Iterative computation of time-optimal control functions on the differential analyzer

Abstract

The time-optimal control functions for sample control systems were computed using the iterative computational procedure proposed by L. W. Neustadt as adapted for differential analyzer solution. The computational procedure investigated was developed from the method of steepest ascent. Adaptation for differential analyzer solution required that finite sized steps be taken during the ascent vice the infinitely small sized steps permissible in theory. This presented one of the problems of the computational procedure. No optimization of the step size was attempted in this work, however, several criteria for the selection of the step size were used with success on the two-dimensional systems. The optimal control functions for two-dimensional systems were readily computed using Neustadt' s iterative computational procedure. Analytic work was performed to verify some computer solutions. Agreement of computer and analytic solutions was favorable. The optimal control function for the three-dimensional system investigated was not obtained. After sixty iterations th ?re was no apparent convergence to an optimal control function. Some refinement of the computational method used in this work would be required to extend the problem solutions to higher order systems. No work was performed to determine the effect computer errors would have on problem solutions.