A Duality Scheme for Convex Control Problems with Time-Delay

In this paper we examine convex optimal control problems with linear dynamics. Time-delays appear in the convex cost and in the linear dynamics. We consider problems where a delay parameter t appears in the dynamics and another delay parameter u appears in the cost function. We produce a Fenchel duality scheme which yields a dual problem similar to the primal problem. Necessary and sufficient optimality conditions of a subdifferential form are obtained.