方块脉冲函数应用于线性时变系统最优控制的动态规划解法及其改进

本将方块脉冲函数应用于线性时变系统最优控制问题。首先将该问题转化成多段动态规划表示形成，通过求解多段动态规划问题，可得原问题的分段常值解。进而，根据最优控制的存在条件下及对边界条件的进一步处理，导出了原问题更为简明的动态规划表示，使求解结果更为简洁，明潦。与献（１），（２），（３）中的求解方法比较，得到的递推算法简单，便于计算机求解，且不必求解ｍ个２ｎ×２ｎ阶逆矩阵，使计算量及存贮空间大为减少

DYNAMIC PROGRAMMING SOLUTIONS TO OPTIMAL CONTROL OF TIME VARYING LINEAR SYSTEMS VIA BLOCK PULSE FUNCTIONS AND IMPROVEMENT

By applying the elegant operational properties of the block pulse functions to time varying linear systems with quadratic performance index,first,the optimal control problems of the time varying linear systems are transformed into a particular class of multi-stage dynamic programming problems. By solving the latter, the piecewise constant solutions to the original problems can be obtained, and second. By further dealing with the boundary conditions, therefore, the optimal control problems are transformed into standard multi-stage dynamic programming problems according to the necessary conditions under which the solutions of time varying linear systems optimal control problems are existent and unique. A new recursive algorithm which is simpler in form and more convenient for computers is developed, compared with the methods in references 1]2]3], the recusive algorithms obtained here are more simple and explicit,the computational requirements and storage spaces of that can be greatly reduced.