The Discrete Maximum Principle and the epsilon-Technique

Abstract

A complete proof of the epsilon-maximum principle for discrete-time system is given. In proving the epsilon-maximum principle, the general linearization of the system equations about the optimum trajectory is avoided. Therefore, the requirements for the system equations are different from those of earlier works. It is shown that the epsilon-maximum principle under some mild conditions does approach the general discrete maximum principle and that the epsilon-maximum principle is always in a strong form. Thus, if e is sufficiently small, the epsilon-problem can approximate the solution of the original problem and the difficulties inherent in abnormal problems can be avoided. It is also pointed out that the indeterminancy in the singular control problem can be avoided by using the epsilon-technique.