引用本文:叶庆凯，王肇明.代数Riccati方程的一种快速解法——单输入情况[J].控制理论与应用,1984,1(3):78~89.[点击复制]
Ye Qingkai, Wang Zhaoming.A FAST METHOD FOR SOLVING ALGEBRAIC MATRIX RICCATI EQUATION ——THE SINGLE INPUT CASE[J].Control Theory and Technology,1984,1(3):78~89.[点击复制]
代数Riccati方程的一种快速解法——单输入情况
A FAST METHOD FOR SOLVING ALGEBRAIC MATRIX RICCATI EQUATION ——THE SINGLE INPUT CASE
摘要点击 1201  全文点击 548  投稿时间：1983-01-29  修订日期：1983-07-08
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DOI编号  
  1984,1(3):78-89
中文关键词  
英文关键词  
基金项目  
作者单位
叶庆凯，王肇明 北京大学 
中文摘要
      为解决线性定常系统在二次性能指标下的最优调节器设计问题，本文通过坐标变换，从系统的可控标准形出发，解决了用Newton迭代法求解代数Riccati方程时出现的两个主要困难：选取初始迭代矩阵与迭代求解Lyapunov方程。最后给出了求解的步骤与计算实例。
英文摘要
      In this paper, a new method is proposed for solving the Linear-Quadratic problem. In this method we solve the algebraic matrix Riccati equation by first transforming the system into its standard canonical form and then using the Newton iterative method. By making use of the special properties of the standard canonical form, the main difficulties of Newton Method (to choose the initial iterative matrix P0 and to solve the Lyapunov equations) are avoided. In obtaining the optimal feedback matrix for an nth order system (single input), the number of multiplication we need to implement is about d=(3+3/8K)n3+5/4rn2, where K=8-15 is the number of iterations, and r is an integer smaller than n.