Nearly Optimal State Feedback Controls for Delay Differential Equations with a Small Parameter

Nearly optimal control of differential delay systems driven by wideband noise processes and with a small parameter is considered in this work. A probabilistic approach is taken, and the methods of weak convergence are employed. By applying optimal or δ-optimal controls of the limit process (a diffusion process) to the wideband noise driven system, a "good" or nearly optimal control for the actual system is obtained.