  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.
