LQ最优控制系统中加权阵的确定

THE DETERMINATION OF WEIGHTING MATRICES IN LQ OPTIMAL CONTROL SYSTEMS

本文研究了LQ最优调节器的逆问题。在控制变量加权矩阵R给定的条件下,通过引入一组自由变量,给出了满足闭环系统特征值要求的状态加权矩阵Q的一种参数化表示结果。基于这种结果,研究了LQ逆问题的矩阵变换解法和一类系统的LQ逆问题的解法。此外,文中还给出了不求解代数矩阵Riccati方程确定系统的最优状态反馈系数矩阵X的方法。

This paper is a study on the inverse problem of LQ optimal regulators. With the control weight given, the state weighting matrix satisfying the closed-loop eigenvalue requirements is parametrized in terms of a set of free variables. Based on the parametrization, an analytic procedure and a matrix transformation method are proposed to determine the state weighting matrix, as well as the free variables. As a result, by using the solved free variables, the optimal controller gain matrix can be determined without solving the algebraic Riccati matrix equation.