  Optimal control problems with a very large time horizon can be tackled with
the Receding Horizon Control (RHC) method, which consists in solving a sequence
of optimal control problems with small prediction horizon. The main result of
this article is the proof of the exponential convergence (with respect to the
prediction horizon) of the control generated by the RHC method towards the
exact solution of the problem. The result is established for a class of
infinite-dimensional linear-quadratic optimal control problems with
time-independent dynamics and integral cost. Such problems satisfy the turnpike
property: the optimal trajectory remains most of the time very close to the
solution to the associated static optimization problem. Specific terminal cost
functions, derived from the Lagrange multiplier associated with the static
optimization problem, are employed in the implementation of the RHC method.
