This paper extends the existence results obtained in Ref.  to the case of infinite dimensional control problems with distributed and boundary control. By appealing to the boundary control theory of Fattorini  and Barbu  we transform the boundary control system to a linear evolution equation on a Hilbert space. This allows us to exploit the results of Ref.  and give sufficient conditions for the "turnpike" property to hold as well as conditions for the existence of overtaking solutions.
Paru en janvier 1986 , 14 pages