  Mechanistic models in biology often involve numerous parameters about which
we do not have direct experimental information. The traditional approach is to
fit these parameters using extensive numerical simulations (e.g. by the
Monte-Carlo method), and eventually revising the model if the predictions do
not correspond to the actual measurements. In this work we propose a
methodology for hybrid automaton model revision, when new type of functions are
needed to capture time varying parameters. To this end, we formulate a hybrid
optimal control problem with intermediate points as successive
infinite-dimensional linear programs (LP) on occupation measures. Then, these
infinite-dimensional LPs are solved using a hierarchy of semidefinite
relaxations. The whole procedure is exposed on a recent model for haemoglobin
production in erythrocytes.
