Solutions for a class of optimal control problems with time delay, part 1

Abstract

The optimal control of a system whose state is governed by a nonlinear autonomous Volterra integrodifferential equation with unbounded time interval is considered. Specifically, it is assumed that the delay occurs only in the state variable. We are concerned with the existence of an overtaking optimal trajectory over an infinite horizon. The existence result that we obtain extends the result of Carlson (Ref. 1) to a situation where the trajectories are not necessary bounded. Also, we study the structure of approximate solutions for the problem on a finite interval.