方块脉冲函数应用于线性时变二次型最优控制的动态规划解法

DYNAMIC PROGRAMMING SOLUTION TO TIME-VARYING LQ OPTIMAL CONTROL VIA BLOCK PULSE FUNCTIONS

本文通过应用方块脉冲函数的一些基本性质，将线性时变二次型最优控制问题化成多段动态规划问题，通过求解得到的动态规划问题，可得原问题的分段常值解，文中给出了形式简单且易于计算机求解的递推算法，与参考文献［１－３］中的方法比较，本文得到的递推算法简单、明了，且计算时间及存储空间极大地减少。文中给出了算法的具体算例，具有明显的优越性。

n this paper, by applying the elemental properties of the block pulse functions to time vary-ing linear systems with quadratic performance index, the time varying LQ optimal control problems are trans-formed into a particular class of multi-stage dynamic programming problems, By solving the latter, the piece- wise constant solutions to the original problems can be obtained. A new recursive algorithm which is moresimple in form and more convenient for computer is developed. Compared with the methods in references[1-3]the recursive algorithm obtained here is more simple and explicit , the computational cost and storagespaces of that can be greatly reduced. The recursive algorithm of solution is illustrated by an appropriate ex-ample.