  This article deals with the problem of maximizing the production of a species
for a chemical network by controlling the temperature. Under the so-called mass
kinetics assumption the system can be modeled as a single-input control system
using the Feinberg-Horn-Jackson graph associated to the reactions network.
Thanks to Pontryagin's Maximum Principle, the candidates as minimizers can be
found among extremal curves, solutions of a (non smooth) Hamiltonian dynamics
and the problem can be stated as a time minimal control problem with a terminal
target of codimension one. Using geometric control and singularity theory the
time minimal syntheses (closed loop optimal control) can be classified near the
terminal manifold under generic conditions. In this article we focus to the
case where the generalized Legendre-Clebsch condition is not satisfied, which
paves the road to complicated syntheses with several singular arcs. In
particular it is related to the situation for a weakly reversible network like
the McKeithan scheme of two reactions.
