  For a particular class of planar dynamics that are linear with respect to the
control variable, we show that the feedback strategy ''null-singular null'' is
minimizing the maximum of a coordinate over infinite horizon, under a L 1
budget constraint on the control. Moreover, we characterize the optimal cost as
a function of the budget. The proof is based on an unusual use of the clock
form. This result generalizes the one obtained formerly for the SIR
epidemiological model to more general Kolmogorov dynamics, that we illustrate
on other biological models.
