Regularity of the steering control for systems with persistent memory

The following fact is known for large classes of distributed control systems: when the target is regular, there exists a regular steering control. This fact is important to prove convergence estimates of numerical algorithms for the approximate computation of the steering control. In this paper we extend this property to a class of systems with persistent memory (of Maxwell/Boltzmann type) and we give a variational characterization of the smooth steering control which may open the way to an extension of the numerical approach proposed by Ervedoza and Zuazua.