ABSTRACT
The mathematical theory of dynamic programming is unlike any other encountered in engineering mathematics. In order to fully explain dynamic programming the author discusses the simplest optimization problem, the minimum path between two points. This example will illustrate the salient features of the theory, which will then be formalized and applied to a first-order dynamic system. The authors then provide the extension to multidimensional systems. They apply the principle of optimality to a scalar dynamic system and then extend the concepts to the general multidimensional system. The feature of the minimization is the multistage feature of dynamic programming. It has successfully divided the overall problem into a succession of simpler ones. The minimization is performed over the sum of a local cost and the remaining optimal cost resulting from changing the grid point due to the local decision.
