Model-Robust Sequential Design of Experiments for Identification Problems

A new criterion for sequential design of experiments for linear regression model is developed. Considering the information provided by previous collected data is a well-known strategy to decide for the next design point in the case of nonlinear models. The paper applies this strategy for linear models. Besides, the problem is addressed in the context of robustness requirement: an unknown deviation from the linear regression model (called model error or misspecification) is supposed to exist and is modeled by a kernel-based representation (Gaussian process). The new approach is applied on a polynomial regression example and the obtained designs are compared with other designs obtained from other approaches that do not consider the information provided by previously collected data.