DP算法与最大值原理的关系及其优越性

The Advantage of DP in Optimal Control and Relation between DP and Maximum Principles

在最优控制中变分法、最大值原理以及动态规划(DP)是经常用到的理论方法,其中,DP法不仅是性能指标取极值最优控制问题的必要条件而且还是充分条件。本文给出了充分条件的证明,显示出DP法的优越性。DP法与最大值原理有着密切的联系,从DP法的HJB方程直接推导得出了最大值原理。

In the methods of optimal control,Calculus of variation 、Maximum principles and DP are usually used.DP is not only the necessary-condition which performance target gets the extremum in the optimal control problem,but also is the sufficient-condition.The sufficient-necessary-condition that the paper demonstrated shows the advantage of DP in the optimal control.There are consanguineous relation between DP and Maximum principles,which the paper demonstrated from HJB equation of DP to Maximum principles.