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

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.