  We consider optimal control problem with an integral cost which is a mean of
a given function. As a particular case, the cost concerned is the Ces\`aro
average. The limit of the value with Ces\`aro mean when the horizon tends to
infinity is widely studied in the literature. We address the more general
question of the existence of a limit when the averaging parameter converges,
for values defined with means of general types.
  We consider a given function and a family of costs defined as the mean of the
function with respect to a family of probability measures -- the evaluations --
on R_+. We provide conditions on the evaluations in order to obtain the uniform
convergence of the associated value function (when the parameter of the family
converges).
  Our main result gives a necessary and sufficient condition in term of the
total variation of the family of probability measures on R_+. As a byproduct,
we obtain the existence of a limit value (for general means) for control
systems having a compact invariant set and satisfying suitable nonexpansive
property.
