Discrete approximations to optimal control of infinite dimensional delay-differential inclusions with continuous initial conditions

This paper deals with the convergence of discrete approximations to the optimization problem (P) described by delay-differential inclusions in infinite dimensional spaces subject to general endpoints constraints. In the first part of the paper, discrete approximations to delay-differential inclusions are constructed using Euler finite difference method and the convergence of discrete approximations is proved. In the second part of the paper, a family of discrete optimization problems (PN) to (P) is constructed and the strong convergence of optimal solutions for (PN) to optimal solutions of (P) is discussed.