Discrete-time optimal control - Comments on dynamic programming

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.