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This paper, which is the natural continuation of a previous paper by the sameauthors, studies a class of optimal control problems with state constraintswhere the state equation is a differential equation with delays. This classincludes some problems arising in economics, in particular the so-called modelswith time to build. The problem is embedded in a suitable Hilbert space H andthe regularity of the associated Hamilton-Jacobi-Bellman (HJB) equation isstudied. Therein the main result is that the value function V solves the HJBequation and has continuous classical derivative in the direction of thepresent. The goal of the present paper is to exploit such result to findoptimal feedback strategies for the problem. While it is easy to defineformally a feedback strategy in classical sense the proof of its existence andof its optimality is hard due to lack of full regularity of V and to theinfinite dimension. Finally, we show some approximation results that allow usto apply our main theorem to obtain epsilon-optimal strategies for a widerclass of problems.

HJB Equations for the Optimal Control of Differential Equations with Delays and State Constraints, II: Optimal Feedbacks and Approximations