Occupation measure methods for modelling and analysis of biological hybrid automata
For biologists and modelers, this provides a systematic method for model revision when time-varying parameters are needed, though it is an incremental extension of existing occupation measure techniques.
The paper proposes a methodology for revising hybrid automaton models in biology by formulating a hybrid optimal control problem with intermediate points as infinite-dimensional linear programs on occupation measures, solved via semidefinite relaxations. The approach is demonstrated on a model for haemoglobin production in erythrocytes.
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.