SUCCESSIVE APPROXIMATION TECHNIQUES FOR TRAJECTORY OPTIMIZATION

Abstract

Three related successive approximation schemes for determination of optimal trajectories are developed with attention to treatment of inequality constraints on control variables. The first is a gradient method based upon a Euclidean metric with appropriate modification for handling of inequalities; the second employs a Min operation without use of a metric; and the third features a special integral-absolute value metric. The Pontryagin Principle is employed for construction of successive control function approximations. All three schemes employ an adjoint system for computation of influence functions and a 'penalty function' technique for handling of constraints on terminal values. illustrative calculations are presented for planar Earth-Mars transfer. The relative merits of the techniques are discussed from the viewpoint of digital computation.