  We study the long-run properties of optimal control problems in continuous
time, where the running cost of a control problem is evaluated by a probability
measure over R_+. Li, Quincampoix and Renault [DCDS-A, 2016] introduced an
asymptotic regularity condition for a sequence of probability measures to study
the limit properties of the value functions with respect to the evaluation. In
the particular case of t-horizon Ces\`aro mean or rho-discounted Abel mean,
this condition implies that the horizon t tends to infinity or the discount
factor rho tends to zero. For the control system defined on a compact domain
and satisfying some nonexpansive condition, Li, Quincampoix and Renault
[DCDS-A, 2016] proved the existence of general limit value, i.e. the value
function uniform converges as the evaluation becomes more and more regular.
Within the same context, we prove the existence of general uniform value, i.e.
for any epsilon>0, there is an optimal control that guarantees the general
limit value up to epsilon for all control problems where the cost is evaluated
by sufficiently regular probability measures.

Optimization and Control