A complete solution for optimal control delay problems

The purpose of this paper is to obtain a critical point solution for optimal control problems with delay. These conditions are sufficient to give a solution when one exists. This will be done by using our earlier work on a Bliss multiplier rule with delays and then reformulating the optimal control problem as an unconstrained problem in the calculus of variations with delays. Important benefits of this formulation are that we will obtain the control, multipliers and excess variables for inequality constraints. In addition, we will be able to obtain general, efficient, and accurate numerical algorithms and methods which we will consider in a future paper.