二次型最优控制问题中的权矩阵与最优控制律  

Relation of weight matrices to optimal control laws in linear quadratic optimal

作　　者：王进华[1] 

机构地区：[1]福州大学电气工程与自动化学院,福州350008

出　　处：《控制与决策》2007年第8期943-945,950,共4页Control and Decision

摘　　要：二次型最优的权矩阵选择是一个包含大量经验与技巧的问题.对此,研究权矩阵与最优控制律的关系:一个最优控制律,其对应的性能指标(权矩阵)是否唯一的问题.不论是单输入还是多输入情形,在系统能控性指数大于2,对应权矩阵的对角线元素有2个不为零的元素,且满足一定条件时,该性能指标对应的最优控制律,必有另一性能指标与之对应.The selection of weight matrices in linear quadratic optimal control needs a lot of experience and skills. Therefore, a question relating to this selection is studied, which is whether the performance function （weight matrix） of a optimal control law is unique. No matter in single input case or multi input case, many performance functions lead to the same optimal control law when the controllable index of system is more than or equal to 2 and the diagonal elements of the weight matrix relating to this control input have two no zero elements.

关 键 词：最优控制 性能指标 权矩阵 LQ问题 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]