连续时间LQR问题的BPF直接解法

重庆交通大学学报（自然科学版） ›› 1988, Vol. 7 ›› Issue (3): 84-95.

连续时间LQR问题的BPF直接解法

许茂增

收稿日期:1987-10-04 出版日期:1988-06-20 发布日期:2016-11-08

A Direct Method for Solution to Problems of Time-continuous LQR Via BPFs

Xu Maozeng

Received:1987-10-04 Online:1988-06-20 Published:2016-11-08

摘要/Abstract

摘要： 本文给出了通过BPF(方块脉冲函数)求解连续时间LQR(线性二次型调节器)问题的一种新方法。这种方法的基本思想是利用BPF的某些性质和引入某些补充量把连续时间LQR问题转化成一类特殊的动态规划问题,进而根据最优性原理进行求解。文中给出了求解的递推算法和算例。与文献[1],[2],[3],[4]给出的算法相比,本文给出的算法的最大优点是避免求2n×2n阶矩阵的逆矩阵,其中n为动态方程的阶数。

Abstract: In this paper a new method for solution to the problems of the time-continuous linear quatratic regulator (LQR) via block-pulse functions (BPFs) is proposed. The basic idea of the method is that a problem of the LQR is first converted to a special kind of problem of multi-stage dynamic programming by using some properties of the BPFs and introducing some implemental quantities. And then a recursive algorithm for solution to the latter is derived by the well-known principle of optimality. Unlike the methods used in literatures[l],[2],[3],[4],the method presented here avoids computing the inverses of matrices with dimension 2n×2n where n is the dimension of the dynamic equation under study. An illustrative example is given,

许茂增. 连续时间LQR问题的BPF直接解法[J]. 重庆交通大学学报（自然科学版）, 1988, 7(3): 84-95.

Xu Maozeng. A Direct Method for Solution to Problems of Time-continuous LQR Via BPFs[J]. Journal of Chongqing Jiaotong University(Natural Science), 1988, 7(3): 84-95.