CONVERGENCE OF A CONDITIONAL GRADIENT METHOD FOR RELAXED CONTROLS IN TIME-LAG CONTROL PROBLEMS.

Abstract

In this paper, we consider a class of optimal control problem with discrete-time delayed arguments and bounded control regions. A conditional gradient algorithm has been obtained by K. H. Wong and K. L. Teo for solving this class of optimal control problem. It is also shown that any L// infinity accumulation points of the control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown that control sequences generated by the algorithm always have accumulation points in the sense of a control measure, and that these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed problem.