Set-based Experiment Design for Model Discrimination Using Bilevel Optimization

Experiment design can be used to discriminate between valid and invalid models. This task is not trivial as models are typically nonlinear and the kinetic parameters and initial conditions are uncertain. In this work, we propose a set-based and bilevel optimization approach to design an input sequence such that nonlinear models with uncertainties can be discriminated with guarantees based on a single measurement. In the outer program of the bilevel optimization program, an input minimizing a given norm and satisfying input constraints is determined. For the determined input sequence, the inner program certifies that the reachable output sets of the models are nonoverlapping at a chosen time-point, thus guaranteeing model discrimination. To be able to provide guarantees despite the nonconvexities of the reachable sets, we convexify the inner program. We demonstrate our approach at the chemostatic signaling system of Dictyostelium discoideum.