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The basis of dynamic programming is described. It is a method for finding the best way to control a system when that system can be controlled by its inputs. As an example, the optimal (or best) control of an electromagnetic brake retarder is derived. In this example the current to the brake retarder is the input being controlled. APL is shown to be a convenient language for writing a dynamic programming algorithm. A set of APL subroutines is provided for solving two-dimensional problems with one input. Adept APL programmers may enjoy the challenge of generalizing this code to problems of arbitrary dimensions.

APL, dynamic programming, and the optimal control of electromagnetic brake retarders