Nonasymptotic E-Optimal Design of Experiments for System Identification Using Sign-Perturbed Sums

Design of experiments (DoE) helps us to obtain an accurate model using system identification. However, most DoE methods rely on asymptotic theory and assume availability of infinite data samples. To overcome this problem, Oshima et al. (2024) proposed a DoE method that evaluates the data quality using the volume of the nonasymptotic confidence region (CR) calculated using sign-perturbed sums (SPS) proposed by Csáji and Weyer (2015). This paper modifies the DoE objective function defined by Oshima et al. (2024) to derive a nonasymptotic counterpart of the E-optimal DoE, which minimizes the length of the longest axis of the asymptotic confidence ellipsoid. The proposed data-quality index is defined by the maximum distance from the center point to the points on the boundaries of the nonasymptotic CR. Moreover, a necessary condition for the points in the parameter space to be on the boundaries of the nonasymptotic CR obtained using the SPS method is theoretically derived. Based on this condition, an algorithm to calculate the maximum distance is proposed. The proposed nonasymptotic E-optimal DoE was validated in a numerical case study, where a 2-input, 3-output ARX system was targeted. As a result, it was shown that the nonasymptotic E-optimal DoE provides a more accurate model compared with the asymptotic E-optimal DoE.