  We consider a control problem where the state must reach asymptotically a
target while paying an integral payoff with a non-negative Lagrangian. The
dynamics is just continuous, and no assumptions are made on the zero level set
of the Lagrangian. Through an inequality involving a positive number $\bar p_0$
and a Minimum Restraint Function $U=U(x)$ --a special type of Control Lyapunov
Function-- we provide a condition implying that (i) the control system is
asymptotically controllable, and (ii) the value function is bounded above by
$U/\bar p_0$.
