Discrete-time optimal control— comments on dynamic programming

DOI编号  10.7641/CTA.2013.21101
2013,30(9):1165-1169

 作者 单位 E-mail 吴受章 西安交通大学 wsz_1@xjtu.edu.cn

阐述离散时间最优控制的特点. 对比3种求解离散时间最优控制的解法, 即: 1) 用非线性规划求解离散时间最优控制; 2) 用无约束优化求解离散时间最优控制; 3) 动态规划及其数值解. 1)和2)都适用于多维静态优化, 计算效率较高, 是高级方法. 在名义上, 3)为动态优化. 实际上, 3)为一维分段无约束静态优化, 计算效率较低, 是初级方法. 本文并用数字实例进一步阐明动态规划及其数值解在求解方面较差, 故动态规划及其数值解已失去实用价值. 在求解离散时间最优控制问题方面, 无法与非线性规划求解相匹敌.

Characteristics of discrete-time optimal control are investigated. Comparisons of three kinds of methods for solving discrete-time optimal control are given; namely: 1) nonlinear programming to solve discrete-time optimal control; 2) unconstrained optimization to solve discrete-time optimal control; 3) dynamic programming and its numerical solution. Methods 1) and 2) are applicable to multidimensional static optimization, the computation efficiency is high; thus, they are the advanced methods. Although 3) is nominally the dynamic optimization, it is actually the one-dimensional unconstrained piecewise static optimization with low computation efficiency. Thus, it is the elementary method only. Numerical examples illustrate that dynamic programming and its numerical solution are worse in problem solving. Hence, dynamic programming and its numerical solution have lost their practical value, and is unable to compete with the nonlinear programming in solving discrete-time optimal control problems.