Experiment design taking nonasymptotic properties of the model into consideration

Experiment design for identification is usually based on asymptotic theory, where an infinite number of samples is assumed. However, such an assumption does not hold in practical cases, and hence, the nonasymptotic properties of system identification should be considered. This paper proposes a new method for experiment design for identification based on the nonasymptotic confidence region of the system parameters calculated using the sign-perturbed-sums (SPS) method for multivariate autoregressive exogenous input (ARX) systems. The objective function based on the volume of the confidence region is introduced in the proposed method. Moreover, the proposed optimization problem is solved using Bayesian optimization because the proposed objective function is calculated from the data obtained only after the experiment. The validity of the proposed method was assessed in an experimental case study of a three-tank system, where the proposed method was compared with the existing D-optimal method. As a result, the model obtained using the proposed method reduced the mean squared control error of model predictive control by 22.9% from that of the existing method.