Model-robust Design of Experiments for sequential identification of ODE parameters

This paper presents the idea of sequential model-robust design of experiments (DOE) for the identification of dynamic systems modeled with an ordinary differential equation (ODE). The studied DOE problem consists in selecting sequentially the instants where the measures will be done in order to best estimate the systempsilas parameter. The robustness is achieved by considering a statistical representation of the model error defined as the difference between the true ODE and the ODE used in the model. The idea of modeling the model error with a statistical representation has been widely explored in the DOE literature for the identification of static systems. However, there have been little previous works that apply this idea for the identification of dynamic systems. This paper initiates an exploration of this idea in the context of first-order ODE. The model error is modeled by using a kernel-based representation (Gaussian process). A new criterion for the instant selection is constructed and tested on an illustrative example. The design reached with the proposed sequential robust criterion is compared with the design reached with the non-robust version of criterion and with the classical uniform design.