  In this paper, problems of optimal control are considered where in the
objective function, in addition to the control cost there is a tracking term
that measures the distance to a desired stationary state. The tracking term is
given by some norm and therefore it is in general not differentiable. In the
optimal control problem, the initial state is prescribed. We assume that the
system is either exactly controllable in the classical sense or nodal profile
controllable.
  We show that both for systems that are governed by ordinary differential
equations and for infinite-dimensional systems, for example for boundary
control systems governed by the wave equation, under certain assumptions the
optimal system state is steered exactly to the desired state after finite time.
