A comparison between steepest ascent and differential correction optimization methods in a problem of Bolza, with a method for obtaining starting values for the adjoint variables from a nominal path
comparisonbetwee00mccu.pdf (3.006Mb)Abstract
The problem of maximum range atmospheric reentry for an orbiting
lifting glider was treated by Bryson and Denham by the method of
"steepest ascent". The same problem is undertaken here by a method
of differential corrections developed by Faulkner , This method makes
use of a Newton-Raphson type iteration based on paths which satisfy
the Euler-Lagrange equations, A comparison of results is made, showing large differences in control variable history, and longer range
for the path obtained by differential corrections. The problem was
characterized by a sharp "ridge" in the domain of the starting values
of the adjoint variables and the effect of this on the convergence of
both methods is discussed. Finally , the difficulty of choosing initial
approximations for the starting values of the adjoint variables is
discussed, and a method is presented for obtaining these from a nominal
path as the first step in the computer routine.
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