LQ最优控制之逆问题的研究

Study on the Inverse Problem of LQ Optimal Control

中文关键词  最优控制  加权矩阵  LQ逆问题  特征值  特征多项式

英文关键词  Optimal control  Weighting matrices  LQ inverse problem  Eigenvalues  Characteristic polynomials.

中文摘要

      本文通过适当地选取LQ性能指标函数中的加权矩阵R，给出了该二次型性能指标函数中的另一个加权矩阵Q与系统的开环特征多项式、闭环特征多项式的系数以及系数的系数矩阵A、B之间的对应关系。如果给定了一个系统以及该系统的一组最优闭环极点，就可以求得矩阵Q。同时，用本文的研究成果，还可以直接确定系统的最优状态反馈系数矩阵。

英文摘要

      In this paper, the relation between the weighting matrix Q in a linear quadratic performance index and the coefficients of the closed-loop characteristic polynomial, Open-loop characteristic polynomial and the coefficients matrices A, B of a system is developed via appropriately choosing the other weighting matrix R in the LQ performance index. With the result, Q can readily be determined if an open-loop system and its desired Optimal closed-loop eigenvalues are given. Besides, the optimal state feedback gain matrix for the system under study is also given through using the proposed results.