The Epsilon Technique: A Constructive Approach to Optimal Control

摘要

Optimal control problems are almost always stated in terms of 'dynamical' equations, whether these be ordinary differential equations, difference-differential equations or integral equations, and all known techniques for computing optimal solutions require the solution of these dynamical equations. The epsilon technique of the title has the unique feature that it avoids having to solve dynamical equations of any kind. In effect, it solves simultaneously the twin problems of integrating the equations and finding the optimal solution. It has provided a constructive derivation of the maximum principle and in particular, a constructive method for obtaining the Lagrange parameters whose existence alone is usually proved. In this paper, we shall apply the technique to the control problems of Lagrange with equality constraints as formulated by M. R. Hestenes. Computational results have been given; the emphasis here will be on the theory. In particular, we shall show how the technique yields a new approach to the control 'synthesis' problem. (Author)