Convergence of a feasible directions algorithm for relaxed controls in time-lag systems

Abstract

In this paper, we consider a class of time-lag optimal control problems involving control and terminal inequality constraints. A feasible direction algorithm has been obtained by Teo, Wong, and Clements for solving this class of optimal control problems. It was shown that anyL ∞ accumulation points of the sequence of controls generated by the algorithm satisfy a necessary condition for optimality. However, suchL ∞ accumulation points need not exist. The aim of this paper is to prove a convergence result, which ensures that the sequence of controls generated by the algorithm always has accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed problem.