Iterative computation of time-optimal control functions on the differential analyzer
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Authors
Berg, Robert Lloyd.
Subjects
Advisors
Gilbert, Elmer G.
Date of Issue
1962-08
Date
Publisher
University of Michigan
Language
en_US
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.
Type
Thesis