Comparison Between Various Gradient- Algorithms in Control Theory. Part 1. Sequential Gradient-Restoration Algorithms

摘要

Two different approaches to the formulation of sequential gradient-restoration algorithms in control theory are compared. The viewpoints compared are those of Miele and Kelley. Each derivation is presented separately and is applied to the simplest problem of the calculus of variations, that of minimizing a line intergral, the endpoints being fixed. It is concluded that Miele's viewpoint is conceptually simpler, and the resulting algorithm is easier to implement than Kelley's algorithm. Also, the control change is optimum in Miele's algorithm, whereas this is not the case in Kelley's algorithm. (Author)