법제공저류방정조적해석해,해방법환위탐토해방정조적수치해제공료사로,야능구구해시체계통최우공제、H∞공제급고계문제.
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 diffi-cult 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.
