On optimal design of experiments for static polynomial approximation of nonlinear systems (Q2203474)

This paper deals with static, single input single output nonlinear system's polynomial approximation using polynomial autoregressive model with exogenous input. The nonlinear dynamic systems identification theory origins from the Weierstrass and Frénchet's theorems that a continuous real functional defined on a compact set of real continuous functions could be approximated by the sum of a finite number of the Volterra functional series' terms. Here readers may refer to the monograph by \textit{D. Sidorov} [Integral dynamical models. Singularities, signals and control. Hackensack, NJ: World Scientific (2015; Zbl 1311.45012)] and its bibliography. It is to be noted, that the identification experiment denoted as design of experiments (DOE) is an essential part of this field of approximation of real systems. There are two main contributions in this article. First, the paper discusses how the system-model mismatch affects the experiment design. Second, it is demonstrated that selection of a higher complexity DOE lead to significantly higher model quality in case of mismatch and it does not significantly change the model quality when the model class matches the system. The relation with the classical V-optimal design is discussed. Proposed approach is validated using Monte Carlo experiment on the polynomial model of different degrees.